結果
| 問題 | No.2442 線形写像 |
| ユーザー |
 ysuzuki5321
|
| 提出日時 | 2024-12-24 07:11:56 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 57,518 bytes |
| コンパイル時間 | 6,936 ms |
| コンパイル使用メモリ | 258,096 KB |
| 実行使用メモリ | 6,820 KB |
| 最終ジャッジ日時 | 2024-12-24 07:12:10 |
| 合計ジャッジ時間 | 8,145 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 3 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | WA | - |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 2 ms
5,248 KB |
| testcase_10 | WA | - |
| testcase_11 | AC | 2 ms
5,248 KB |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | AC | 2 ms
5,248 KB |
| testcase_15 | AC | 10 ms
5,248 KB |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | AC | 29 ms
6,816 KB |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
ソースコード
#include <stdio.h>
#include <sstream>
#include <string.h>
#include <vector>
#include <map>
#include <algorithm>
#include <utility>
#include <set>
#include <cctype>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <deque>
#include <limits>
#include <iomanip>
#include <ctype.h>
#include <unordered_map>
#include <random>
#include <numeric>
#include <iostream>
#include <array>
#include <atcoder/all>
#include <functional>
#define _USE_MATH_DEFINES
#include <iostream>
#include <fstream>
#include <math.h>
#include <bitset>
#include <unordered_set>
#pragma intrinsic(_umul128)
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, double> pld;
typedef pair<double, double> pdd;
typedef pair<double, ll> pdl;
typedef pair<int, char> pic;
typedef vector<ll> vl;
typedef vector<double> vd;
typedef vector<ull> vul;
typedef vector<pll> vpll;
typedef vector<int> vi;
typedef vector<string> table;
typedef priority_queue<ll, vector<ll>, greater<ll>> llgreaterq;
typedef priority_queue<pll, vector<pll>, greater<pll>> pllgreaterq;
typedef priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> plpllgreaterq;
typedef priority_queue<vi, vector<vi>, greater<vi>> vigreaterq;
typedef priority_queue<vl, vector<vl>, greater<vl >> vlgreaterq;
typedef vector<vl> mat;
typedef vector<mat> thd;
typedef modint1000000007 mint7;
typedef modint998244353 mint9;
typedef modint mint;
template <class o, class p>
using pairq = priority_queue<pair<o, p>, vector<pair<o, p>>, greater<pair<o, p>>>;
template <class o, class p, class q>
using tuple3q = priority_queue<tuple<o, p, q>, vector<tuple<o, p, q>>, greater<tuple<o, p, q>>>;
template <class o, class p, class q, class r>
using tuple4q = priority_queue<tuple<o, p, q, r>, vector<tuple<o, p, q, r>>, greater<tuple<o, p, q, r>>>;
template <class o, class p, class q, class r, class s>
using tuple5q = priority_queue<tuple<o, p, q, r, s>, vector<tuple<o, p, q, r, s>>, greater<tuple<o, p, q, r, s>>>;
vl dx = { 1,0,-1,0 };
vl dy = { 0,1,0,-1 };
int dxe[] = { 1,1,0,-1,-1,-1,0,1 };
int dye[] = { 0,1,1,1,0,-1,-1,-1 };
#define bit(x,v) ((ll)x << v)
#define rep(x,n) for(ll x = 0;x < n;x++)
#define rep2(x,f,v) for(ll x=f;x<v;x++)
#define repe(v,x) for(auto v : x)
// 許容する誤差ε
#define EPS (1e-10)
// 2つのスカラーが等しいかどうか
#define EQ(a,b) (std::abs(a-b) < EPS)
// 2つのベクトルが等しいかどうか
#define EQV(a,b) ( EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()) )
#define all(a) a.begin(),a.end()
#define all0(a) memset(a,0,sizeof(a))
#define allm1(a) memset(a,-1,sizeof(a))
#define set_float() cout << fixed << setprecision(12);
#define coutl(s) cout <<s <<endl
#define pln(s) cout<<s<<"\n"
#define ple pln(-1)
#define plm(s) cout<<(s).val()<<"\n"
#define plm17(s) cout<<modint1000000007(s).val()<<"\n"
#define plm9(s) cout<<modint998244353(s).val()<<"\n"
#define put_float(v) set_float() \
pln(v)
#define vinsert(v,p,x) v.insert(v.begin() + p,x)
#define verase(v,f,t) v.erase(v.begin()+f,v.begin()+t+1)
#define vsort(v) sort(all(v));
#define vdesc(v) vsort(v); \
reverse(all(v))
#define gete(u,v) ll u,v; cin>>u>>v; u--;v--;
#define getpair(a,b) ll a,b;cin>>a>>b;
#define dup(v) v.erase(unique(all(v)),v.end())
#define cub(a) (a)*(a)*(a)
#define ion(i,j) (i & (1LL << j))
#define Len size()
#define psp(a,b) push_back(make_pair(a,b))
#define psp2(a,b) push(make_pair(a,b))
#define cini(a) a; cin >> a
#define infa(a,b) (a + b) % INF
#define infm(a,b) (a * b) % INF
#define infd(a,b) (a * INFinv(b)) % INF
#define infs(a,b) (a + INF - inff(b)) % INF
#define inf(a) (a) %= INF
#define inff(a) ((a + INF) % INF)
#define No cout << "No" << endl
#define Yes cout << "Yes" << endl
#define NO cout << "NO" << endl
#define YES cout << "YES" << endl
#define errm1 pln(-1);return;
#define smal -(ll)1000000009*1000000009
#define big (ll)1000000009*1000000009
#define frontpop(q) q.front();q.pop()
#define toppop(q) q.top();q.pop()
#define arr(a,s) a[s]; all0(a);
#define nxt(cu) (cu+1) % 2
#define chkover(x,y,h,w) (x<0||y<0||x>=h||y>=w)
#define psb(v) ll value;cin>>value;v.push_back(value);
#define lower_b(v,p) lower_bound(all(v), p)
#define lower_bp(v,p) lower_bound(all(v), p) - v.begin()
#define upper_b(v,p) upper_bound(all(v), p)
#define upper_bp(v,p) upper_bound(all(v), p) - v.begin()
#define allpln(v) for(auto &e:v)pln(e)
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define msize 216;
#define revarr(p,l,r) reverse(p.begin()+l,p.begin()+r+1)
#define reverse_all(p) reverse(all(p))
#define cill(x) ll x;cin>>x
#define cilll(x,y) ll x,y;cin>>x>>y
#define bitn(x,k)(((x)>>(k))&1)
#define iotan(a,n) iota(all(a),n)
#define cline(a,k) vl a(k); rep(i,k){cin>>a[i];}
#define clineu(a,k) vul a(k); rep(i,k){cin>>a[i];}
#define clines(a,k) vector <string> a(k); rep(i,k){cin>>a[i];}
#define cindec(a) ll a; cin>> a; a--;
template <typename T, typename U>
T SUM(const vector<U>& A) {
T sum = 0;
for (auto&& a : A) sum += a;
return sum;
}
ll ceil(ll a, ll b) { return a > 0 ? (a - 1) / b + 1 : a / b; }
ll n, m;
bool chmin(ll& a, ll b) {
if (a > b) {
a = b; return 1;
}
return 0;
}
bool chmind(double& a, double b) {
if (a > b) {
a = b; return 1;
}
return 0;
}
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
ll INF = 1000000007;
const int MAX = 3000010;
void cout2(ll val) {
if (val >= big) {
pln(-1);
}
else {
pln(val);
}
}
void cout3(ll val) {
if (val >= INF) {
pln(-1);
}
else {
pln(val);
}
}
template <typename T>
vector<T> merge_arr(vector<T>& a, vector<T>& b) {
vector<T> c(a.size() + b.size());
std::merge(all(a), all(b), c.begin());
return c;
}
string padleft(string x, ll dig, char c) {
ll si = x.size();
for (ll i = 0; i < dig - si; i++)
{
x = c + x;
}
return x;
}
long long fac[MAX], finv[MAX], inv[MAX], called;
void COMinit() {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for (int i = 2; i < MAX; i++) {
fac[i] = fac[i - 1] * i % INF;
inv[i] = INF - inv[INF % i] * (INF / i) % INF;
finv[i] = finv[i - 1] * inv[i] % INF;
}
}
void COMinit998244353() {
INF = 998244353;
COMinit();
called = 1;
}
void COMinit1000000007() {
INF = 1000000007;
COMinit();
called = 1;
}
ll gfac(ll x) {
if (!called) {
COMinit();
called = 1;
}
return fac[x];
}
// 二項係数計算
long long COM(int n, int k) {
if (!called) {
COMinit();
called = 1;
}
if (n < k) return 0;
if (n < 0 || k < 0) return 0;
return fac[n] * (finv[k] * finv[n - k] % INF) % INF;
}
modint998244353 COM2(ll n, ll k) {
modint998244353 res = 1;
rep(i, k) {
res *= (n - i);
res /= (i + 1);
}
return res;
}
ll getpow(ll b, ll x, ll md) {
ll t = b % md;
ll res = 1;
while (x > 0)
{
if (x & 1) {
res *= t;
res %= md;
}
x >>= 1;
t *= t;
t %= md;
}
return res % md;
}
ull getpowul(ull b, ull x, ull md) {
ull t = b % md;
ull res = 1;
while (x > 0)
{
if (x & 1) {
res *= t;
res %= md;
}
x >>= 1;
t *= t;
t %= md;
}
return res % md;
}
ll getpow(ll b, ll x) {
return getpow(b, x, INF);
}
/// 素数を法とする場合
ll modinv(ll x) {
return getpow(x, INF - 2);
}
ll extgcd(ll a, ll b, ll& x, ll& y) {
ll d = a;
if (b != 0) {
d = extgcd(b, a % b, y, x);
y -= (a / b) * x;
}
else {
x = 1; y = 0;
}
return d;
}
/// <summary>
/// 素数を法としない場合
/// </summary>
/// <param name="a"></param>
/// <param name="m"></param>
/// <returns></returns>
ll modinv(ll a, ll m) {
ll x, y;
extgcd(a, m, x, y);
return (m + x % m) % m;
}
ll gcd(ll a, ll b) {
if (b == 0) return a;
return gcd(b, a % b);
}
class m_random {
std::mt19937 mt;
std::uniform_int_distribution<> rand100;
public:
m_random(ll mi, ll ma) {
init_random(mi, ma);
}
void init_random(ll mi, ll ma) {
std::random_device rnd; // 非決定的な乱数生成器を生成
mt = std::mt19937(rnd()); // メルセンヌ・ツイスタの32ビット版、引数は初期シード値
rand100 = std::uniform_int_distribution<>(mi, ma);
}
ll get() {
return rand100(mt);
}
};
class m_sampling {
std::mt19937 mt;
std::normal_distribution<double> rand;
public:
m_sampling(double sigma) {
init_sampling(sigma);
}
void init_sampling(double sigma) {
std::random_device rnd;
mt = std::mt19937(rnd());
rand = std::normal_distribution<double>(0.0, sigma);
}
double get() {
return rand(mt);
}
};
typedef vector<modint998244353> vml;
typedef vector<vml> matm;
typedef vector<modint1000000007> vml2;
typedef vector<vml2> matm2;
typedef vector<modint> vml3;
typedef vector<vml3> matm3;
#define cmat(n,s,ss) mat n(s,vl(ss))
#define cmatm(n,s,ss) matm n(s,vml(ss))
#define cmatm2(n,s,ss) matm2 n(s,vml2(ss))
#define cmatm3(n,s,ss) matm3 n(s,vml3(ss))
// Union find
vl pr;
vl lank;
vl udpt;
void uini(int _n) {
_n++; // 一個拡張しておく
pr = vl(_n + 1);
lank = vl(_n + 1);
udpt = vl(_n + 1, 0);
for (ll i = 0; i <= _n; i++)
{
pr[i] = i;
lank[i] = 1;
}
}
int parent(int x) {
if (x == pr[x]) return x;
auto paren = parent(pr[x]);
udpt[x] = udpt[paren] + 1;
return pr[x] = paren;
}
int same(int x, int y) {
return parent(x) == parent(y);
}
bool unit(int x, int y) {
int px = parent(x);
int py = parent(y);
if (px == py) return false;
if (lank[py] <= lank[px]) {
pr[py] = px;
lank[px] += lank[py];
}
else {
pr[px] = py;
lank[py] += lank[px];
}
return true;
}
ll unisize(ll i) {
return lank[parent(i)];
}
bool unitm(int x, int y) {
int px = parent(x);
int py = parent(y);
if (px == py) return false;
if (lank[py] < lank[px]) {
pr[py] = px;
lank[px] += lank[py];
}
else {
pr[px] = py;
lank[py] += lank[px];
}
return true;
}
/// <summary>
/// 数字の小さい方を親にするように処理
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
bool unitlow(int x, int y) {
int px = parent(x);
int py = parent(y);
if (px == py) return false;
if (py < px) {
pr[py] = px;
lank[px] += lank[py];
}
else {
pr[px] = py;
lank[py] += lank[px];
}
return true;
}
ll clamp(ll t, ll l, ll r) {
return max(l, min(r, t));
}
int H;
int left(int i) {
return i * 2 + 1;
}
int right(int i) {
return i * 2 + 2;
}
class edge {
public:
int from, to, i;
ll val;
ll cap, rev, icap;
edge() {}
edge(ll to) : to(to) {}
edge(ll to, ll i) : to(to), i(i) {}
edge(ll from, ll to, ll val) : from(from), to(to), val(val) {}
void flowEdge(ll _to, ll _cap, ll _rev) {
to = _to;
cap = _cap;
icap = _cap;
rev = _rev;
}
};
typedef vector<vector<edge>> vve;
class LCA {
private:
vector<vector<edge>> v;
vector<vector<int>> parent;
vector<int> depth;
ll root;
void dfs(int n, int m, int d) {
parent[0][n] = m;
depth[n] = d;
for (auto x : v[n]) {
if (x.to != m) dfs(x.to, n, d + 1);
}
}
public:
LCA() {}
LCA(ll N, ll root, vector<vector<edge>>& tree) {
v = tree;
this->root = root;
parent = vector<vector<int>>(21, vector<int>(N + 1, 0));
depth = vector<int>(N + 1, 0);
dfs(root, -1, 0);
for (int j = 0; j + 1 < 20; j++) {
for (int i = 1; i <= N; i++) {
if (parent[j][i] < 0) parent[j + 1][i] = -1;
else parent[j + 1][i] = parent[j][parent[j][i]];
}
}
}
int lca(int n, int m) {
if (depth[n] > depth[m]) swap(n, m);
if (n == root)
return root;
for (int j = 0; j < 20; j++) {
if ((depth[m] - depth[n]) >> j & 1) m = parent[j][m];
}
if (n == m) return n;
for (int j = 19; j >= 0; j--) {
if (parent[j][n] != parent[j][m]) {
n = parent[j][n];
m = parent[j][m];
}
}
return parent[0][n];
}
int dep(int n) { return depth[n]; }
};
ll k;
int _rank[1010];
int temp[1010];
bool compare_sa(int i, int j) {
if (_rank[i] != _rank[j]) return _rank[i] < _rank[j];
else {
int ri = i + k <= n ? _rank[i + k] : -1;
int rj = j + k <= n ? _rank[j + k] : -1;
return ri < rj;
}
}
void construct_sa(string S, int* sa) {
n = S.length();
for (ll i = 0; i <= n; i++)
{
sa[i] = i;
_rank[i] = i < n ? S[i] : -1;
}
for (k = 1; k <= n; k *= 2)
{
sort(sa, sa + n + 1, compare_sa);
// saはソート後の接尾辞の並びになっている、rankは元の位置のindexを保持したまま、更新されている。
// ピンとこなかった部分
temp[sa[0]] = 0;
for (ll i = 1; i <= n; i++)
{
temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);
}
for (ll i = 0; i <= n; i++)
{
_rank[i] = temp[i];
}
}
}
bool contain(string S, int* sa, string T) {
int a = 0, b = S.length();
// sa は 接尾辞が辞書順に並んでいる、入っているのはその位置のインデックス
while (b - a > 1) {
int c = (a + b) / 2;
if (S.compare(sa[c], T.length(), T) < 0) a = c;
else b = c;
}
return S.compare(sa[b], T.length(), T) == 0;
}
#define bit(x,v) ((ll)x << v)
class BIT {
static const int MAX_N = 500010;
public:
vl bit;
ll n;
BIT() { bit = vl(MAX_N + 1, 0); }
BIT(ll _n) {
bit = vl(_n * 2 + 10, 0);
n = _n;
}
ll sum(int i) {
ll s = 0;
while (i > 0)
{
s += bit[i];
i -= i & -i;
}
return s;
}
void add(int i, int x) {
while (i <= n)
{
bit[i] += x;
i += i & -i;
}
}
};
struct UnionFind {
vector<int> A;
UnionFind(int n) : A(n, -1) {}
int find(int x) {
if (A[x] < 0) return x;
return A[x] = find(A[x]);
}
void unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return;
if (A[x] > A[y]) swap(x, y);
A[x] += A[y];
A[y] = x;
}
int ngroups() {
int ans = 0;
for (auto a : A) if (a < 0) ans++;
return ans;
}
};
vector<ll> getp(ll n) {
vector<ll> res;
if (n % 2 == 0) {
res.push_back(2);
while (n % 2 == 0)n /= 2;
}
for (ll i = 3; i * i <= n; i += 2)
{
if (n % i == 0) {
res.push_back(i);
while (n % i == 0)n /= i;
}
}
if (n != 1) res.push_back(n);
return res;
}
vector<ll> getpp(ll n) {
vector<ll> res;
if (n % 2 == 0) {
res.push_back(2);
while (n % 2 == 0)n /= 2;
}
for (ll i = 3; i * i * i <= n; i += 2)
{
if (n % i == 0) {
res.push_back(i);
while (n % i == 0)n /= i;
}
}
if (n != 1) res.push_back(n);
return res;
}
vector<ll> getp2(ll n) {
vector<ll> res;
if (n % 2 == 0) {
while (n % 2 == 0) { n /= 2; res.push_back(2); }
}
for (ll i = 3; i * i <= n; i += 2)
{
if (n % i == 0) {
while (n % i == 0) { n /= i; res.push_back(i); }
}
}
if (n != 1) res.push_back(n);
return res;
}
vector<pll> getp3(ll n) {
vector<pll> res;
int si = 0;
if (n % 2 == 0) {
res.push_back(make_pair(2, 0));
while (n % 2 == 0) { n /= 2; res[si].second++; }
si++;
}
for (ll i = 3; i * i <= n; i += 2)
{
if (n % i == 0) {
res.push_back(make_pair(i, 0));
while (n % i == 0) { n /= i; res[si].second++; }
si++;
}
}
if (n != 1) { res.push_back(make_pair(n, 1)); }
return res;
}
vector<ll> getDivisors(ll n) {
vector<ll> res;
res.push_back(1);
if (1 < n)
res.push_back(n);
for (ll i = 2; i * i <= n; i++)
{
if (n % i == 0) {
res.push_back(i);
if (n / i != i)
res.push_back(n / i);
}
}
vsort(res);
return res;
}
struct ve {
public:
vector<ve> child;
int _t = INF;
ve(int t) :_t(t) {}
ve(ve _left, ve _right) {
_t = _left._t + _right._t;
child.push_back(_left);
child.push_back(_right);
}
bool operator<(const ve& t) const {
return _t > t._t;
}
};
vector<bool> elas(ll n) {
n++;
vector<bool> r(n, 1);
r[0] = 0;
r[1] = 0;
ll tw = 4;
while (tw < n) {
r[tw] = false;
tw += 2;
}
ll th = 6;
while (th < n) {
r[th] = false;
th += 3;
}
ll fv = 10;
while (fv < n) {
r[fv] = false;
fv += 5;
}
for (ll i = 6; i * i < n; i += 6)
{
ll bf = i - 1;
if (r[bf]) {
ll ti = bf * 2;
while (ti < n)
{
r[ti] = false;
ti += bf;
}
}
ll nx = i + 1;
if (r[nx]) {
ll ti = nx * 2;
while (ti < n)
{
r[ti] = false;
ti += nx;
}
}
}
return r;
}
bool isPrime(ll v) {
if (v == 1 || v == 0)
return false;
for (ll i = 2; i * i <= v; i++)
{
if (v % i == 0) return false;
}
return true;
}
class SegTree {
public:
const static int MAX_N = 1000100;
const static int DAT_SIZE = (1 << 20) - 1;
int N, Q;
int A[MAX_N];
ll MAX = big;
ll data[DAT_SIZE], datb[DAT_SIZE];
void init(int _n) {
N = 1;
while (N < _n) N <<= 1;
memset(data, 0, sizeof(data));
memset(datb, 0, sizeof(datb));
}
void init(int _n, ll iv) {
N = 1;
while (N < _n) N <<= 1;
rep(i, DAT_SIZE) {
data[i] = iv;
datb[i] = iv;
}
}
void initRMQ(int _n) {
N = 1;
while (N < _n) N *= 2;
// 全ての値をbigに
rep(i, 2 * N - 1)
data[i] = MAX;
}
void updateRMQ(int k, ll a) {
k += N - 1;
data[k] = a;
while (k > 0) {
k = (k - 1) / 2;
data[k] = min(data[k * 2 + 1], data[k * 2 + 2]);
}
}
ll RMQ(int a, int b) {
return queryRMQ(a, b + 1, 0, 0, N);
}
ll queryRMQ(int a, int b, int k, int l, int r) {
if (r <= a || b <= l)
return MAX;
// [a,b)が[l,r)を完全に含んでいれば
if (a <= l && r <= b)
return data[k];
// そうでなければ２つの子の最小値
// n=16
// 0,16→0,8 8,16
// 0,4 4,8 8,12 12,16
ll vl = queryRMQ(a, b, k * 2 + 1, l, (l + r) / 2);
ll vr = queryRMQ(a, b, k * 2 + 2, (l + r) / 2, r);
return min(vl, vr);
}
void add(int a, int b, int x) {
add(a, b + 1, x, 0, 0, N);
}
void add(int a, int b, int x, int k, int l, int r) {
if (a <= l && r <= b) {
data[k] += x;
}
else if (l < b && a < r) {
datb[k] += (min(b, r) - max(a, l)) * x;
add(a, b, x, k * 2 + 1, l, (l + r) / 2);
add(a, b, x, k * 2 + 2, (l + r) / 2, r);
}
}
void change(int a, int b, int x) {
change(a, b + 1, x, 0, 0, N);
}
void change(int a, int b, int x, int k, int l, int r) {
if (a <= l && r <= b) {
data[k] = x;
}
else if (l < b && a < r) {
datb[k] = x;
change(a, b, x, k * 2 + 1, l, (l + r) / 2);
change(a, b, x, k * 2 + 2, (l + r) / 2, r);
}
}
ll sum(int a, int b) {
return sum(a, b + 1, 0, 0, N);
}
ll sum(int a, int b, int k, int l, int r) {
if (b <= l || r <= a) {
return 0;
}
if (a <= l && r <= b) {
return data[k] * (r - l) + datb[k];
}
ll res = (min(b, r) - max(a, l)) * data[k];
res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
return res;
}
};
class LazySegTree {
private:
int N;
vl node, lazy;
public:
void init(int _n) {
N = 1;
while (N < _n) N <<= 1;
node.resize(2 * N, 0);
lazy.resize(2 * N, 0);
}
// k 番目のノードについて遅延評価を行う
void eval(int k, int l, int r) {
// 遅延配列が空でない場合、自ノード及び子ノードへの
// 値の伝播が起こる
if (lazy[k] != 0) {
node[k] += lazy[k];
// 最下段かどうかのチェックをしよう
// 子ノードは親ノードの 1/2 の範囲であるため、
// 伝播させるときは半分にする
if (r - l > 1) {
lazy[2 * k + 1] += lazy[k] / 2;
lazy[2 * k + 2] += lazy[k] / 2;
}
// 伝播が終わったので、自ノードの遅延配列を空にする
lazy[k] = 0;
}
}
void add(int a, int b, ll x) {
addbody(a, b + 1, x);
}
void addbody(int a, int b, ll x, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
// k 番目のノードに対して遅延評価を行う
eval(k, l, r);
// 範囲外なら何もしない
if (b <= l || r <= a) return;
// 完全に被覆しているならば、遅延配列に値を入れた後に評価
if (a <= l && r <= b) {
lazy[k] += (r - l) * x;
eval(k, l, r);
}
// そうでないならば、子ノードの値を再帰的に計算して、
// 計算済みの値をもらってくる
else {
addbody(a, b, x, 2 * k + 1, l, (l + r) / 2);
addbody(a, b, x, 2 * k + 2, (l + r) / 2, r);
node[k] = node[2 * k + 1] + node[2 * k + 2];
}
}
ll getsum(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (b <= l || r <= a) return 0;
// 関数が呼び出されたら評価！
eval(k, l, r);
if (a <= l && r <= b) return node[k];
ll vl = getsum(a, b, 2 * k + 1, l, (l + r) / 2);
ll vr = getsum(a, b, 2 * k + 2, (l + r) / 2, r);
return vl + vr;
}
ll getMax(int a, int b) {
// 半開区間に変換
return getMaxBdy(a, b + 1);
}
ll getMaxBdy(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (b <= l || r <= a) return -big;
// 関数が呼び出されたら評価！
eval(k, l, r);
if (a <= l && r <= b) return node[k];
ll vl = getMaxBdy(a, b, 2 * k + 1, l, (l + r) / 2);
ll vr = getMaxBdy(a, b, 2 * k + 2, (l + r) / 2, r);
return max(vl, vr);
}
};
class LazySegTreeRMQ {
private:
int N;
vl node, lazy;
public:
void init(int _n) {
N = 1;
while (N < _n) N <<= 1;
node.resize(2 * N, 0);
lazy.resize(2 * N, 0);
}
// k 番目のノードについて遅延評価を行う
void eval(int k, int l, int r) {
if (lazy[k] != 0) {
node[k] = lazy[k];
if (r - l > 1) {
lazy[2 * k + 1] = lazy[k];
lazy[2 * k + 2] = lazy[k];
}
lazy[k] = 0;
}
}
void evalAdd(int k, int l, int r) {
if (lazy[k] != 0) {
node[k] += lazy[k];
if (r - l > 1) {
lazy[2 * k + 1] += lazy[k];
lazy[2 * k + 2] += lazy[k];
}
lazy[k] = 0;
}
}
void add(int a, int b, ll x) {
addbody(a, b + 1, x);
}
void addbody(int a, int b, ll x, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
// k 番目のノードに対して遅延評価を行う
evalAdd(k, l, r);
// 範囲外なら何もしない
if (b <= l || r <= a) return;
// 完全に被覆しているならば、遅延配列に値を入れた後に評価
if (a <= l && r <= b) {
lazy[k] += x;
evalAdd(k, l, r);
}
// そうでないならば、子ノードの値を再帰的に計算して、
// 計算済みの値をもらってくる
else {
addbody(a, b, x, 2 * k + 1, l, (l + r) / 2);
addbody(a, b, x, 2 * k + 2, (l + r) / 2, r);
node[k] = max(node[2 * k + 1], node[2 * k + 2]);
}
}
void update(int a, int b, ll v) {
updateBdy(a, b + 1, v);
}
void updateBdy(int a, int b, ll x, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
// k 番目のノードに対して遅延評価を行う
eval(k, l, r);
// 範囲外なら何もしない
if (b <= l || r <= a) return;
// 完全に被覆しているならば、遅延配列に値を入れた後に評価
if (a <= l && r <= b) {
if (x > node[k]) {
lazy[k] = x;
eval(k, l, r);
}
}
// そうでないならば、子ノードの値を再帰的に計算して、
// 計算済みの値をもらってくる
else {
updateBdy(a, b, x, 2 * k + 1, l, (l + r) / 2);
updateBdy(a, b, x, 2 * k + 2, (l + r) / 2, r);
node[k] = max(node[2 * k + 1], node[2 * k + 2]);
}
}
ll getMaxAdd(int a, int b) {
// 半開区間に変換
return getMaxAddBdy(a, b + 1);
}
ll getMaxAddBdy(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (b <= l || r <= a) return -big;
// 関数が呼び出されたら評価！
evalAdd(k, l, r);
if (a <= l && r <= b) return node[k];
ll vl = getMaxAddBdy(a, b, 2 * k + 1, l, (l + r) / 2);
ll vr = getMaxAddBdy(a, b, 2 * k + 2, (l + r) / 2, r);
return max(vl, vr);
}
ll getMax(int a, int b) {
// 半開区間に変換
return getMaxBdy(a, b + 1);
}
ll getMaxBdy(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0) r = N;
if (b <= l || r <= a) return -big;
// 関数が呼び出されたら評価！
eval(k, l, r);
if (a <= l && r <= b) return node[k];
ll vl = getMaxBdy(a, b, 2 * k + 1, l, (l + r) / 2);
ll vr = getMaxBdy(a, b, 2 * k + 2, (l + r) / 2, r);
return max(vl, vr);
}
};
class Segment;
class Circle;
class Point {
public:
double x, y;
Point(double x = 0, double y = 0) :x(x), y(y) {}
Point operator + (Point p) { return Point(x + p.x, y + p.y); }
Point operator - (Point p) { return Point(x - p.x, y - p.y); }
Point operator * (double a) { return Point(a * x, a * y); }
Point operator / (double a) { return Point(x / a, y / a); }
double abs() { return sqrt(norm()); }
double norm() { return x * x + y * y; }
bool operator < (const Point& p)const {
return x != p.x ? x < p.x : y < p.y;
}
bool operator == (const Point& p) const {
return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
}
// 内積
static double dot(Point a, Point b) {
return a.x * b.x + a.y * b.y;
}
// 外積
static double cross(Point a, Point b) {
return a.x * b.y - a.y * b.x;
}
static bool isOrthogonal(Point a, Point b) {
return EQ(dot(a, b), 0.0);
}
static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
return isOrthogonal(a1 - a2, b1 - b2);
}
static bool isOrthogonal(Segment s1, Segment s2);
static bool isPalallel(Point a, Point b) {
return EQ(cross(a, b), 0.0);
}
static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {
return isPalallel(a1 - a2, b1 - b2);
}
static bool isPalallel(Segment s1, Segment s2);
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;
static int bbw(Point p0, Point p1, Point p2) {
// 線分はp0とp1でp2がどこにあるかを探る
Point a = p1 - p0;
Point b = p2 - p0;
if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
if (cross(a, b) < -EPS) return CLOCKWISE;
if (dot(a, b) < -EPS) return ONLINE_BACK;
if (a.norm() < b.norm()) return ONLINE_FRONT;
return ON_SEGMENT;
}
// 交差しているか
static bool intersect(Point p1, Point p2, Point p3, Point p4) {
return (bbw(p1, p2, p3) * bbw(p1, p2, p4) <= 0
&& bbw(p3, p4, p1) * bbw(p3, p4, p2) <= 0);
}
static bool intersect(Segment s1, Segment s2);
static Point project(Segment s, Point p);
static Point reflect(Segment s, Point p);
static double getDistance(Point a, Point b) {
return (a - b).abs();
}
static double getDistanceLP(Segment s, Point p);
static double getDistanceSP(Segment s, Point p);
static double getDistance(Segment s1, Segment s2);
static Point getIntersection(Segment s1, Segment s2);
static pair<Point, Point> crossPoints(Circle c, Segment s);
static int contains(vector<Point> g, Point p) {
int n = g.size();
bool x = false;
rep(i, n) {
Point a = g[i] - p, b = g[(i + 1) % n] - p;
// 線の上に載っているか
if (std::abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;
// pを基準として上下にあるか
// または外積が正か?(→にあるか)
if (a.y > b.y) swap(a, b);
if (a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
}
return x ? 2 : 0;
}
static vector<Point> andrewScan(vector<Point> s) {
vector<Point> u, l;
ll si = s.size();
if (si < 3) return s;
sort(all(s));
u.push_back(s[0]);
u.push_back(s[1]);
l.push_back(s[si - 1]);
l.push_back(s[si - 2]);
for (int i = 2; i < si; i++) {
for (int _n = u.size(); _n >= 2 && bbw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {
u.pop_back();
}
u.push_back(s[i]);
}
for (int i = s.size() - 3; i >= 0; i--) {
for (int _n = l.size(); _n >= 2 && bbw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {
l.pop_back();
}
l.push_back(s[i]);
}
reverse(all(l));
for (int i = u.size() - 2; i >= 1; i--)
{
l.push_back(u[i]);
}
return l;
}
void get_cin() {
cin >> x >> y;
}
static Point rotate(double r, Point p) {
Point ret;
ret.x = cos(r) * p.x - sin(r) * p.y;
ret.y = sin(r) * p.x + cos(r) * p.y;
return ret;
}
static double computePerimeter(const vector<Point>& hull) {
double perimeter = 0.0;
for (size_t i = 0; i < hull.size(); i++) {
perimeter += getDistance(hull[i], hull[(i + 1) % hull.size()]);
}
return perimeter;
}
};
class Segment {
public:
Point p1, p2;
Segment() {}
Segment(Point p1, Point p2) :p1(p1), p2(p2) {}
void get_cin() {
cin >> p1.x >> p1.y >> p2.x >> p2.y;
}
Point p1tp2() {
return p2 - p1;
}
Point p2tp1() {
return p1 - p2;
}
double abs() {
return (p2 - p1).abs();
}
double norm() {
return (p2 - p1).norm();
}
};
// 直行
bool Point::isOrthogonal(Segment s1, Segment s2) {
return EQ(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
// 平行
bool Point::isPalallel(Segment s1, Segment s2) {
return EQ(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);
}
// 交差しているか
bool Point::intersect(Segment s1, Segment s2) {
return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
Point Point::project(Segment s, Point p) {
Point base = s.p2 - s.p1;
double r = Point::dot(p - s.p1, base) / base.norm();
return s.p1 + base * r;
}
Point Point::reflect(Segment s, Point p) {
return (project(s, p) * 2) - p;
}
double Point::getDistanceLP(Segment s, Point p) {
return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());
}
double Point::getDistanceSP(Segment s, Point p) {
if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
return getDistanceLP(s, p);
}
double Point::getDistance(Segment s1, Segment s2) {
if (intersect(s1, s2)) return 0.0;
return min({ getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)
,getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2) });
}
Point Point::getIntersection(Segment s1, Segment s2) {
// (s1.p1 - s2.p1).norm()
auto bs = s1.p2 - s1.p1;
auto n1 = s2.p1 - s1.p1;
auto n2 = s2.p2 - s1.p1;
auto c1 = std::abs(cross(n1, bs)) / bs.norm();
auto c2 = std::abs(cross(n2, bs)) / bs.norm();
return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));
// c1:c2=t:1-t
// c2t=(1-t)c1
// t/(1-t)=c1/(c1+c2)
//
}
double arg(Point p) { return atan2(p.y, p.x); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
class Circle {
public:
Point c;
double r;
Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
void get_cin() {
cin >> c.x >> c.y >> r;
}
static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
double d = (c1.c - c2.c).abs(); // 中心点どうしの距離
double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
double t = arg(c2.c - c1.c);
return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}
};
pair<Point, Point> Point::crossPoints(Circle c, Segment s) {
auto pp = project(s, c.c);
auto f = (pp - c.c).norm();
auto mu = sqrt(c.r * c.r - f);
// 単位ベクトル
auto e = s.p1tp2() / s.p1tp2().abs();
return make_pair(pp + e * mu, pp - e * mu);
}
ll divRm(string s, ll x) {
ll r = 0;
for (ll i = 0; i < s.size(); i++)
{
r *= 10;
r += s[i] - '0';
r %= x;
}
return r;
}
ll cmbi(ll x, ll b) {
ll res = 1;
for (size_t i = 0; i < b; i++)
{
res *= x - i;
res %= INF;
res *= inv[b - i];
res %= INF;
}
return res;
}
map<ll, ll> dgmemo;
ll digsum(ll x) {
if (dgmemo.count(x))return dgmemo[x];
ll res = 0;
while (x > 0)
{
res += x % 10;
x /= 10;
}
return res;
}
bool check_parindrome(string s) {
int n = s.size();
rep(i, n / 2) {
if (s[i] != s[n - i - 1]) {
return false;
}
}
return true;
}
ll npr(ll n, ll r) {
if (r == 0)
return 1;
return inff(fac[n] * modinv(fac[n - r]));
}
vl zalgo(string s) {
ll c = 0;
vl a(s.size());
ll si = s.size();
rep2(i, 1, s.size()) {
if (i + a[i - c] < c + a[c])
{
a[i] = a[i - c];
}
else {
ll j = max(0LL, a[c] - (i - c));
while (i + j < si && s[j] == s[i + j])
{
j++;
}
a[i] = j;
c = i;
}
}
a[0] = s.size();
return a;
}
// 数値文字列の除算
string divStrNum(string s, ll v) {
ll si = s.size();
ll val = 0;
string res = "";
for (ll i = 0; i < si; i++)
{
val *= 10;
val += s[i] - '0';
ll add = val / v;
val %= v;
if (add == 0 && res == "")
continue;
res += add + '0';
}
if (res == "")
return "0";
return res;
}
// 数値文字列の減算
string difStrNum(string s, ll v) {
ll si = s.size();
bool dec = false;
for (ll i = si - 1; i >= 0; i--)
{
if (v == 0)
break;
ll t = v % 10;
v /= 10;
ll u = (s[i] - '0');
if (dec) {
if (u == 0) {
s[i] = 9 - t;
dec = true;
continue;
}
u--;
}
if (u < t) {
s[i] = 10 - (t - u);
dec = true;
}
else {
s[i] -= t;
dec = false;
}
}
return s;
}
// 数値文字列を1減らした数
string decStrNum(string s) {
ll si = s.size();
for (int i = si - 1; i >= 0; i--)
{
if (s[i] == '0') {
s[i] = '9';
continue;
}
s[i] = s[i] - 1;
break;
}
return s;
}
void dateCal(int x) {
int lp = x / 7;
string date[] = { "月曜日","火曜日","水曜日","木曜日","金曜日","土曜日","日曜日" };
rep(i, 7) {
int st = i;
rep(j, lp) {
cout << "\t" << date[i] << x << "-" << st << "\t" << "NULL" << "\t" << x << "\t" << st << "\t" << 0 << endl;
st += 7;
}
}
}
// 行列べき乗計算
mat mul(mat& A, mat& B) {
ll as = A.size();
ll bs = B.size();
mat C(A.size(), vl(B[0].size()));
rep(i, as) {
rep(t, bs) {
ll bz = B[0].size();
rep(j, bz) {
C[i][j] = inff(C[i][j] + A[i][t] * B[t][j]);
}
}
}
return C;
}
mat pow(mat A, ll x) {
if (A.size() == 0)return A;
mat B(A.size(), vl(A.size()));
rep(i, A.size()) {
B[i][i] = 1;
}
while (x > 0)
{
if (x & 1)
B = mul(B, A);
A = mul(A, A);
x >>= 1;
}
return B;
}
class dinic {
public:
vve G;
vl level;
vl iter;
dinic(int _n) : dinic(vve(_n + 1)) {
}
dinic(vve g) {
G = g;
level = vl(g.size());
iter = vl(g.size());
}
void add_edge(ll from, ll to, ll cap) {
auto e1 = edge();
auto e2 = edge();
e1.flowEdge(to, cap, G[to].size());
G[from].push_back(e1);
e2.flowEdge(from, 0, G[from].size() - 1);
G[to].push_back(e2);
}
void bfs(ll s) {
fill(all(level), -1);
queue<ll> q;
level[s] = 0;
q.push(s);
while (!q.empty())
{
ll v = frontpop(q);
for (auto e : G[v]) {
if (e.cap > 0 && level[e.to] < 0) {
level[e.to] = level[v] + 1;
q.push(e.to);
}
}
}
}
ll dfs(ll v, ll t, ll f) {
if (v == t)
return f;
for (ll& i = iter[v]; i < G[v].size(); i++) {
edge& e = G[v][i];
if (e.cap > 0 && level[v] < level[e.to]) {
ll d = dfs(e.to, t, min(f, e.cap));
if (d > 0) {
e.cap -= d;
G[e.to][e.rev].cap += d;
return d;
}
}
}
return 0;
}
ll max_flow(ll s, ll t) {
ll flow = 0;
for (;;) {
bfs(s);
if (level[t] < 0)
return flow;
fill(all(iter), 0);
ll f;
while ((f = dfs(s, t, big)) > 0)
{
flow += f;
}
}
}
};
const ull BS = 1000000007;
// aはbに含まれているか？
bool rolling_hash(string a, string b) {
int al = a.size(), bl = b.size();
if (al > bl)
return false;
// BSのal乗を計算
ull t = 1;
rep(i, al)t *= BS;
// aとbの最初のal文字に関するハッシュ値を計算
ull ah = 0, bh = 0;
rep(i, al) ah = ah * BS + a[i];
rep(i, al) bh = bh * BS + b[i];
// bの場所を一つずつ進めながらハッシュ値をチェック
for (ll i = 0; i + al <= bl; i++)
{
if (ah == bh)
return true;
if (i + al < bl)bh = bh * BS + b[i + al] - b[i] * t;
}
return false;
}
mat sans(9, vl(9, -1));
bool srec(ll x, ll y) {
if (x == 9)
return true;
vl use(10, 0);
rep(i, 9) {
if (sans[i][y] == -1)
continue;
use[sans[i][y]] = 1;
}
rep(j, 9) {
if (sans[x][j] == -1)
continue;
use[sans[x][j]] = 1;
}
ll px = x % 3;
ll py = y % 3;
ll tx = x - px + 3;
ll ty = y - py + 3;
rep2(i, x - px, tx) {
rep2(j, y - py, ty) {
if (sans[i][j] == -1)
continue;
use[sans[i][j]] = 1;
}
}
ll nx, ny;
if (y == 8) {
nx = x + 1;
ny = 0;
}
else {
nx = x;
ny = y + 1;
}
if (sans[x][y] != -1) {
if (srec(nx, ny)) {
return true;
}
return false;
}
rep2(i, 1, 10) {
if (use[i])
continue;
sans[x][y] = i;
if (srec(nx, ny)) {
return true;
}
sans[x][y] = -1;
}
return false;
}
void sudoku() {
vector<string> tb;
rep(i, 9) {
string s;
cin >> s;
tb.push_back(s);
rep(j, 9) {
if (tb[i][j] != '.') {
sans[i][j] = tb[i][j] - '0';
}
}
}
srec(0, 0);
rep(i, 9) {
rep(j, 9) {
cout << sans[i][j];
}
cout << endl;
}
}
mint ncr(ll n, ll r) {
mint v = 1;
rep(i, r) {
v *= (n - i);
v *= inv[i + 1];
}
return v;
}
modint1000000007 ncr2(ll n, ll r) {
modint1000000007 v = 1;
rep(i, r) {
v *= (n - i);
v /= i + 1;
}
return v;
}
ll ncr3(ll n, ll r) {
ll v = 1;
rep(i, r) {
v *= (n - i);
v /= i + 1;
}
return v;
}
ll sq(ll x) {
return x * x;
}
ll phi(ll x) {
auto p = getp(x);
ll res = x;
for (auto v : p) {
res /= v;
res *= v - 1;
}
return res;
}
const ull MASK30 = (1ULL << 30) - 1;
const ull MASK31 = (1ULL << 31) - 1;
const ull MOD = 2305843009213693953UL;
const ull MASK61 = (1ULL << 61UL) - 1UL;
//mod 2^61-1を計算する関数
ull calc_mod_61(ull x)
{
ull xu = x >> 61;
ull xd = x & MASK61;
ull res = xu + xd;
if (res >= MOD) res -= MOD;
return res;
}
ull mul_61(ull a, ull b)
{
ull au = a >> 31;
ull ad = a & MASK31;
ull bu = b >> 31;
ull bd = b & MASK31;
ull mid = ad * bu + au * bd;
ull midu = mid >> 30;
ull midd = mid & MASK30;
return calc_mod_61(au * bu * 2 + midu + (midd << 31) + ad * bd);
}
vl mulMatVec(mat a, vl b)
{
int n = b.size(); vl ret(n, 0);
rep(i, n) rep(j, n)
ret[j] = inff(ret[j] + inff(a[i][j] * b[i]));
return ret;
}
ll isqrt(ll N) {
ll sqrtN = sqrt(N) - 1;
while (sqrtN + 1 <= N / (sqrtN + 1))sqrtN++;
return sqrtN;
}
ll cross(pll l, pll r) {
return l.first * r.second - l.second * r.first;
}
void rotate(vl& v) {
v.push_back(v.front());
v.erase(v.begin());
}
class ConvexHullDynamic
{
typedef long long coef_t;
typedef long long coord_t;
typedef long long val_t;
/*
* Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* and 'xLeft' which is intersection with previous line in hull(first line has -INF)
*/
private:
struct Line
{
coef_t a, b;
double xLeft;
enum Type
{
line, maxQuery, minQuery
} type;
coord_t val;
explicit Line(coef_t aa = 0, coef_t bb = 0) : a(aa), b(bb), xLeft(-INFINITY), type(Type::line), val(0) {}
val_t valueAt(coord_t x) const { return a * x + b; }
friend bool areParallel(const Line& l1, const Line& l2) { return l1.a == l2.a; }
friend double intersectX(const Line& l1, const Line& l2) { return areParallel(l1, l2) ? INFINITY : 1.0 * (l2.b - l1.b) / (l1.a - l2.a); }
bool operator<(const Line& l2) const
{
if (this->type == maxQuery)
return this->val < l2.xLeft;
if (this->type == minQuery)
return this->val > l2.xLeft;
if (l2.type == line)
return this->a < l2.a;
if (l2.type == maxQuery)
return this->xLeft < l2.val;
if (l2.type == minQuery)
return this->xLeft > l2.val;
}
};
bool isMax; //whether or not saved envelope is top(search of max value)
public:
std::set< Line > hull; //envelope itself
private:
/*
* INFO: Check position in hull by iterator
* COMPLEXITY: O(1)
*/
bool hasPrev(std::set< Line >::iterator it) { return it != hull.begin(); }
bool hasNext(std::set< Line >::iterator it) { return it != hull.end() && std::next(it) != hull.end(); }
/*
* INFO: Check whether line l2 is irrelevant
* NOTE: Following positioning in hull must be true
* l1 is next left to l2
* l2 is right between l1 and l3
* l3 is next right to l2
* COMPLEXITY: O(1)
*/
bool irrelevant(const Line& l1, const Line& l2, const Line& l3) { return intersectX(l1, l3) <= intersectX(l1, l2); }
bool irrelevant(std::set< Line >::iterator it)
{
return hasPrev(it) && hasNext(it)
&& (isMax && irrelevant(*std::prev(it), *it, *std::next(it))
|| !isMax && irrelevant(*std::next(it), *it, *std::prev(it)));
}
/*
* INFO: Updates 'xValue' of line pointed by iterator 'it'
* COMPLEXITY: O(1)
*/
std::set< Line >::iterator updateLeftBorder(std::set< Line >::iterator it)
{
if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
return it;
double val = intersectX(*it, isMax ? *std::prev(it) : *std::next(it));
Line buf(*it);
it = hull.erase(it);
buf.xLeft = val;
it = hull.insert(it, buf);
return it;
}
public:
explicit ConvexHullDynamic(bool isMax = false) : isMax(isMax) {}
/*
* INFO: Adding line to the envelope
* Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* COMPLEXITY: Adding N lines(N calls of function) takes O(N*log N) time
*/
void addLine(coef_t a, coef_t b)
{
//find the place where line will be inserted in set
Line l3 = Line(a, b);
auto it = hull.lower_bound(l3);
//if parallel line is already in set, one of them becomes irrelevant
if (it != hull.end() && areParallel(*it, l3)) {
if (isMax && it->b < b || !isMax && it->b > b)
it = hull.erase(it);
else
return;
}
//try to insert
it = hull.insert(it, l3);
if (irrelevant(it)) {
hull.erase(it);
return;
}
//remove lines which became irrelevant after inserting line
while (hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it));
while (hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it));
//refresh 'xLine'
it = updateLeftBorder(it);
if (hasPrev(it))
updateLeftBorder(std::prev(it));
if (hasNext(it))
updateLeftBorder(std::next(it));
}
val_t getBest(coord_t x) const
{
Line q;
q.val = x;
q.type = isMax ? Line::Type::maxQuery : Line::Type::minQuery;
auto bestLine = hull.lower_bound(q);
if (isMax) --bestLine;
return bestLine->valueAt(x);
}
};
class treelib {
public:
mat es;
vl stop;
vl d;
treelib(mat _es) : es(_es) {
stop.resize(_es.size() + 1, 0);
d.resize(_es.size() + 1);
}
/*
* first: depth.second : leaf;
*/
pll deepest(ll x, ll f) {
ll a = 0, b = -1;
for (auto v : es[x]) {
if (stop[v])continue;
if (v == f)continue;
d[v] = d[x] + 1;
auto p = deepest(v, x);
if (p.first > a) {
a = p.first;
b = p.second;
}
}
if (b == -1) {
return { 1,x };
}
else {
return { a + 1,b };
}
}
};
class treelib2 {
public:
vector<vpll> es;
vl stop;
vl d;
treelib2(vector<vpll> _es) : es(_es) {
stop.resize(_es.size() + 1, 0);
d.resize(_es.size() + 1);
}
/*
* first: depth.second : leaf;
*/
pll deepest(ll x, ll f) {
ll a = 0, b = -1;
for (auto v : es[x]) {
ll t = v.first;
if (stop[t])continue;
if (t == f)continue;
d[t] = d[x] + v.second;
auto p = deepest(t, x);
if (p.first > a) {
a = p.first;
b = p.second;
}
}
if (b == -1) {
return { 1,x };
}
else {
return { a + 1,b };
}
}
};
struct scompress {
vl mapped, dup;
map<ll, ll> mp;
};
scompress compress(vl& v) {
ll n = v.size();
vl b(n);
rep(i, n) {
b[i] = v[i];
}
vsort(b);
dup(b);
map<ll, ll> mp;
rep(i, b.size()) {
mp[b[i]] = i;
}
vl res(n);
rep(i, n) {
res[i] = mp[v[i]];
}
vl bb(b.size());
rep(i, b.size()) {
bb[i] = mp[b[i]];
}
return { res,bb,mp };
}
using ld = double;
using P = Point;
template <class iter>
Circle min_ball(iter left, iter right, int seed = 1333) {
const int n = right - left;
assert(n >= 1);
if (n == 1) {
return { *left, ld(0) };
}
std::mt19937 mt(seed);
std::shuffle(left, right, mt);
// std::random_shuffle(left, right); // simple but deprecated
iter ps = left;
using circle = Circle;
auto make_circle_3 = [](P& a, P& b, P& c) -> circle {
ld A = (b - c).norm(), B = (c - a).norm(), C = (a - b).norm(),
S = Point::cross(b - a, c - a);
P p = (a * (A * (B + C - A)) + (b * B * (C + A - B)) + c * C * (A + B - C))
/ (4 * S * S);
ld r2 = (p - a).norm();
return { p, r2 };
};
auto make_circle_2 = [](P& a, P& b) -> circle {
P c = (a + b) / (ld)2;
ld r2 = (a - c).norm();
return { c, r2 };
};
auto in_circle = [](P& a, circle& c) -> bool {
return (a - c.c).norm() <= c.r + EPS;
};
circle c = make_circle_2(ps[0], ps[1]);
// MiniDisc
for (int i = 2; i < n; ++i) {
if (!in_circle(ps[i], c)) {
// MiniDiscWithPoint
c = make_circle_2(ps[0], ps[i]);
for (int j = 1; j < i; ++j) {
if (!in_circle(ps[j], c)) {
// MiniDiscWith2Points
c = make_circle_2(ps[i], ps[j]);
for (int k = 0; k < j; ++k) {
if (!in_circle(ps[k], c)) {
c = make_circle_3(ps[i], ps[j], ps[k]);
}
}
}
}
}
}
return c;
}
vml2 kitamasadfs(vml2 a, vml2 d, ll n) {
if (d.size() == n)
return d;
vml2 res(d.size());
if (n < d.size() * 2 || (n & 1)) {
auto f = kitamasadfs(a, d, n - 1);
res[0] = f[k - 1] * d[0];
rep2(i, 1, d.size()) {
res[i] = f[i - 1] + f[k - 1] * d[i];
}
}
else {
auto v = kitamasadfs(a, d, n / 2);
matm2 f(d.size(), vml2(d.size()));
f[0] = v;
rep2(i, 1, d.size()) {
f[i][0] = f[i - 1][k - 1] * d[0];
rep2(j, 1, d.size()) {
f[i][j] = f[i - 1][j - 1] + f[i - 1][k - 1] * d[j];
}
}
rep(i, d.size()) {
rep(j, d.size()) {
res[j] += f[i][j] * v[i];
}
}
}
return res;
}
modint1000000007 kitamasa(vml2 a, vml2 d, ll n) {
auto v = kitamasadfs(a, d, n);
modint1000000007 res = 0;
rep(i, d.size()) {
res += v[i] * a[i];
}
return res;
}
void belman_temp(vector<vpll>& es, vl& d, ll s) {
d[s] = 0;
rep(i, n + 1) {
queue<ll> q;
rep2(j, 1, n + 1) {
if (d[j] == big)continue;
for (auto& v : es[j]) {
if (chmin(d[v.first], d[j] + v.second)) {
q.push(v.first);
}
}
}
if (i < n)continue;
while (!q.empty())
{
auto p = frontpop(q);
for (auto& v : es[p]) {
if (chmin(d[v.first], -big)) {
q.push(v.first);
}
}
}
}
}
vl getpath(mat& es, vl& d, ll s, ll g) {
vl res;
ll x = s;
while (x != g)
{
res.push_back(x);
for (auto v : es[x]) {
if (d[v] == d[x] - 1) {
x = v;
break;
}
}
}
res.push_back(x);
reverse(all(res));
return res;
}
/// <summary>
/// ベルマンフォード
/// </summary>
/// <param name="es"></param>
/// <param name="d"></param>
/// <param name="s"></param>
bool belman(vector<vpll>& es, ll n, vl& d, ll s) {
d.resize(n, big);
d[s] = 0;
rep(i, n) {
bool e = false;
rep(f, n) {
if (d[f] == big)continue;
for (auto& v : es[f]) {
if (chmin(d[v.first], d[f] + v.second)) {
e = true;
}
}
}
if (!e) break;
}
queue<ll> q;
rep(f, n) {
if (d[f] == big)continue;
for (auto& v : es[f]) {
if (chmin(d[v.first], d[f] + v.second)) {
q.push(v.first);
}
}
}
bool e = false;
while (!q.empty())
{
auto p = frontpop(q);
for (auto& v : es[p]) {
if (d[v.first] > -big) {
e = true;
d[v.first] = -big;
q.push(v.first);
}
}
}
return e;
}
template<class t>
void put_line(vector<t>& p) {
rep(i, p.size()) {
cout << p[i] << " ";
}
cout << endl;
}
mat tablecut(ll h, ll w, vector<string> t) {
ll top = 0;
rep(i, h) {
bool ok = true;
rep(j, w) {
if (t[i][j] == '#') {
ok = false;
break;
}
}
if (!ok)break;
top++;
}
ll bot = h;
for (int i = h - 1; i >= 0; i--)
{
bool ok = true;
rep(j, w) {
if (t[i][j] == '#') {
ok = false;
break;
}
}
if (!ok)break;
bot--;
}
ll lf = 0;
rep(i, w) {
bool ok = true;
rep(j, h) {
if (t[j][i] == '#') {
ok = false;
break;
}
}
if (!ok)break;
lf++;;
}
ll ri = w;
for (int i = w - 1; i >= 0; i--)
{
bool ok = true;
rep(j, h) {
if (t[j][i] == '#') {
ok = false;
break;
}
}
if (!ok)break;
ri--;
}
mat tb(bot - top, vl(ri - lf));
rep2(i, top, bot) {
rep2(j, lf, ri) {
if (t[i][j] == '#') {
tb[i - top][j - lf] = 1;
}
}
}
return tb;
}
mat tablerotate(ll h, ll w, mat& a) {
mat b(w, vl(h));
rep(i, h) {
rep(j, w) {
b[w - j - 1][i] = a[i][j];
}
}
return b;
}
ll rangeadd_op(ll l, ll r) {
return max(l, r);
}
ll rangeadd_e() {
return -big;
}
ll range_add_map(ll l, ll r) {
if (l == -big)return r;
if (r == -big)return l;
return l + r;
}
ll range_add_comp(ll l, ll r) {
return l + r;
}
ll rangeadd_id() {
return 0;
}
ll rangesum_op(ll l, ll r) {
return max(0LL, l) + max(0LL, r);
}
ll rsum_op(ll l, ll r) {
return l + r;
}
ll rangesum_e() {
return -big;
}
struct Qusm {
ll a = 0, sz = 0;
};
Qusm opQusm(Qusm l, Qusm r) {
return { l.a + r.a,l.sz + r.sz };
}
Qusm eQusm() {
Qusm q;
return q;
}
Qusm mapQusm(ll l, Qusm v) {
return { v.a + v.sz * l,v.sz };
}
ll cmpQusm(ll ne, ll ol) {
return ne + ol;
}
ll idQusm() {
return 0;
}
lazy_segtree<ll, rangeadd_op, rangeadd_e, ll, range_add_map, range_add_comp, rangeadd_id>
create_range_add_st(ll n) {
return lazy_segtree<ll,
rangeadd_op,
rangeadd_e,
ll,
range_add_map,
range_add_comp,
rangeadd_id>(n + 1);
}
lazy_segtree<Qusm, opQusm, eQusm, ll, mapQusm, cmpQusm, idQusm>
create_range_add_st3(ll n) {
return lazy_segtree<Qusm, opQusm, eQusm, ll, mapQusm, cmpQusm, idQusm>(n + 1);
}
lazy_segtree<ll, rangesum_op, rangesum_e, ll, range_add_map, range_add_comp, rangeadd_id>
create_range_add_stv2(vl a) {
return lazy_segtree<ll,
rangesum_op,
rangesum_e,
ll,
range_add_map,
range_add_comp,
rangeadd_id>(a);
}
class rolhash_lib {
string s;
vl v, p;
ll n;
public:
rolhash_lib() {
}
rolhash_lib(string _s) : s(_s) {
n = s.size();
v.resize(n + 1);
p.resize(n + 1);
p[0] = 1;
rep(i, n) {
v[i + 1] = calc_mod_61(mul_61(v[i], INF) + s[i]);
p[i + 1] = mul_61(p[i], INF);
}
}
ll get_hash(ll l, ll r) {
l--;
return calc_mod_61(v[r] + MOD * 4 - mul_61(v[l], p[r - l]));
}
};
template<class t>
class zobhash_lib {
vector<t> s;
vul v, p;
ll n;
public:
zobhash_lib() {
}
zobhash_lib(vector<t> _s, vector<t> vals) : s(_s) {
n = s.size();
v.resize(n + 1);
p.resize(n + 1);
p[0] = 1;
map<t, ull> mp;
ull q = INF;
rep(i, vals.size()) {
mp[vals[i]] = mul_61(vals[i], q);
q = mul_61(q, INF);
}
rep(i, n) {
v[i + 1] = calc_mod_61(v[i] + mp[s[i]]);
}
}
ull get_hash(ll l, ll r) {
l--;
return calc_mod_61(v[r] + MOD * 4 - v[l]);
}
};
long long llceil(long long a, long long b) {
if (a % b == 0) { return a / b; }
if (a >= 0) { return (a / b) + 1; }
else { return -((-a) / b); }
}
long long llfloor(long long a, long long b) {
if (a % b == 0) { return a / b; }
if (a >= 0) { return (a / b); }
else { return -((-a) / b) - 1; }
}
using pl = pair<long long, long long>;
pl findseg(pl seg, long long ini, long long step) {
if (step > 0) {
return { llceil(seg.first - ini,step), llfloor(seg.second - ini,step) };
}
else {
step *= -1;
return { llceil(ini - seg.second,step), llfloor(ini - seg.first,step) };
}
}
ll matsum(mat& a, ll i, ll j, ll x, ll y) {
return a[i][j] - a[i - x][j] - a[i][j - y] + a[i - x][j - y];
}
ll __parity(ll t) {
ll c = 0;
while (t > 0)
{
c += t & 1;
t >>= 1;
}
return c % 2;
}
ll lcm(ll a, ll b) {
return a * b / gcd(a, b);
}
ll popcount(ll x) {
ll c = 0;
while (x > 0)
{
c += x & 1;
x >>= 1;
}
return c;
}
struct centroid_decomposition {
int n;
int centor;
mat G;
vector<int>size;
vector<vector<array<ll, 3>>>child; //child[i]=iが重心の木の、iを根としたときの子の(index,size,centoroid index)
vector<bool>removed; //作業用
centroid_decomposition(mat& g) {
G = g;
n = G.size();
size.resize(n);
child.resize(n);
removed.resize(n);
decompose();
};
int find_centroid(int v, int pre, int cnt) {
// 残っている頂点でなす、vを含む連結成分における重心のindexを返す
// early returnはせず、sizeの再計算を全部やる
size[v] = 1;
bool ok = true;
int centor = -1;
for (auto vv : G[v]) {
if (vv == pre)continue;
if (removed[vv])continue;
centor = max(centor, find_centroid(vv, v, cnt));
size[v] += size[vv];
ok &= size[vv] <= cnt / 2;
}
ok &= cnt - size[v] <= cnt / 2;
return ok ? v : centor;
}
int decompose_recursive(int v, int cnt) {
int vv = find_centroid(v, -1, cnt);
removed[vv] = true;
for (auto vvv : G[vv])if (!removed[vvv]) {
int bbc = size[vvv] < size[vv] ? size[vvv] : cnt - size[vv];
child[vv].push_back({ vvv,bbc,-1 });
}
for (auto& item : child[vv])item[2] = decompose_recursive(item[0], item[1]);
return vv;
}
void decompose() {
centor = decompose_recursive(0, n);
}
};
template <typename T>
vl argsort(const vector<T>& A) {
// stable
vl ids(A.size());
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vector<T> rearrange(const vector<T>& A, const vl& I) {
int n = A.size();
vector<T> B(n);
rep(i, n) B[i] = A[I[i]];
return B;
}
bool intersection(ll f, ll t, ll ff, ll tt) {
return !(tt <= f || t <= ff);
}
vpll calcMovementCostCircle(ll n, ll frm, ll to, ll ng) {
vpll res;
if (to != ng) {
if (min(frm, to) < ng && ng < max(frm, to)) {
res.emplace_back(n - abs(frm - to), ng);
}
else {
res.emplace_back(abs(frm - to), ng);
}
}
if (frm < ng) {
if (to < frm || ng <= to) {
res.emplace_back((to - frm + n) % n + (to - ng + n) % n + 1, (to + 1) % n);
}
if (frm < to && to <= ng) {
res.emplace_back(n - (to - frm) + (ng - to) + 1, to - 1);
}
}
else {
if (ng <= to && to < frm) {
res.emplace_back(n - (frm - to) + to - ng + 1, (to + 1) % n);
}
if (frm < to || to <= ng) {
res.emplace_back((frm - to + n) % n + (ng - to + n) % n + 1, (to - 1 + n) % n);
}
}
return res;
}
// ここまでライブラリ
// ここからコード
struct C {
ll a, mi;
};
struct O {
ll l, r, q;
};
struct S {
ll sz, val;
};
S op(S l, S r) {
return { l.sz + r.sz,l.val + r.val };
}
S e() {
return { 0,0 };
}
ll ore() {
return 0;
}
S mapping(ll f, S s) {
if (f == -1)return s;
return { s.sz,f * s.sz };
}
ll mapma(ll v, ll x) {
if (v < 0)return x;
return v;
}
ll composition(ll ne, ll ol) {
if (ne < 0)return ol;
if (ol < 0)return ne;
return ne;
}
ll id() {
return -1;
}
ll opmin(ll l, ll r) {
return min(l, r);
}
ll emin() {
return big;
}
ll opma(ll l, ll r) {
return max(l, r);
}
ll ema() {
return -big;
}
ll mamapping(ll ne, ll o) {
if (ne < 0)return o;
return ne;
}
ll changeCom(ll ne, ll ol) {
if (ne < 0)return ol;
return ne;
}
ll changeee() {
return -1;
}
ll oppp(ll l, ll r) {
return max(l, r);
}
ll ee() {
return -big;
}
modint998244353 o1(modint998244353 l, modint998244353 r) {
return l + r;
}
modint998244353 e1() {
return 0;
}
struct F {
ll lz = 0, lo = 0, rz = 0, ro = 0, mz = 0, mo = 0, len = 0;
};
F ost(F l, F r) {
if (l.len == -1)return r;
if (r.len == -1)return l;
ll lz = l.lz;
ll lo = l.lo;
ll rz = r.rz;
ll ro = r.ro;
if (rz == r.len) {
rz += l.rz;
}
if (ro == r.len) {
ro += l.ro;
}
if (lz == l.len) {
lz += r.lz;
}
if (lo == l.len) {
lo += r.lo;
}
ll sm = l.len + r.len;
ll mo = max({ l.mo ,r.mo,l.ro + r.lo });
ll mz = max({ l.mz,r.mz, l.rz + r.lz });
return { lz,lo,rz,ro,mz,mo,sm };
}
F est() {
return { -1,-1,-1,-1,-1,-1,-1 };
}
F maest(ll v, F s) {
if (v % 2 == 0)return s;
return { s.lo,s.lz,s.ro,s.rz,s.mo,s.mz,s.len };
}
vl o157(vl l, vl r) {
if (l.empty())return r;
if (r.empty())return l;
rep(i, 26) {
r[i] += l[i];
}
return r;
}
vl e157() {
return {};
}
double ops(double l, double r) {
return l + r;
}
double ope() {
return 0;
}
pair<vl, vl> opx(pair<vl, vl> l, pair<vl, vl> r) {
if (l.first.empty())return r;
if (r.first.empty())return l;
vl cn(26), tn(26);
for (int i = 25; i >= 0; i--)
{
cn[i] = l.first[i];
if (i < 25) {
cn[i] += cn[i + 1];
if (r.first[i] > 0)
r.second[i] += cn[i + 1];
}
r.second[i] += l.second[i];
r.first[i] += l.first[i];
}
return r;
}
pair<vl, vl> epx() {
return { {},{} };
}
char cnt[162000001];
pll op299(pll l, pll r) {
if (l.first == -1)return r;
if (r.first == -1)return l;
if (l.first < r.first)return l;
if (l.first > r.first)return r;
if (l.second < r.second)return l;
return r;
}
pll e299() {
return { -1,-1 };
}
pair<ull, ull> oprol(pair<ull, ull> l, pair<ull, ull> r) {
pair<ull, ull> nx;
nx.first = calc_mod_61(l.first + mul_61(r.first, l.second));
nx.second = mul_61(l.second, r.second);
return nx;
}
pair<ull, ull> erol() {
return { 0,1 };
}
ll opa(ll l, ll r) {
return l | r;
};
ll eaa() {
return 0;
}
struct Qu {
mint9 a = 1, b = 0;
};
void solv() {
/*
私は素因数分解を使うべきところで、エラトステネスを使ってハマりました。
私は「lからrまでを数としてみた時、7で割り切れるか？」を「lからrまでを数としてみた時、『各桁の和を』7で割り切れるか？」と誤解しました。
私は累積和を使うべきところで、遅延セグ木を使ってTLEを食らいました。
tをn進法にする時は素直にwhile(t>0)の条件で処理しよう
問題を誤読すると痛いよ！
愚直解テストはレンジの小さい範囲も入念に試しておきたい(https://atcoder.jp/contests/abc309/tasks/abc309_f)
next_permutation使う時は基本的にはソートするんや
m回接続(ループ)してその中を計算するタイプの問題、確定している分はしっかりmから引く事
ARCでは特に、愚直解との比較で間違っている箇所は出来る限り出す
中央値を使う総和の計算の左側は、カッコを忘れない事→x*lf-(s[i]-s[i-lf])
lazy_segtreeは分解した式で考える
double の値を10^x倍して小数点四捨五入するときはroundlを使う
*/
cin >> n;
ll nn = 1LL << n;
clineu(a, nn);
vul b(n);
rep(i, n) {
b[i] = a[1LL << i];
}
rep(i, nn) {
ull g = 0;
rep(j, n) {
if (ion(n, i)) {
g ^= b[j];
}
}
if (g != a[i]) {
No; return;
}
}
Yes;
}
int main()
{
cin.tie(0);
ios::sync_with_stdio(false);
INF = 998244353;
solv();
return 0;
}