#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ～ 2^63 = 9 * 10^18（int は -2^31 ～ 2^31 = 2 * 10^9） using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左） const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004004004004004LL; double EPS = 1e-12; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能） #define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能） #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索（昇順） #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順） #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す） template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す） // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } // 手元環境（Visual Studio） #ifdef _MSC_VER #include "local.hpp" // 提出用（gcc） #else inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif #endif // 折りたたみ用 //--------------AtCoder 専用-------------- #include using namespace atcoder; using mint = modint1000000007; //using mint = modint998244353; //using mint = modint; // mint::set_mod(m); istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } using vm = vector; using vvm = vector; using vvvm = vector; //---------------------------------------- //【局面のニム値】O(?)（遅いので実験用） /* * 初期局面 p から遷移可能な局面とそのニム値のリストを nim に格納する． * nxt(p, nps) を呼ぶと，p から遷移可能な局面のリストを nps に格納するものとする． */ template void calc_nimber(const T& p, function&)>& nxt, map& nim) { nim.clear(); function calc_nimber = [&](const T& p) { if (nim.count(p)) return nim[p]; vector nps; nxt(p, nps); vi next_nimbers; repe(np, nps) { next_nimbers.push_back(calc_nimber(np)); } uniq(next_nimbers); int i = 0; while (i < sz(next_nimbers) && next_nimbers[i] == i) i++; nim[p] = i; return nim[p]; }; calc_nimber(p); } void zikken() { using T = vi; function&)> nxt = [&](const T& p, vector& nps) { rep(i, sz(p)) { if (p[i] == 1) continue; if ((i == 0 || p[i - 1] == 1) && (i == sz(p) - 1 || p[i + 1] == 1)) { T np(p); np[i] = 1; nps.push_back(np); } } repi(i, 1, sz(p) - 2) { if (p[i - 1] == 1 || p[i] == 1 || p[i + 1] == 1) continue; T np1(p); np1[i] = np1[i - 1] = 1; nps.push_back(np1); T np2(p); np2[i] = np2[i + 1] = 1; nps.push_back(np2); } }; repi(n, 0, 25) { T p(n + 1); p[0] = 1; map nim; calc_nimber(p, nxt, nim); dump(n, nim[p]); } exit(0); repi(n, 0, 25) { T p(n + 2); p[0] = p[n + 1] = 1; map nim; calc_nimber(p, nxt, nim); dump(n, nim[p]); } exit(0); } /* 片側の開いた長さ i の '0' の連 0 0 1 1 2 0 3 0 4 1 5 2 6 2 7 1 8 4 9 0 10 1 11 4 12 2 13 1 14 4 15 0 16 1 17 4 18 2 19 1 20 4 21 2 22 1 23 0 24 2 25 1 両側とも閉じた長さ i の '0' の連 0 0 1 1 2 0 3 0 4 1 5 2 6 2 7 1 8 4 9 0 10 1 11 4 12 2 13 1 14 4 15 0 16 1 17 4 18 2 19 1 20 4 21 2 22 1 23 0 24 2 25 1 http://oeis.org/A071430 Sprague-Grundy values for octal game .16 山から 1 つの石を取り除く場合，残る山の数を 0 にすることができる． 山から 2 つの石を取り除く場合，残る山の数を 1 または 2 にすることができる． Sequence is eventually periodic with period 149459. The last exception is at n=105350. */ vi g{ 0,1,0,0,1,2,2,1,4,0,1,4,2,1,4,0,1,4,2,1,4,2,1,0,2,1,4,2,1,4,5,1,4,2,1,4,2,1,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,1,4,2,3,3,2,5,4,2,5,4,2,3,1,2,5,4,2,3,4,2,5,4,2,3,3,2,5,4,2,5,3,2,5,3,2,1,4,2,5,3,2,5,4,2,5,3,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,6,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,2,3,4,5,3,4,5,8,2,5,3,4,5,3,2,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,5,3,4,2,3,4,2,3,4,5,7,4,2,3,4,8,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,8,3,4,2,5,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,3,2,5,4,2,5,4,2,3,4,2,5,4,2,3,4,2,5,4,2,3,8,2,5,4,2,5,8,2,5,8,2,5,4,2,5,3,2,5,4,2,5,8,2,5,6,2,5,8,2,5,8,2,5,8,4,5,3,6,5,8,4,5,3,6,5,3,4,5,8,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,8,4,5,3,4,7,8,4,5,3,4,5,3,4,5,8,4,5,8,4,5,8,4,5,8,2,5,8,4,7,3,4,5,8,4,7,8,4,3,8,4,9,7,4,3,7,4,9,8,4,3,8,4,3,5,4,3,8,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,4,3,5,2,3,5,4,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,3,5,2,4,5,2,3,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,8,4,3,8,4,3,8,4,3,2,4,3,8,4,3,5,4,3,8,4,3,5,2,3,8,4,3,8,2,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,2,8,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,9,2,8,1,2,8,14,2,8,3,2,8,3,2,4,9,2,4,3,2,4,1,2,4,3,2,8,3,2,4,1,2,8,3,2,8,1,2,8,1,2,4,1,2,4,1,2,8,3,2,8,1,2,8,3,2,8,1,2,8,3,2,8,3,9,8,3,2,8,3,2,8,3,2,8,3,2,8,3,9,8,3,9,8,3,4,8,3,4,2,3,4,0,3,4,5,3,4,8,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,4,2,5,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,3,2,5,4,2,5,3,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,4,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,5,3,4,2,3,4,8,3,4,5,3,4,8,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,14,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,4,2,5,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,8,2,5,4,2,5,8,2,5,4,2,5,4,6,5,4,8,5,4,8,5,15,8,5,15,4,5,15,6,5,15,4,5,15,6,5,15,6,5,15,6,5,8,6,5,8,4,5,8,4,5,2,4,5,8,4,5,8,4,5,8,4,5,8,4,5,2,4,5,2,4,5,2,4,7,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,8,4,3,2,4,7,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,2,4,3,5,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,4,3,5,2,3,5,8,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,2,8,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,5,2,8,3,2,8,5,2,4,5,2,8,3,2,4,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,2,4,3,8,4,3,2,4,3,2,4,3,8,4,3,8,4,3,14,4,3,8,4,3,8,4,3,8,2,3,8,4,3,5,4,3,16,2,3,5,2,3,8,2,3,16,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,14,2,3,14,2,3,9,2,3,14,2,8,5,2,3,9,2,3,14,2,8,14,2,8,9,2,8,14,2,8,14,2,8,14,2,8,3,2,5,9,2,5,9,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,8,2,5,4,2,5,8,2,5,3,2,5,3,2,5,8,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,14,3,4,8,3,4,14,3,4,14,3,4,14,3,4,14,8,4,14,8,4,14,8,4,14,5,4,14,5,4,2,5,4,14,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,15,8,5,4,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,4,5,2,8,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,2,4,3,5,4,3,5,4,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,3,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,9,4,3,14,4,3,9,4,3,2,4,3,9,4,3,9,8,3,9,8,3,9,8,3,9,2,3,9,2,3,5,2,3,9,8,3,5,2,3,5,2,3,5,2,3,9,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,3,9,2,8,9,2,5,9,2,5,9,2,3,9,2,5,9,2,5,9,2,5,9,2,5,9,2,5,3,2,5,3,2,5,3,2,5,9,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,2,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,8,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,2,5,3,4,5,8,4,5,8,4,5,3,4,5,8,4,14,8,4,14,8,4,14,8,4,14,8,4,14,8,4,14,8,4,14,8,4,14,8,4,14,5,4,14,5,4,14,5,4,14,5,4,2,5,4,14,5,4,8,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,3,5,2,3,5,2,4,5,2,3,5,2,3,5,2,4,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,8,4,3,8,4,3,5,4,3,8,4,3,8,4,3,8,4,3,8,4,3,8,2,3,8,2,3,8,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,9,8,3,9,8,3,9,8,3,9,8,3,9,8,3,4,8,3,4,8,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,8,3,4,8,3,4,8,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,8,2,5,8,2,5,8,2,5,4,2,5,8,8,5,15,14,5,15,8,5,15,8,5,15,4,5,15,4,5,15,4,5,15,8,5,3,4,5,3,4,5,3,4,5,15,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,7,8,4,3,8,4,14,2,4,3,8,4,3,8,4,3,8,4,3,8,4,3,8,4,3,5,4,3,2,4,3,2,4,3,5,4,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,5,4,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,5,2,3,5,2,3,5,2,4,5,2,4,5,2,4,5,2,8,5,2,4,3,2,4,3,2,4,5,2,4,5,2,4,3,2,4,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,8,4,3,2,4,3,2,4,3,8,4,3,8,4,3,8,4,3,8,4,3,8,2,3,5,2,3,8,4,3,5,4,3,5,2,3,5,2,3,8,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,8,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,3,2,8,5,2,8,9,2,4,3,2,4,3,2,8,3,2,8,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,4,3,2,8,3,2,8,3,2,8,3,2,8,3,4,8,3,9,8,3,2,8,3,2,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,2,3,4,2,3,4,5,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,8,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,8,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,3,4,2,3,4,8,5,4,2,5,4,2,5,4,2,5,4,8,5,15,8,5,15,8,5,15,8,5,15,8,5,15,8,5,15,8,5,15,8,5,15,8,5,15,4,5,15,4,5,15,4,5,15,4,5,15,4,5,3,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,5,8,4,3,8,4,3,8,4,3,8,4,3,8,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,4,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,8,4,3,8,4,3,8,4,3,8,4,3,8,4,3,15,4,3,8,4,3,15,2,3,8,2,3,8,2,3,15,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,9,2,3,14,2,3,14,2,3,9,2,3,14,2,8,14,2,8,14,2,8,14,2,8,14,2,8,14,2,8,9,2,8,14,2,5,9,2,8,3,2,5,3,2,8,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,8,2,5,8,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,14,3,4,14,3,4,5,3,4,5,3,4,14,3,4,14,3,4,14,8,4,14,3,4,14,5,4,14,3,4,14,8,4,14,8,4,2,5,4,2,5,4,14,5,4,14,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,8,5,4,2,5,4,8,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,15,8,5,15,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,4,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,5,2,4,3,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,2,4,3,5,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,4,3,5,4,3,5,2,3,5,2,3,5,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,5,2,4,5,2,8,3,2,4,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,2,4,3,2,4,3,8,4,3,8,4,3,16,4,3,8,4,3,8,4,3,16,2,3,16,8,3,16,8,3,16,2,3,5,2,3,16,2,3,16,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,14,2,3,5,2,3,9,2,3,5,2,3,16,2,3,9,2,3,9,2,3,9,2,3,9,2,3,14,2,8,9,2,3,9,2,3,14,2,5,14,2,5,9,2,5,14,2,5,14,2,5,9,2,5,3,2,5,4,2,5,9,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,5,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,8,2,5,8,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,9,4,5,9,4,14,16,4,14,15,4,14,15,4,14,9,4,14,9,4,14,9,4,14,9,4,14,9,4,14,5,4,14,5,4,14,5,4,14,5,4,2,5,4,2,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,2,8,5,4,8,5,2,8,5,2,8,5,2,8,5,2,3,5,2,3,5,2,3,5,2,4,5,2,8,5,2,4,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,9,4,3,2,4,3,9,4,3,9,4,3,9,4,3,9,2,3,9,2,3,9,2,3,9,2,3,5,4,3,5,2,3,5,2,3,5,2,3,9,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,3,2,8,3,2,8,3,2,4,5,2,4,3,2,4,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,8,3,2,4,3,2,8,3,2,8,3,2,8,3,9,8,3,9,8,3,9,8,3,9,8,3,2,8,3,4,8,3,9,8,3,4,8,3,9,2,3,4,2,3,4,2,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,8,3,4,5,3,4,5,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,9,2,5,4,2,5,4,2,5,9,2,5,9,8,5,9,2,5,9,8,5,9,2,5,9,4,5,9,8,5,9,8,5,9,4,5,3,4,5,9,4,5,9,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,9,4,5,3,4,5,9,4,5,3,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,14,9,4,5,9,4,3,15,4,3,9,4,3,9,4,3,9,4,3,9,4,3,9,4,3,5,4,3,15,4,3,5,4,3,5,4,3,5,4,3,2,4,3,5,4,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,3,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,9,4,3,9,4,3,9,4,3,2,4,3,9,4,3,9,4,3,9,4,3,9,4,3,9,2,3,9,2,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,9,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,9,2,8,3,2,8,3,2,8,3,2,8,9,2,4,3,2,4,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,2,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,2,4,5,2,4,5,2,4,5,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,4,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,8,5,2,8,3,2,8,3,2,4,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,2,4,3,8,4,3,8,4,3,8,4,3,15,4,3,8,4,3,8,4,3,8,2,3,15,4,3,8,2,3,15,2,3,5,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,8,2,3,5,2,3,8,2,3,15,2,3,8,2,3,8,2,3,8,2,3,8,2,14,15,2,3,15,2,14,15,2,14,15,2,14,15,2,14,15,2,5,15,2,5,15,2,5,3,2,5,15,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,9,2,5,9,2,5,9,2,5,3,2,5,9,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,8,3,4,8,3,4,8,3,4,8,3,4,8,9,4,8,9,4,8,9,4,8,9,4,8,5,4,8,5,4,8,5,4,8,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,4,5,2,4,5,2,4,5,2,4,5,2,4,5,2,3,5,2,3,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,5,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,4,3,2,4,3,2,4,3,5,4,3,5,4,3,5,4,3,5,4,3,5,2,3,5,2,3,5,4,3,5,4,3,5,2,3,5,2,3,8,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,8,5,2,8,5,2,3,5,2,3,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,3,2,4,3,2,4,5,2,4,5,2,4,3,2,4,3,2,8,3,2,8,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,8,4,3,2,4,3,2,4,3,8,8,3,15,14,3,15,8,3,15,8,3,15,2,3,15,2,3,15,8,3,15,8,3,5,2,3,5,2,3,15,2,3,15,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,3,8,2,5,8,2,5,8,2,3,4,2,3,15,2,5,15,2,5,8,2,5,8,2,5,8,2,5,3,2,5,3,2,5,4,2,5,8,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,2,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,5,3,4,5,3,4,2,3,4,2,3,4,5,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,3,4,2,3,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,3,2,5,8,2,5,8,2,5,3,2,5,3,2,5,15,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,4,5,3,2,5,3,2,5,9,4,5,9,4,5,3,4,5,3,4,5,9,4,8,9,4,8,14,4,8,14,4,8,9,4,8,9,4,8,9,4,8,9,4,8,9,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,2,5,4,2,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,4,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,8,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,4,5,2,3,3,2,4,5,2,4,5,2,3,5,2,4,5,2,3,5,2,4,5,2,3,3,2,4,5,2,4,3,2,4,3,2,4,5,2,4,3,2,4,5,2,4,3,2,4,5,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,8,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,5,4,3,2,4,3,5,4,3,5,4,3,2,4,3,5,4,3,2,4,3,8,4,3,2,4,3,8,4,3,8,4,3,5,4,3,5,4,3,8,2,3,5,4,3,5,2,3,8,4,3,5,2,3,8,2,3,5,2,3,8,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,4,5,2,3,5,2,8,5,2,3,5,2,8,5,2,8,5,2,8,5,2,4,5,2,8,3,2,4,5,2,4,3,2,8,5,2,4,3,2,8,3,2,4,3,2,14,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,4,3,2,8,3,16,8,3,2,8,3,15,8,3,2,8,3,15,8,3,15,8,3,15,8,3,15,8,3,4,2,3,4,8,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,3,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,3,2,5,8,2,5,3,2,5,4,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,2,5,3,4,5,3,2,5,3,4,5,3,2,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,2,3,4,2,3,4,2,3,4,8,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,3,4,2,5,4,2,5,4,2,5,4,2,3,4,2,5,4,2,5,4,2,5,4,2,5,4,2,5,9,2,5,9,2,5,9,2,5,9,8,5,9,8,5,9,8,5,9,8,5,9,8,5,9,4,5,9,4,5,9,4,5,9,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,3,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,5,9,4,8,9,4,8,9,4,8,9,4,3,9,4,3,9,4,3,9,4,3,9,14 }; void solve_under_10000(int n, ll k, vl a) { a.insert(a.begin(), 0); a.push_back(k + 1); int res = 0; rep(i, n + 1) { ll w = a[i + 1] - a[i] - 1; dump(w); if (w >= 149459 + 105350) { w = (w - 105350) % 149459 + 105350; } dump(w); if (w > 10000) EXIT("Yes"); res ^= g[w]; } Yes(res); exit(0); } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); int n; ll k; cin >> n >> k; vl a(n); cin >> a; solve_under_10000(n, k, a); a.insert(a.begin(), 0); a.push_back(k + 1); vi nim{ 0, 1, 0, 0, 1, 2, 2, 1, 4, 0, 1, 4 }; int res = 0; rep(i, n + 1) { ll w = a[i + 1] - a[i] - 1; dump(w); if (w >= 12) w = w % 6 + 6; res ^= nim[w]; } Yes(res); }