結果
問題 | No.906 Y字グラフ |
ユーザー | Suunn |
提出日時 | 2019-10-12 01:26:32 |
言語 | Java21 (openjdk 21) |
結果 |
WA
|
実行時間 | - |
コード長 | 28,460 bytes |
コンパイル時間 | 3,595 ms |
コンパイル使用メモリ | 101,212 KB |
実行使用メモリ | 54,432 KB |
最終ジャッジ日時 | 2024-11-26 02:07:16 |
合計ジャッジ時間 | 8,198 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
(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 | 99 ms
41,240 KB |
testcase_01 | AC | 108 ms
40,164 KB |
testcase_02 | AC | 97 ms
40,912 KB |
testcase_03 | AC | 115 ms
40,972 KB |
testcase_04 | AC | 112 ms
41,624 KB |
testcase_05 | AC | 106 ms
40,024 KB |
testcase_06 | AC | 105 ms
40,332 KB |
testcase_07 | AC | 110 ms
41,188 KB |
testcase_08 | AC | 114 ms
41,048 KB |
testcase_09 | AC | 113 ms
41,752 KB |
testcase_10 | AC | 103 ms
40,080 KB |
testcase_11 | AC | 122 ms
41,264 KB |
testcase_12 | AC | 123 ms
41,264 KB |
testcase_13 | AC | 121 ms
41,028 KB |
testcase_14 | AC | 117 ms
41,104 KB |
testcase_15 | AC | 117 ms
40,872 KB |
testcase_16 | AC | 106 ms
40,916 KB |
testcase_17 | AC | 106 ms
41,040 KB |
testcase_18 | AC | 104 ms
40,080 KB |
testcase_19 | AC | 106 ms
40,120 KB |
testcase_20 | AC | 111 ms
41,048 KB |
testcase_21 | AC | 117 ms
41,176 KB |
testcase_22 | AC | 103 ms
40,640 KB |
testcase_23 | AC | 103 ms
41,088 KB |
testcase_24 | AC | 117 ms
41,316 KB |
testcase_25 | AC | 108 ms
40,164 KB |
testcase_26 | AC | 107 ms
41,192 KB |
testcase_27 | AC | 116 ms
41,136 KB |
testcase_28 | WA | - |
testcase_29 | AC | 104 ms
40,364 KB |
testcase_30 | AC | 100 ms
40,200 KB |
testcase_31 | AC | 109 ms
41,152 KB |
ソースコード
import java.io.IOException; import java.io.PrintWriter; import java.util.ArrayDeque; import java.util.ArrayList; import java.util.Collections; import java.util.Comparator; import java.util.HashMap; import java.util.HashSet; import java.util.NoSuchElementException; import java.util.Objects; import java.util.PriorityQueue; import java.util.Queue; import java.util.Random; import java.util.Scanner; import java.util.TreeMap; import java.util.TreeSet; import java.util.function.BiFunction; public class Main{ static Scanner scn = new Scanner(System.in); static FastScanner sc = new FastScanner(); static Mathplus mp = new Mathplus(); static PrintWriter ot = new PrintWriter(System.out); static Random rand = new Random(); static int mod = 1000000007; static long inf = (long)1e17; public static void main(String[] args) { long N = sc.nextLong(); N -= 4; long ans1 = 0; long ans2 = 0; long ans3 = 0; if(N%3==0)ans1=1; ans2=(N/2)+1; if(ans1==1)ans2--; N %= mod; ans3 = (N+2)*(N+1); ans3 /= 2; ans3 -= ans1; ans3 -= ans2*3; ans3 += mod; ans3 %= mod; ans3 *= mp.rev(6); ans2 %= mod; ans3 %= mod; System.out.println((ans1+ans2+ans3)%mod); } } class GridGraph extends Graph{ int N; int M; String[] S; HashMap<Character,Integer> map; GridGraph(int n,int m,String[] s,char[] c){ super(n*m); N = n; M = m; S = s; map = new HashMap<Character,Integer>(); for(int i=0;i<n-1;i++) { for(int j=0;j<m;j++) { if(S[i].charAt(j)!='#'&&S[i+1].charAt(j)!='#') { addEdge(toint(i,j),toint(i+1,j)); addEdge(toint(i+1,j),toint(i,j)); } } } for(int i=0;i<n;i++) { for(int j=0;j<m-1;j++) { if(S[i].charAt(j)!='#'&&S[i].charAt(j+1)!='#') { addEdge(toint(i,j),toint(i,j+1)); addEdge(toint(i,j+1),toint(i,j)); } } } for(int i=0;i<n;i++) { for(int j=0;j<m;j++) { for(int k=0;k<c.length;k++) { if(S[i].charAt(j)==c[k])map.put(c[k],toint(i,j)); } } } } int toint(int i,int j) { return i*M+j; } } class BetterGridGraph{ int N; int M; String[] S; HashMap<Character,Integer> map; int[] dx = {0,1,0,-1}; int[] dy = {1,0,-1,0}; BetterGridGraph(int n,int m,String[] s,char[] c){ N = n; M = m; S = s; map = new HashMap<Character,Integer>(); for(int i=0;i<n;i++) { for(int j=0;j<m;j++) { for(int k=0;k<c.length;k++) { if(S[i].charAt(j)==c[k])map.put(c[k],toint(i,j)); } } } } int toint(int i,int j) { return i*M+j; } long[] bfs(char C) { int s = map.get(C); long[] L = new long[N*M]; for(int i=0;i<N*M;i++){ L[i] = -1; } L[s] = 0; ArrayDeque<Integer> Q = new ArrayDeque<Integer>(); Q.add(s); Range X = new Range(0,N-1); Range Y = new Range(0,M-1); while(!Q.isEmpty()){ int v = Q.poll(); for(int i=0;i<4;i++){ int x = v/M; int y = v%M; int nx = x+dx[i]; int ny = y+dy[i]; if(X.isIn(nx)&&Y.isIn(ny)&&S[nx].charAt(ny)!='#') { int w = toint(nx,ny); if(L[w]==-1){ L[w] = L[v] + 1; Q.add(w); } } } } return L; } } class StringManager{ ArrayList<Character> S; static Mathplus mp; static boolean calced; static int base; static long baserev; ArrayList<Long> l; StringManager(String s){ S = new ArrayList<Character>(); for(int i=0;i<s.length();i++) { S.add(s.charAt(i)); } if(!calced) { calced = true; mp = new Mathplus(); base = 1000003; baserev = mp.rev(base); mp.buildpow(base,1000050); mp.buildrevpow((int) baserev,1000050); } l = new ArrayList<Long>(); l.add((long)S.get(0)); for(int i=1;i<S.size();i++) { char c = S.get(i); l.add((l.get(i-1) + mp.pow[i] * c)%mp.mod); } } void add(char C){ int i = S.size(); S.add(C); l.add((l.get(i-1) + mp.pow[i] * C)%mp.mod); } long gethash(int le,int ri) { long res = l.get(ri); if(le!=0) { res -= l.get(le-1); res += mp.mod; res %= mp.mod; res *= mp.revpow[le]; res %= mp.mod; } return res; } } class Trie{ int nodenumber = 1; ArrayList<TrieNode> l; Trie(){ l = new ArrayList<TrieNode>(); l.add(new TrieNode()); } void add(String S,int W){ int now = 0; for(int i=0;i<S.length();i++) { TrieNode n = l.get(now); char c = S.charAt(i); if(n.Exist[c-'a']!=-1) { now = n.Exist[c-'a']; }else { l.add(new TrieNode()); n.Exist[c-'a'] = nodenumber; now = nodenumber; nodenumber++; } } l.get(now).weight = W; } void find(String S,int i,int[] dp) { int now = 0; dp[i+1] = Math.max(dp[i],dp[i+1]); for(int j=0;;j++) { TrieNode n = l.get(now); dp[i+j] = Math.max(dp[i+j],dp[i]+n.weight); int slook = i+j; if(slook>=S.length())return; char c = S.charAt(slook); if(n.Exist[c-'a']==-1)return; now = n.Exist[c-'a']; } } } class TrieNode{ int[] Exist = new int[26]; int weight = 0; TrieNode(){ for(int i=0;i<26;i++) { Exist[i] = -1; } } } class SizeComparator implements Comparator<Edge>{ int[] size; SizeComparator(int[] s) { size = s; } public int compare(Edge o1, Edge o2) { return size[o1.to]-size[o2.to]; } } class ConvexHullTrick { long[] A, B; int len; public ConvexHullTrick(int n) { A = new long[n]; B = new long[n]; } private boolean check(long a, long b) { return (B[len - 2] - B[len - 1]) * (a - A[len - 1]) >= (B[len - 1] - b) * (A[len - 1] - A[len - 2]); } public void add(long a, long b) { while (len >= 2 && check(a, b)) { len--; } A[len] = a; B[len] = b; len++; } public long query(long x) { int l = -1, r = len - 1; while (r - l > 1) { int mid = (r + l) / 2; if (get(mid,x)>=get(mid+1,x)) { l = mid; } else { r = mid; } } return get(r,x); } private long get(int k, long x) { return A[k] * x + B[k]; } } class Range{ int l; int r; int length; Range(int L,int R){ l = L; r = R; length = R-L+1; } boolean isIn(int x) { return (l<=x&&x<=r); } } class LeftComparator implements Comparator<Range>{ public int compare(Range P, Range Q) { return P.l-Q.l; } } class RightComparator implements Comparator<Range>{ public int compare(Range P, Range Q) { return P.r-Q.r; } } class LengthComparator implements Comparator<Range>{ public int compare(Range P, Range Q) { return P.length-Q.length; } } class SegmentTree<T,E>{ int N; BiFunction<T,T,T> f; BiFunction<T,E,T> g; T d1; ArrayList<T> dat; SegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,T D1,T[] v){ int n = v.length; f = F; g = G; d1 = D1; init(n); build(v); } void init(int n) { N = 1; while(N<n)N*=2; dat = new ArrayList<T>(); } void build(T[] v) { for(int i=0;i<2*N;i++) { dat.add(d1); } for(int i=0;i<v.length;i++) { dat.set(N+i-1,v[i]); } for(int i=N-2;i>=0;i--) { dat.set(i,f.apply(dat.get(i*2+1),dat.get(i*2+2))); } } void update(int k,E a) { k += N-1; dat.set(k,g.apply(dat.get(k),a)); while(k>0){ k = (k-1)/2; dat.set(k,f.apply(dat.get(k*2+1),dat.get(k*2+2))); } } T query(int a,int b, int k, int l ,int r) { if(r<=a||b<=l) return d1; if(a<=l&&r<=b) return dat.get(k); T vl = query(a,b,k*2+1,l,(l+r)/2); T vr = query(a,b,k*2+2,(l+r)/2,r); return f.apply(vl, vr); } T query(int a,int b){ return query(a,b,0,0,N); } } class LazySegmentTree<T,E> extends SegmentTree<T,E>{ BiFunction<E,E,E> h; BiFunction<E,Integer,E> p = (E a,Integer b) ->{return a;}; E d0; ArrayList<E> laz; LazySegmentTree(BiFunction<T,T,T> F,BiFunction<T,E,T> G,BiFunction<E,E,E> H,T D1,E D0,T[] v){ super(F,G,D1,v); int n = v.length; h = H; d0 = D0; Init(n); } void build() { } void Init(int n){ laz = new ArrayList<E>(); for(int i=0;i<2*N;i++) { laz.add(d0); } } void eval(int len,int k) { if(laz.get(k).equals(d0)) return; if(k*2+1<N*2-1) { laz.set(k*2+1,h.apply(laz.get(k*2+1),laz.get(k))); laz.set(k*2+2,h.apply(laz.get(k*2+2),laz.get(k))); } dat.set(k,g.apply(dat.get(k), p.apply(laz.get(k), len))); laz.set(k,d0); } T update(int a,int b,E x,int k,int l,int r) { eval(r-l,k); if(r<=a||b<=l) { return dat.get(k); } if(a<=l&&r<=b) { laz.set(k,h.apply(laz.get(k),x)); return g.apply(dat.get(k),p.apply(laz.get(k),r-l)); } T vl = update(a,b,x,k*2+1,l,(l+r)/2); T vr = update(a,b,x,k*2+2,(l+r)/2,r); dat.set(k,f.apply(vl,vr)); return dat.get(k); } T update(int a,int b,E x) { return update(a,b,x,0,0,N); } T query(int a,int b,int k,int l,int r) { eval(r-l,k); if(r<=a||b<=l) return d1; if(a<=l&&r<=b) return dat.get(k); T vl = query(a,b,k*2+1,l,(l+r)/2); T vr = query(a,b,k*2+2,(l+r)/2,r); return f.apply(vl, vr); } T query(int a,int b){ return query(a,b,0,0,N); } } class AddSumLazySegmentTree { int N; long[] dat; long[] laz; AddSumLazySegmentTree(long[] v){ init(v.length); for(int i=0;i<v.length;i++) { dat[N+i-1]=v[i]; } for(int i=N-2;i>=0;i--) { dat[i]=dat[i*2+1]+dat[i*2+2]; } } void init(int n) { N = 1; while(N<n)N*=2; dat = new long[2*N]; laz = new long[2*N]; } void eval(int len,int k) { if(laz[k]==0) return; if(k*2+1<N*2-1) { laz[k*2+1] += laz[k]; laz[k*2+2] += laz[k]; } dat[k] += laz[k] * len; laz[k] = 0; } long update(int a,int b,long x,int k,int l,int r) { eval(r-l,k); if(r<=a||b<=l) { return dat[k]; } if(a<=l&&r<=b) { laz[k] += x; return dat[k]+laz[k]*(r-l); } long vl = update(a,b,x,k*2+1,l,(l+r)/2); long vr = update(a,b,x,k*2+2,(l+r)/2,r); return dat[k] = vl+vr; } long update(int a,int b,long x) { return update(a,b,x,0,0,N); } long query(int a,int b,int k,int l,int r) { eval(r-l,k); if(r<=a||b<=l) return 0; if(a<=l&&r<=b) return dat[k]; long vl = query(a,b,k*2+1,l,(l+r)/2); long vr = query(a,b,k*2+2,(l+r)/2,r); return vl+vr; } long query(int a,int b){ return query(a,b,0,0,N); } } class BinaryIndexedTree{ int[] val; BinaryIndexedTree(int N){ val = new int[N+1]; } long sum(int i) { if(i==0)return 0; long s = 0; while(i>0) { s += val[i]; i -= i & (-i); } return s; } void add(int x,int i) { if(i==0)return; while(i<val.length){ val[i] += x; i += i & (-i); } } } class UnionFindTree { int[] root; int[] rank; int[] size; UnionFindTree(int N){ root = new int[N]; rank = new int[N]; size = new int[N]; for(int i=0;i<N;i++){ root[i] = i; size[i] = 1; } } public int find(int x){ if(root[x]==x){ return x; }else{ return find(root[x]); } } public void unite(int x,int y){ x = find(x); y = find(y); if(x==y){ return; }else{ if(rank[x]<rank[y]){ root[x] = y; size[y] += size[x]; }else{ root[y] = x; size[x] += size[y]; if(rank[x]==rank[y]){ rank[x]++; } } } } public boolean same(int x,int y){ return find(x)==find(y); } } class ParticalEternalLastingUnionFindTree extends UnionFindTree{ int[] time; int now; ParticalEternalLastingUnionFindTree(int N){ super(N); time = new int[N]; for(int i=0;i<N;i++) { time[i] = 1000000007; } } public int find(int t,int i) { if(time[i]>t) { return i; }else { return find(t,root[i]); } } public void unite(int x,int y,int t) { now = t; x = find(t,x); y = find(t,y); if(x==y)return; if(rank[x]<rank[y]){ root[x] = y; size[y] += size[x]; time[x] = t; }else{ root[y] = x; size[x] += size[y]; if(rank[x]==rank[y]){ rank[x]++; } time[y] = t; } } public int sametime(int x,int y) { if(find(now,x)!=find(now,y)) return -1; int ok = now; int ng = 0; while(ok-ng>1) { int mid = (ok+ng)/2; if(find(mid,x)==find(mid,y)) { ok = mid; }else { ng = mid; } } return ok; } } class Graph { ArrayList<Edge>[] list; int size; TreeSet<LinkEdge> Edges = new TreeSet<LinkEdge>(new LinkEdgeComparator()); @SuppressWarnings("unchecked") Graph(int N){ size = N; list = new ArrayList[N]; for(int i=0;i<N;i++){ list[i] = new ArrayList<Edge>(); } } void addEdge(int a,int b){ list[a].add(new Edge(b,1)); } void addWeightedEdge(int a,int b,long c){ list[a].add(new Edge(b,c)); } void addEgdes(int[] a,int[] b){ for(int i=0;i<a.length;i++){ list[a[i]].add(new Edge(b[i],1)); } } void addWeighterEdges(int[] a ,int[] b ,int[] c){ for(int i=0;i<a.length;i++){ list[a[i]].add(new Edge(b[i],c[i])); } } long[] bfs(int s){ long[] L = new long[size]; for(int i=0;i<size;i++){ L[i] = -1; } L[s] = 0; ArrayDeque<Integer> Q = new ArrayDeque<Integer>(); Q.add(s); while(!Q.isEmpty()){ int v = Q.poll(); for(Edge e:list[v]){ int w = e.to; long c = e.cost; if(L[w]==-1){ L[w] = L[v] + c; Q.add(w); } } } return L; } long[] bfs2(int[] d,int s){ long[] L = new long[size]; for(int i=0;i<size;i++){ L[i] = -1; } int p = 0; L[s] = 0; d[s] = p; p++; ArrayDeque<Integer> Q = new ArrayDeque<Integer>(); Q.add(s); while(!Q.isEmpty()){ int v = Q.poll(); for(Edge e:list[v]){ int w = e.to; long c = e.cost; if(L[w]==-1){ d[w] = p; p++; L[w] = L[v] + c; Q.add(w); } } } return L; } int[] isTwoColor(){ int[] L = new int[size]; for(int i=0;i<size;i++){ L[i] = -1; } L[0] = 0; ArrayDeque<Integer> Q = new ArrayDeque<Integer>(); Q.add(0); while(!Q.isEmpty()){ int v = Q.poll(); for(Edge e:list[v]){ int w = e.to; if(L[w]==-1){ L[w] = 1-L[v]; Q.add(w); }else{ if(L[v]+L[w]!=1){ L[0] = -2; } } } } return L; } long[] dijkstra(int s){ long[] L = new long[size]; for(int i=0;i<size;i++){ L[i] = -1; } int[] v = new int[size]; L[s] = 0; PriorityQueue<LongIntPair> Q = new PriorityQueue<LongIntPair>(new LongIntSampleComparator()); Q.add(new LongIntPair(0,s)); while(!Q.isEmpty()){ LongIntPair C = Q.poll(); if(v[C.b]==0){ L[C.b] = C.a; v[C.b] = 1; for(Edge D:list[C.b]) { if(L[D.to]==-1||L[D.to]>L[C.b]+D.cost) { L[D.to]=L[C.b]+D.cost; Q.add(new LongIntPair(L[C.b]+D.cost,D.to)); } } } } return L; } ArrayList<Graph> makeapart(){ ArrayList<Graph> ans = new ArrayList<Graph>(); boolean[] b = new boolean[size]; int[] num = new int[size]; for(int i=0;i<size;i++){ if(b[i])continue; int sz = 0; ArrayList<Integer> l = new ArrayList<Integer>(); ArrayDeque<Integer> Q = new ArrayDeque<Integer>(); Q.add(i); b[i] = true; while(!Q.isEmpty()){ int v = Q.poll(); num[v] = sz; sz++; l.add(v); for(Edge e:list[v]){ if(!b[e.to]){ Q.add(e.to); b[e.to] = true; } } } Graph H = new Graph(sz); for(int e:l){ for(Edge E:list[e]){ H.addWeightedEdge(num[e],num[E.to],E.cost); } } ans.add(H); } return ans; } long[] bellmanFord(int s) { long inf = 1000000000; inf *= inf; long[] d = new long[size]; boolean[] n = new boolean[size]; d[s] = 0; for(int i=1;i<size;i++){ d[i] = inf; d[i] *= d[i]; } for(int i=0;i<size-1;i++){ for(int j=0;j<size;j++){ for(Edge E:list[j]){ if(d[j]!=inf&&d[E.to]>d[j]+E.cost){ d[E.to]=d[j]+E.cost; } } } } for(int i=0;i<size;i++){ for(int j=0;j<size;j++){ for(Edge e:list[j]){ if(d[j]==inf) continue; if(d[e.to]>d[j]+e.cost) { d[e.to]=d[j]+e.cost; n[e.to] = true; } if(n[j])n[e.to] = true; } } } for(int i=0;i<size;i++) { if(n[i])d[i] = inf; } return d; } long[] maxtra(int s,long l){ long[] L = new long[size]; for(int i=0;i<size;i++){ L[i] = -1; } int[] v = new int[size]; L[s] = -1; PriorityQueue<Pair> Q = new PriorityQueue<Pair>(new SampleComparator()); Q.add(new Pair(l,s)); while(!Q.isEmpty()){ Pair C = Q.poll(); if(v[(int)C.b]==0){ L[(int)C.b] = C.a; v[(int) C.b] = 1; for(Edge D:list[(int) C.b])Q.add(new Pair(Math.max(L[(int)C.b],D.cost),D.to)); } } return L; } long Kruskal(){ long r = 0; for(int i=0;i<size;i++) { for(Edge e:list[i]) { Edges.add(new LinkEdge(e.cost,i,e.to)); } } UnionFindTree UF = new UnionFindTree(size); for(LinkEdge e:Edges){ if(e.a>=0&&e.b>=0) { if(!UF.same(e.a,e.b)){ r += e.L; UF.unite(e.a,e.b); } } } return r; } ArrayList<Integer> Kahntsort(){ ArrayList<Integer> ans = new ArrayList<Integer>(); PriorityQueue<Integer> q = new PriorityQueue<Integer>(); int[] in = new int[size]; for(int i=0;i<size;i++) { for(Edge e:list[i])in[e.to]++; } for(int i=0;i<size;i++) { if(in[i]==0)q.add(i); } while(!q.isEmpty()) { int v = q.poll(); ans.add(v); for(Edge e:list[v]) { in[e.to]--; if(in[e.to]==0)q.add(e.to); } } for(int i=0;i<size;i++) { if(in[i]>0)return new ArrayList<Integer>(); } return ans; } RootedTree dfsTree(int i) { int[] u = new int[size]; RootedTree r = new RootedTree(size); dfsTree(i,u,r); return r; } private void dfsTree(int i, int[] u, RootedTree r) { u[i] = 1; for(Edge e:list[i]) { if(u[e.to]==0) { r.list[i].add(e); u[e.to] = 1; dfsTree(e.to,u,r); } } } } class Tree extends Graph{ public Tree(int N) { super(N); } long[] tyokkei(){ long[] a = bfs(0); System.out.println(); int md = -1; long m = 0; for(int i=0;i<size;i++){ if(m<a[i]){ m = a[i]; md = i; } } long[] b = bfs(md); int md2 = -1; long m2 = 0; for(int i=0;i<size;i++){ if(m2<b[i]){ m2 = b[i]; md2 = i; } } long[] r = {m2,md,md2}; return r; } } class RootedTree extends Graph{ RootedTree(int N){ super(N); } } class LinkEdge{ long L; int a ; int b; LinkEdge(long l,int A,int B){ L = l; a = A; b = B; } public boolean equals(Object o){ LinkEdge O = (LinkEdge) o; return O.a==this.a&&O.b==this.b&&O.L==this.L; } public int hashCode(){ return Objects.hash(L,a,b); } } class Edge{ int to; long cost; Edge(int a,long b){ to = a; cost = b; } } class LinkEdgeComparator implements Comparator<LinkEdge>{ public int compare(LinkEdge P, LinkEdge Q) { long t = P.L-Q.L; if(t==0){ if(P.a>Q.a){ return 1; }else{ return P.b>Q.b?1:-1; } } return t>=0?1:-1; } } class Triplet{ long a; long b; long c; Triplet(long p,long q,long r){ a = p; b = q; c = r; } public boolean equals(Object o){ Triplet O = (Triplet) o; return O.a==this.a&&O.b==this.b&&O.c==this.c?true:false; } public int hashCode(){ return Objects.hash(a,b,c); } } class TripletComparator implements Comparator<Triplet>{ public int compare(Triplet P, Triplet Q) { long t = P.a-Q.a; if(t==0){ long tt = P.b-Q.b; if(tt==0) { if(P.c>Q.c) { return 1; }else if(P.c<Q.c){ return -1; }else { return 0; } } return tt>0?1:-1; } return t>=0?1:-1; } } class Pair{ long a; long b; Pair(long p,long q){ this.a = p; this.b = q; } public boolean equals(Object o){ Pair O = (Pair) o; return O.a==this.a&&O.b==this.b; } public int hashCode(){ return Objects.hash(a,b); } } class SampleComparator implements Comparator<Pair>{ public int compare(Pair P, Pair Q) { long t = P.a-Q.a; if(t==0){ return P.b>=Q.b?1:-1; } return t>=0?1:-1; } } class LongIntPair{ long a; int b; LongIntPair(long p,int q){ this.a = p; this.b = q; } public boolean equals(Object o){ Pair O = (Pair) o; return O.a==this.a&&O.b==this.b; } public int hashCode(){ return Objects.hash(a,b); } } class LongIntSampleComparator implements Comparator<LongIntPair>{ public int compare(LongIntPair P, LongIntPair Q) { long t = P.a-Q.a; if(t==0){ if(P.b>Q.b){ return 1; }else{ return -1; } } return t>=0?1:-1; } } class IntIntPair{ int a; int b; IntIntPair(int p,int q){ this.a = p; this.b = q; } public boolean equals(Object o){ Pair O = (Pair) o; return O.a==this.a&&O.b==this.b; } public int hashCode(){ return Objects.hash(a,b); } } class IntIntSampleComparator implements Comparator<IntIntPair>{ public int compare(IntIntPair P, IntIntPair Q) { int t = P.a-Q.a; if(t==0){ return P.b-Q.b; } return t; } } class FastScanner { private final java.io.InputStream in = System.in; private final byte[] b = new byte[1024]; private int p = 0; private int bl = 0; private boolean hNB() { if (p<bl) { return true; }else{ p = 0; try { bl = in.read(b); } catch (IOException e) { e.printStackTrace(); } if (bl<=0) { return false; } } return true; } private int rB() { if (hNB()) return b[p++]; else return -1;} private static boolean iPC(int c) { return 33 <= c && c <= 126;} private void sU() { while(hNB() && !iPC(b[p])) p++;} public boolean hN() { sU(); return hNB();} public String next() { if (!hN()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = rB(); while(iPC(b)) { sb.appendCodePoint(b); b = rB(); } return sb.toString(); } public long nextLong() { if (!hN()) throw new NoSuchElementException(); long n = 0; boolean m = false; int b = rB(); if (b=='-') { m=true; b=rB(); } if (b<'0'||'9'<b) { throw new NumberFormatException(); } while(true){ if ('0'<=b&&b<='9') { n *= 10; n += b - '0'; }else if(b == -1||!iPC(b)){ return (m?-n:n); }else{ throw new NumberFormatException(); } b = rB(); } } public int nextInt() { if (!hN()) throw new NoSuchElementException(); long n = 0; boolean m = false; int b = rB(); if (b == '-') { m = true; b = rB(); } if (b<'0'||'9'<b) { throw new NumberFormatException(); } while(true){ if ('0'<=b&&b<='9') { n *= 10; n += b-'0'; }else if(b==-1||!iPC(b)){ return (int) (m?-n:n); }else{ throw new NumberFormatException(); } b = rB(); } } } class Mathplus{ int mod = 1000000007; long[] fac; long[][] comb; long[] pow; long[] revpow; boolean isBuild = false; boolean isBuildc = false; boolean isBuildp = false; int mindex = -1; int maxdex = -1; void buildFac(){ fac = new long[3000003]; fac[0] = 1; for(int i=1;i<=3000002;i++){ fac[i] = (fac[i-1] * i)%mod; } isBuild = true; } public long[][] buildrui(int[][] a) { int n = a.length; int m = a[0].length; long[][] ans = new long[n][m]; for(int i=1;i<n;i++) { for(int j=1;j<m;j++) { ans[i][j] = a[i][j]; } } for(int i=1;i<n;i++) { for(int j=1;j<m;j++) { ans[i][j] += ans[i][j-1] + ans[i-1][j] - ans[i-1][j-1]; } } return ans; } long divroundup(long n,long d) { if(n==0)return 0; return (n-1)/d+1; } public long sigma(long i) { return i*(i+1)/2; } public int digit(long i) { int ans = 1; while(i>=10) { i /= 10; ans++; } return ans; } public int popcount(int i) { int ans = 0; while(i>0) { ans += i%2; i /= 2; } return ans; } public boolean contains(int S,int i) {return (S>>i&1)==1;} public int bitremove(int S,int i) {return S-(1<<i);} public int bitadd(int S,int i) {return S+(1<<i);} public boolean isSubSet(int S,int T) {return (S-T)==(S^T);} public boolean isDisjoint(int S,int T) {return (S+T)==(S^T);} public int isBigger(int[] d, int i) { int ok = d.length; int ng = -1; while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d[mid]>i) { ok = mid; }else { ng = mid; } } return ok; } public int isSmaller(int[] d, int i) { int ok = -1; int ng = d.length; while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d[mid]<i) { ok = mid; }else { ng = mid; } } return ok; } public int isBigger(long[] d, long i) { int ok = d.length; int ng = -1; while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d[mid]>i) { ok = mid; }else { ng = mid; } } return ok; } public int isSmaller(long[] d, long i) { int ok = -1; int ng = d.length; while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d[mid]<i) { ok = mid; }else { ng = mid; } } return ok; } public int isBigger(ArrayList<Long> d, long i) { int ok = d.size(); int ng = -1; while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d.get(mid)>i) { ok = mid; }else { ng = mid; } } return ok; } public int isSmaller(ArrayList<Long> d, long i) { int ok = -1; int ng = d.size(); while(Math.abs(ok-ng)>1) { int mid = (ok+ng)/2; if(d.get(mid)<i) { ok = mid; }else { ng = mid; } } return ok; } public HashSet<Integer> primetable(int m) { HashSet<Integer> pt = new HashSet<Integer>(); for(int i=2;i<=m;i++) { boolean b = true; for(int d:pt) { if(i%d==0) { b = false; break; } } if(b) { pt.add(i); } } return pt; } public ArrayList<Integer> primetablearray(int m) { ArrayList<Integer> al = new ArrayList<Integer>(); Queue<Integer> q = new ArrayDeque<Integer>(); for(int i=2;i<=m;i++) { q.add(i); } boolean[] b = new boolean[m+1]; while(!q.isEmpty()) { int e = q.poll(); if(!b[e]) { al.add(e); for(int j=1;e*j<=1000000;j++) { b[e*j] = true; } } } return al; } public HashMap<Integer,Integer> hipPush(ArrayList<Integer> l){ HashMap<Integer,Integer> r = new HashMap<Integer,Integer>(); TreeSet<Integer> s = new TreeSet<Integer>(); for(int e:l)s.add(e); int p = 0; for(int e:s) { r.put(e,p); p++; } return r; } public TreeMap<Integer,Integer> thipPush(ArrayList<Integer> l){ TreeMap<Integer,Integer> r = new TreeMap<Integer,Integer>(); Collections.sort(l); int b = -(mod+9393); int p = 0; for(int e:l) { if(b!=e) { r.put(e,p); p++; } b=e; } return r; } long max(long[] a){ long M = 0; for(int i=0;i<a.length;i++){ if(M<a[i]){ M =a[i]; maxdex = i; } } return M; } int max(int[] a){ int M = 0; for(int i=0;i<a.length;i++){ if(M<a[i]){ M =a[i]; maxdex = i; } } return M; } long min(long[] a){ long m = Long.MAX_VALUE; for(int i=0;i<a.length;i++){ if(m>a[i]){ m =a[i]; mindex = i; } } return m; } int min(int[] a){ int m = Integer.MAX_VALUE; for(int i=0;i<a.length;i++){ if(m>a[i]){ m =a[i]; mindex = i; } } return m; } long sum(long[] a){ long s = 0; for(int i=0;i<a.length;i++)s += a[i]; return s; } long sum(int[] a){ long s = 0; for(int i=0;i<a.length;i++)s += a[i]; return s; } long gcd(long a, long b){ if(a%b==0) return b; else return gcd(b,a%b); } int igcd(int a, int b) { if(a%b==0) return b; else return igcd(b,a%b); } long lcm(long a, long b) {return a / gcd(a,b) * b;} public long perm(int a,int num) { if(!isBuild)buildFac(); return fac[a]*(rev(fac[a-num]))%mod; } void buildComb(int N) { comb = new long[N+1][N+1]; comb[0][0] = 1; for(int i=1;i<=N;i++) { comb[i][0] = 1; for(int j=1;j<N;j++) { comb[i][j] = comb[i-1][j-1]+comb[i-1][j]; if(comb[i][j]>mod)comb[i][j]-=mod; } comb[i][i] = 1; } } public long comb(int a,int num){ if(a-num<0)return 0; if(num<0)return 0; if(!isBuild)buildFac(); return fac[a] * (rev(fac[num])*rev(fac[a-num])%mod)%mod; } long mulchoose(int n,int k) { if(k==0) return 1; return comb(n+k-1,k); } long rev(long l) {return pow(l,mod-2);} void buildpow(int l,int i) { pow = new long[i+1]; pow[0] = 1; for(int j=1;j<=i;j++) { pow[j] = pow[j-1]*l; if(pow[j]>mod)pow[j] %= mod; } } void buildrevpow(int l,int i) { revpow = new long[i+1]; revpow[0] = 1; for(int j=1;j<=i;j++) { revpow[j] = revpow[j-1]*l; if(revpow[j]>mod) revpow[j] %= mod; } } long pow(long l, long i) { if(i==0)return 1; else{ if(i%2==0){ long val = pow(l,i/2); return val * val % mod; } else return pow(l,i-1) * l % mod; } } }