---
/*==============================================*
| Code Library
*==============================================*/
/** head-file **/
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <algorithm>
/** define-for **/
#define REP(i, n) for (int i=0;i<int(n);++i)
#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)
#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)
#define REP_1(i, n) for (int i=1;i<=int(n);++i)
#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)
#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)
#define REP_N(i, n) for (i=0;i<int(n);++i)
#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)
#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)
#define REP_1_N(i, n) for (i=1;i<=int(n);++i)
#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)
#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)
/** define-useful **/
#define clr(x,a) memset(x,a,sizeof(x))
#define sz(x) int(x.size())
#define see(x) cerr<<#x<<" "<<x<<endl
#define se(x) cerr<<" "<<x
#define pb push_back
#define mp make_pair
/** test **/
#define Display(A, n, m) {
REP(i, n){
REP(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
#define Display_1(A, n, m) {
REP_1(i, n){
REP_1(j, m) cout << A[i][j] << " ";
cout << endl;
}
}
using namespace std;
/** typedef **/
typedef long long LL;
/** Add - On **/
const int direct4[4][2]={ {0,1},{1,0},{0,-1},{-1,0} };
const int direct8[8][2]={ {0,1},{1,0},{0,-1},{-1,0},{1,1},{1,-1},{-1,1},{-1,-1} };
const int direct3[6][3]={ {1,0,0},{0,1,0},{0,0,1},{-1,0,0},{0,-1,0},{0,0,-1} };
const int MOD = 1000000007;
const int INF = 0x3f3f3f3f;
const long long INFF = 1LL << 60;
const double EPS = 1e-9;
const double OO = 1e15;
const double PI = acos(-1.0); //M_PI;
const int maxn=11111;
const int maxm=1111111;
int n,m;
/*==============================================*
| 建图
| INIT: init(int n):void
| CALL: addedge(int u,int v,int c):void
*==============================================*/
struct EdgeNode{
int to;
int w;
int next;
};
struct Graph{
int head[maxn];
EdgeNode edges[maxm];
int edge,n;
void init(int n){
memset(head,-1,sizeof(head));
this->n=n;
edge=0;
}
void addedge(int u,int v,int c){
edges[edge].w=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
};
/*==============================================*
| Dijkstra+堆优化
| INIT: init(n);addedge(u,v,c);节点编号0~n
| CALL: dijkstra(int s);dis[]:最短路;pre[]:前驱
*==============================================*/
struct HeapNode{
int d,u;
HeapNode(){}
HeapNode(int a,int b):d(a),u(b){}
bool operator<(const HeapNode& rhs) const{
return d>rhs.d;
}
};
struct Dijkstra{
EdgeNode edges[maxm];
int head[maxn];
int edge,n;
void init(int n){
this->n=n;
memset(head,-1,sizeof(head));
edge=0;
}
void addedge(int u,int v,int c){
edges[edge].w=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
bool done[maxn];
int dis[maxn];
int pre[maxn];
void dijkstra(int s){
priority_queue<HeapNode>que;
for (int i=0;i<=n;i++) dis[i]=INF;
dis[s]=0;
memset(done,0,sizeof(done));
que.push(HeapNode(0,s));
while (!que.empty()){
HeapNode x=que.top();
que.pop();
int u=x.u;
if (done[u]) continue;
done[u]=true;
for (int i=head[u];i!=-1;i=edges[i].next){
int v=edges[i].to;
int w=edges[i].w;
if (dis[v]>dis[u]+w){
dis[v]=dis[u]+w;
pre[v]=u;
que.push(HeapNode(dis[v],v));
}
}
}
}
};
/*==============================================*
| BellmanFord+队列优化
| INIT: init(n);addedge(u,v,c);节点编号0~n
| CALL: spfa(int s):bool;dist[]:最短路
*==============================================*/
struct BellmanFord{
EdgeNode edges[maxm];
int head[maxn],edge,n;
bool vis[maxn];
int outque[maxn];
queue<int>que;
int dis[maxn];
void addedge(int u,int v,int c){
edges[edge].w=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
void init(int n){
memset(head,-1,sizeof(head));
edge=0;
this->n=n;
}
bool spfa(int s){
int u;
for (int i=0;i<=n;i++) dis[i]=INF;
memset(vis,0,sizeof(vis));
memset(outque,0,sizeof(outque));
while (!que.empty()) que.pop();
que.push(s);
vis[s]=true;
dis[s]=0;
while (!que.empty()){
u=que.front();
que.pop();
vis[u]=false;
outque[u]++;
if (outque[u]>n) return false;
for (int i=head[u];i!=-1;i=edges[i].next){
int v=edges[i].to;
int w=edges[i].w;
if (dis[v]==INF||dis[v]>dis[u]+w){
dis[v]=dis[u]+w;
if (!vis[v]){
vis[v]=true;
que.push(v);
}
}
}
}
return true;
}
};
/*==============================================*
| 强连通分量-Tarjan
| INIT: init(n);addedge(u,v);节点编号0~n-1
| CALL: find_scc();sccno[x]:节点x所属强连通分量
*==============================================*/
struct Tarjan{
int head[maxn];
EdgeNode edges[maxm];
int edge,n;
void init(int n){
memset(head,-1,sizeof(head));
this->n=n;
edge=0;
}
void addedge(int u,int v,int c=0){
edges[edge].w=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
int pre[maxn],lowlink[maxn],sccno[maxn],scc_cnt,dfs_clock;
stack<int>stk;
void dfs(int u){
pre[u]=lowlink[u]=++dfs_clock;
stk.push(u);
for (int i=head[u];i!=-1;i=edges[i].next){
int v=edges[i].to;
if (!pre[v]){
dfs(v);
lowlink[u]=min(lowlink[u],lowlink[v]);
}
else if (!sccno[v]){
lowlink[u]=min(lowlink[u],pre[v]);
}
}
if (lowlink[u]==pre[u]){
scc_cnt++;
int x;
do{
x=stk.top();
stk.pop();
sccno[x]=scc_cnt;
}while (x!=u);
}
}
void find_scc(){
dfs_clock=scc_cnt=0;
memset(sccno,0,sizeof(sccno));
memset(pre,0,sizeof(pre));
while (!stk.empty()) stk.pop();
for (int i=0;i<n;i++) if (!pre[i]) dfs(i);
}
};
/*==============================================*
| 点双连通/割点/桥/边双连通
| INIT: init(n);addedge(u,v);无向图;节点编号1~n
| CALL: find_bcc():点双连通/割点/桥
| find_block():边双连通,先要求出桥
| iscut[]:割点;EdgeNode_1.cut:桥
| vector<int>bcc[x]:双连通分量x所包含的节点
| bccno[x]:节点x所属的点双连通分量,割点的值无意义
| block[x]:节点x所属的边双连通分量
*==============================================*/
struct EdgeNode_1{
int to;
int w;
int next;
bool cut;
};
struct Edge{
int u;
int v;
Edge(){}
Edge(int a,int b):u(a),v(b){}
};
struct Bcc_Graph{
int head[maxn];
EdgeNode_1 edges[maxm];
int edge,n;
void init(int n){
memset(head,-1,sizeof(head));
this->n=n;
edge=0;
}
void addedge(int u,int v,int c=0){
edges[edge].cut=0,edges[edge].w=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
//点双连通/割点/桥
int dfn[maxn],low[maxn],bccno[maxn],dfs_clock,bcc_cnt;
bool iscut[maxn];
vector<int>bcc[maxn];
stack<Edge>stk;
int dfs(int u,int fa){
int lowu=dfn[u]=++dfs_clock;
int child=0;
for (int i=head[u];i!=-1;i=edges[i].next){
int v=edges[i].to;
if (v==fa) continue;
Edge e=Edge(u,v);
if (!dfn[v]){
stk.push(e);
child++;
int lowv=dfs(v,u);
lowu=min(lowu,lowv);
if (dfn[u]<=lowv){
iscut[u]=true;//割点
//BEGIN 求点双连通分量
bcc_cnt++;
bcc[bcc_cnt].clear();
Edge x;
do{
x=stk.top();
stk.pop();
if (bccno[x.u]!=bcc_cnt){
bcc[bcc_cnt].push_back(x.u);
bccno[x.u]=bcc_cnt;
}
if (bccno[x.v]!=bcc_cnt){
bcc[bcc_cnt].push_back(x.v);
bccno[x.v]=bcc_cnt;
}
}while (x.u!=u||x.v!=v);
//END
}
if (dfn[u]<lowv){//cut 桥
edges[i].cut=true;
edges[i^1].cut=true;
}
}
else if (dfn[v]<dfn[u]){
stk.push(e);//BEGIN-END 点双连通
lowu=min(lowu,dfn[v]);
}
}
if (fa<0&&child==1) iscut[u]=0;//割点
low[u]=lowu;
return lowu;
}
void find_bcc(){
while (!stk.empty()) stk.pop();
memset(dfn,0,sizeof(dfn));
memset(iscut,0,sizeof(iscut));
memset(bccno,0,sizeof(bccno));
dfs_clock=bcc_cnt=0;
for (int i=1;i<=n;i++){
if (!dfn[i]) dfs(i,-1);
}
}
//边双连通分量
int block[maxn];
int vis[maxn];
int b_num;
void b_dfs(int u){
vis[u]=true;
block[u]=b_num;
for (int i=head[u];i!=-1;i=edges[i].next)
{
if (edges[i].cut) continue;
int v=edges[i].to;
if (!vis[v]) b_dfs(v);
}
}
void find_block(){
memset(block,0,sizeof(block));
memset(vis,0,sizeof(vis));
b_num=0;
for (int i=1;i<=n;i++){
if (!vis[i]){
b_num++;
b_dfs(i);
}
}
}
};
/*==============================================*
| TwoSAT
| INIT: init(n);addedge(u,v);节点编号0~n-1
| CALL: add_clause(x,xval,y,yval) x=xval or y=yval
| add_con(x,xval) x=xval
| solve():bool;mark[i]:选取i
*==============================================*/
struct TwoSAT{
int head[maxn*2];
EdgeNode edges[maxm*2];
int edge,n;
bool mark[maxn*2];
int S[maxn*2],c;
void init(int n){
this->n=n;
memset(mark,0,sizeof(mark));
memset(head,-1,sizeof(head));
edge=0;
}
void addedge(int u,int v){
edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
// x = xval or y = yval
void add_clause(int x,int xval,int y,int yval){
x=x*2+xval;
y=y*2+yval;
addedge(x^1,y);
addedge(y^1,x);
}
// x = xval
void add_con(int x,int xval){
x=x*2+xval;
addedge(x^1,x);
}
bool dfs(int x){
if (mark[x^1]) return false;
if (mark[x]) return true;
mark[x]=true;
S[c++]=x;
for (int i=head[x];i!=-1;i=edges[i].next)
if (!dfs(edges[i].to)) return false;
return true;
}
bool solve(){
for (int i=0;i<n*2;i+=2)
if (!mark[i]&&!mark[i+1]){
c=0;
if (!dfs(i)){
while (c>0) mark[S[--c]]=false;
if (!dfs(i+1)) return false;
}
}
return true;
}
};
/*==============================================*
| TwoSAT-Tarjan强连通
| INIT: init(n),addedge(u,v),节点0~n-1
| CALL: add_self(x,xval,y,yval) x!=xval->y=yval
| solve():bool
*==============================================*/
struct TWOSAT{
int head[maxn*2];
EdgeNode edges[maxm*2];
int edge,n;
void init(int n){
this->n=2*n;
memset(head,-1,sizeof(head));
edge=0;
}
void addedge(int u,int v){
edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
}
// x = xval or y = yval
void add_clause(int x,int xval,int y,int yval){
x=x*2+xval;
y=y*2+yval;
addedge(x^1,y);
addedge(y^1,x);
}
//x=xval
void add_con(int x,int xval){
x=x*2+xval;
addedge(x^1,x);
}
//x!=xval->y=yval
void add_self(int x,int xval,int y,int yval){
x=x*2+xval;
y=y*2+yval;
addedge(x,y);
}
int pre[maxn],lowlink[maxn],sccno[maxn],scc_cnt,dfs_clock;
stack<int>stk;
void dfs(int u){
pre[u]=lowlink[u]=++dfs_clock;
stk.push(u);
for (int i=head[u];i!=-1;i=edges[i].next){
int v=edges[i].to;
if (!pre[v]){
dfs(v);
lowlink[u]=min(lowlink[u],lowlink[v]);
}
else if (!sccno[v]){
lowlink[u]=min(lowlink[u],pre[v]);
}
}
if (lowlink[u]==pre[u]){
scc_cnt++;
int x;
do{
x=stk.top();
stk.pop();
sccno[x]=scc_cnt;
}while (x!=u);
}
}
void find_scc(int n){
dfs_clock=scc_cnt=0;
memset(sccno,0,sizeof(sccno));
memset(pre,0,sizeof(pre));
while (!stk.empty()) stk.pop();
for (int i=0;i<n;i++) if (!pre[i]) dfs(i);
}
bool solve(){
find_scc(n);
for (int i=0;i<n;i+=2){
if (sccno[i]==sccno[i^1]) return false;
}
return true;
}
};
/*==============================================*
| Dinic最大流
| INIT: prepare(n,S,T);addedge(u,v,c);节点0~n
| CALL: Dinic_flow():int
*==============================================*/
struct edgenode{
int to,flow,next;
};
struct Dinic{
int node,src,dest,edge;
int head[maxn],work[maxn],dis[maxn],q[maxn];
edgenode edges[maxm];
void prepare(int _node,int _src,int _dest){
node=_node,src=_src,dest=_dest;
memset(head,-1,sizeof(head));
edge=0;
}
void addedge(int u,int v,int c){
edges[edge].flow=c,edges[edge].to=v,edges[edge].next=head[u],head[u]=edge++;
edges[edge].flow=0,edges[edge].to=u,edges[edge].next=head[v],head[v]=edge++;
}
bool Dinic_bfs(){
int i,u,v,l,r=0;
for (i=0; i<node; i++) dis[i]=-1;
dis[q[r++]=src]=0;
for (l=0; l<r; l++){
for (i=head[u=q[l]]; i!=-1; i=edges[i].next){
if (edges[i].flow&&dis[v=edges[i].to]<0){
dis[q[r++]=v]=dis[u]+1;
if (v==dest) return true;
}
}
}
return false;
}
int Dinic_dfs(int u,int exp){
if (u==dest) return exp;
for (int &i=work[u],v,tmp; i!=-1; i=edges[i].next){
if (edges[i].flow&&dis[v=edges[i].to]==dis[u]+1&&
(tmp=Dinic_dfs(v,min(exp,edges[i].flow)))>0){
edges[i].flow-=tmp;
edges[i^1].flow+=tmp;
return tmp;
}
}
return 0;
}
int Dinic_flow(){
int i,ret=0,delta;
while (Dinic_bfs()){
for (i=0;i<node;i++) work[i]=head[i];
while (delta=Dinic_dfs(src,INF)) ret+=delta;
}
return ret;
}
};
/*==============================================*
| 最小费用最大流
| INIT: prepare(n,S,T);addedge(u,v,f,c);编号0~n-1
| CALL: spfaflow():int
*==============================================*/
struct edgenode_1{
int to;//边的指向
int flow;//边的容量
int cost;//边的费用
int next;//链表的下一条边
};
struct MinCost{
edgenode_1 edges[maxm];
int node,src,dest,edge;//node节点数，src源点，dest汇点，edge边数
int head[maxn],p[maxn],dis[maxn],q[maxn],vis[maxn];
//head链表头，p记录可行流上节点对应的反向边，dis计算距离
void prepare(int _node=0,int _src=0,int _dest=0){
node=_node,src=_src,dest=_dest;
memset(head,-1,sizeof(head));
memset(vis,0,sizeof(vis));
edge=0;
}
void addedge(int u,int v,int f,int c){
edges[edge].flow=f;edges[edge].cost=c;edges[edge].to=v;
edges[edge].next=head[u];head[u]=edge++;
edges[edge].flow=0;edges[edge].cost=-c;edges[edge].to=u;
edges[edge].next=head[v];head[v]=edge++;
}
bool spfa(){
int i,u,v,l,r=0,tmp;
for (i=0;i<node;i++) dis[i]=INF;
dis[q[r++]=src]=0;
p[src]=p[dest]=-1;
for (l=0;l!=r;((++l>=maxn)?l=0:l)){
for (i=head[u=q[l]],vis[u]=false;i!=-1;i=edges[i].next){
if (edges[i].flow&&dis[v=edges[i].to]>(tmp=dis[u]+edges[i].cost)){
dis[v]=tmp;
p[v]=i^1;
if (vis[v]) continue;
vis[q[r++]=v]=true;
if (r>=maxn) r=0;
}
}
}
return p[dest]>=0;
}
int spfaflow(){
int i,ret=0,delta;
while (spfa()){//按记录原路返回求流量
for (i=p[dest],delta=INF;i>=0;i=p[edges[i].to]){
delta=min(delta,edges[i^1].flow);
}
for (int i=p[dest];i>=0;i=p[edges[i].to]){
edges[i].flow+=delta;
edges[i^1].flow-=delta;
}
ret+=delta*dis[dest];
}
return ret;
}
};
---
---
/*==============================================*
| 最大公约数-辗转相除
*==============================================*/
int gcd(int a,int b){
if (b==0) return a;
return gcd(b,a%b);
}
/*==============================================*
| 扩展欧几里得
| ax+by=gcd(a,b)
*==============================================*/
int extgcd(int a,int b,int& x,int& y){
int d=a;
if (b!=0){
d=extgcd(b,a%b,y,x);
y-=(a/b)*x;
}else{
x=1;y=0;
}
return d;
}
/*==============================================*
| 素数-埃氏筛法
*==============================================*/
int prime[maxn];
bool is_prime[maxn+1];
int sieve(int n){
int p=0;
for (int i=0;i<=n;i++) is_prime[i]=true;
is_prime[0]=is_prime[1]=false;
for (int i=2;i<=n;i++){
if (is_prime[i]){
prime[p++]=i;
for (int j=2*i;j<=n;j+=i) is_prime[j]=false;
}
}
return p;
}
/*==============================================*
| 快速幂
*==============================================*/
LL modPow(LL x,LL n,LL mod){
if (n==0) return 1;
LL res=modPow(x*x%mod,n/2,mod);
if (n&1) res=res*x%mod;
return res;
}
/*==============================================*
| 高斯消元-列主元
| 求解Ax=b,A为矩阵 无解/多解时返回空数组
*==============================================*/
const double eps=1e-8;
typedef vector<double>vec;
typedef vector<vec>mat;
vec gaussJordan(const mat& A,const vec& b){
int n=A.size();
mat B(n,vec(n+1));
for (int i=0;i<n;i++)
for (int j=0;j<n;j++) B[i][j]=A[i][j];
for (int i=0;i<n;i++) B[i][n]=b[i];
for (int i=0;i<n;i++){
int pivot=i;
for (int j=i;j<n;j++){
if (abs(B[j][i])>abs(B[pivot][i])) pivot=j;
}
swap(B[i],B[pivot]);
if (abs(B[i][i]<eps)) return vec();//无解或多解
for (int j=i+1;j<=n;j++) B[i][j]/=B[i][i];
for (int j=0;j<n;j++){
if (i!=j){
for (int k=i+1;k<=n;k++) B[j][k]-=B[j][i]*B[i][k];
}
}
}
vec x(n);
for (int i=0;i<n;i++) x[i]=B[i][n];
return x;
}
/*==============================================*
| 逆元
| ax≡b(mod m) x=a逆×b
| gcd(a,m)!=1逆元不存在
*==============================================*/
int modInverse(int a,int m){
int x,y;
extgcd(a,m,x,y);
return (m+x%m)%m;
}
---
/*==============================================*
| 矩阵快速幂
*==============================================*/
const int M=10000;
typedef vector<int>vec;
typedef vector<vec>mat;
mat mul(mat &A,mat &B){
mat C(A.size(),vec(B[0].size()));
for (int i=0;i<(int)A.size();i++){
for (int k=0;k<(int)B.size();k++){
for (int j=0;j<(int)B[0].size();j++){
C[i][j]=(C[i][j]+A[i][k]*B[k][j])%M;
}
}
}
return C;
}
mat pow(mat A,LL n){
mat B(A.size(),vec(A.size()));
for (int i=0;i<(int)A.size();i++){
B[i][i]=1;
}
while (n>0){
if (n&1) B=mul(B,A);
A=mul(A,A);
n>>=1;
}
return B;
}
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