#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
const ll mod=998244353;
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}

-------------------------------------------------------------


namespace Input
{
    const int BUF = 65536;
    char buf[BUF + 1];
    char *head = buf, *tail = buf;
}
inline char inputchar()
{
    using namespace Input;
    if(head == tail)
        *(tail = (head = buf) + fread(buf, 1, BUF, stdin)) = 0;
    return *head++;
}
inline void input(int &ret)
{
    char ch = inputchar();
    while(ch < '0' || ch > '9')
        ch = inputchar();
    ret = ch - '0';
    ch = inputchar();
    while(ch >= '0' && ch <= '9')
    {
        ret = ret * 10 + ch - '0';
        ch = inputchar();
    }
}
inline void input(ll &ret)
{
    char ch = inputchar();
    while(ch < '0' || ch > '9')
        ch = inputchar();
    ret = ch - '0';
    ch = inputchar();
    while(ch >= '0' && ch <= '9')
    {
        ret = ret * 10 + ch - '0';
        ch = inputchar();
    }
}





//----------------------------------------------------------
#ifndef online_judge
    freopen("test.in","r",stdin);
    freopen("test.out","w",stdout);
#endif



#ifndef online_judge
    fclose(stdin);
    fclose(stdout);
#endif


const double PI=acos(-1);
const double eps=1e-6;
//-------------------------------------------------------
//并查集
int F[MAXN];//初始化为-1
int find(int x)
{
    if(F[x]==-1)return x;
    return F[x]=find(x);
}
//merge
void bing(int u,int v)
{
    int t1=find(u);
    int t2=find(v);
    if(t1!=t2)
    {
        F[t1]=t2;
    }
}


//---------------------------------------


//建图
bool vis[MAXN];
int ancestor[MAXN];//祖先
struct Edge
{
    int to,next;
}edge[MAXN<<2];
int head[MAXN],tot;
void add_edge(int u,int v)
{
    edge[tot].to=v;
    edge[tot].next=head[u];
    head[u]=tot++;
};

//----------------------------------------


int main()
{
    std::ios::sync_with_stdio(false);
}