CodeForces242D：Connected Components （不错的并查集）

We already know of the large corporation where Polycarpus works as a system administrator. The computer network there consists of n computers and m cables that connect some pairs of computers. In other words, the computer network can be represented as some non-directed graph with n nodes and m edges. Let's index the computers with integers from 1 to n, let's index the cables with integers from 1 to m.

Polycarpus was given an important task — check the reliability of his company's network. For that Polycarpus decided to carry out a series of k experiments on the computer network, where the i-th experiment goes as follows:

1. Temporarily disconnect the cables with indexes from l_i to r_i, inclusive (the other cables remain connected).
2. Count the number of connected components in the graph that is defining the computer network at that moment.
3. Re-connect the disconnected cables with indexes from l_i to r_i (that is, restore the initial network).

Help Polycarpus carry out all experiments and for each print the number of connected components in the graph that defines the computer network through the given experiment. Isolated vertex should be counted as single component.

Input

The first line contains two space-separated integers n, m (2 ≤ n ≤ 500; 1 ≤ m ≤ 10⁴) — the number of computers and the number of cables, correspondingly.

The following m lines contain the cables' description. The i-th line contains space-separated pair of integers x_i, y_i (1 ≤ x_i, y_i ≤ n; x_i ≠ y_i) — the numbers of the computers that are connected by the i-th cable. Note that a pair of computers can be connected by multiple cables.

The next line contains integer k (1 ≤ k ≤ 2·10⁴) — the number of experiments. Next k lines contain the experiments' descriptions. The i-th line contains space-separated integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ m) — the numbers of the cables that Polycarpus disconnects during the i-th experiment.

Output

Print k numbers, the i-th number represents the number of connected components of the graph that defines the computer network during the i-th experiment.

Example

Input

6 5
1 2
5 4
2 3
3 1
3 6
6
1 3
2 5
1 5
5 5
2 4
3 3

Output

4
5
6
3
4
2

问题：给定N个点，M条边，Q个问题。对于每个问题，给出l，r，问删去编号在l到r的这些边后有多少个连通块。

思路：开始以为需要上面数据结构来处理，没有想出来。

由于问题的特殊性，只有提问，没有更改，所以可以利用并查集的特殊性求解。令L是从前往后的并查集，R是从后往前的并查集，然后对每个问题，合并L[l-1]和R[r+1]即可。

合并：开始ans=N，合并一次，ans--。

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<algorithm>
using namespace std;
const int maxn=;
int N,M,Q;
struct DSU
{
    int fa[],num;
    void init()
    {
        num=;
        for(int i=;i<=N;i++)
          fa[i]=i;
    }
    int find(int u)
    {
        if(fa[u]==u) return u;
        fa[u]=find(fa[u]);
        return fa[u];
    }
    void Union(int u,int v)
    {
        int fau=find(u);
        int fav=find(v);
        if(fau!=fav) num++,fa[fau]=fav;
    }
}L[maxn],R[maxn];

int x[maxn],y[maxn],anc[maxn];
int main()
{
    scanf("%d%d",&N,&M);
    for(int i=;i<=M;i++) {
        scanf("%d%d",&x[i],&y[i]);
    }

    L[].init();
    for(int i=;i<=M;i++){
        L[i]=L[i-];
        L[i].Union(x[i],y[i]);
    }
    R[M+].init();
    for(int i=M;i>=;i--){
        R[i]=R[i+];
        R[i].Union(x[i],y[i]);
    }

    int l,r,ans; scanf("%d",&Q);
    while(Q--){
        scanf("%d%d",&l,&r);
        ans=;
        DSU tmp=L[l-];
        for(int i=;i<=N;i++){
            tmp.Union(i,R[r+].find(i));
        }
        printf("%d\n",N-tmp.num);
    }
    return ;
}