题意:给你一个边权为1的图,s1到t1最多不能超过l1时间,s2到t2最多不能超过l2时间,问你最多能删多少条边

思路:首先因为边权为1,所以最短路的时间就是边数,那么可以直接枚举重复的区间然后相减即可



#include<bits/stdc++.h>
using namespace std;
const int maxn = 3005;
#define INF 1e9
vector<int>e[maxn];
int vis[maxn];
int d[maxn][maxn];
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	for(int i = 0;i<m;i++)
	{
		int u,v;
		scanf("%d%d",&u,&v);
		e[u].push_back(v);
		e[v].push_back(u);
	}
	int s1,t1,s2,t2,l1,l2;
	scanf("%d%d%d",&s1,&t1,&l1);
	scanf("%d%d%d",&s2,&t2,&l2);
	for(int i = 1;i<=n;i++)
	{
        memset(vis,0,sizeof(vis));
		d[i][i]=0;
		queue<int>q;
		q.push(i);
		vis[i]=1;
        while(!q.empty())
		{
			int now = q.front();
			q.pop();
			for(int j = 0;j<e[now].size();j++)
			{
				int v = e[now][j];
				if(vis[v])
					continue;
				d[i][v]=d[i][now]+1;
				if(!vis[v])
					q.push(v);
				vis[v]=1;
				
			}
		}
	}
	if(d[s1][t1]>l1 || d[s2][t2]>l2)
	{
		printf("-1\n");
		return 0;
	}
	int ans = d[s1][t1]+d[s2][t2];
	for(int i = 1;i<=n;i++)
	{
		for(int j = 1;j<=n;j++)
		{
			 if(d[s1][i]+d[i][j]+d[j][t1]<=l1 && d[s2][i]+d[i][j]+d[j][t2]<=l2)
				 ans = min(ans,d[s1][i]+d[i][j]+d[j][t1]+d[s2][i]+d[j][t2]);
			 if(d[s1][i]+d[i][j]+d[j][t1]<=l1 && d[t2][i]+d[i][j]+d[j][s2]<=l2)
				 ans = min(ans,d[s1][i]+d[i][j]+d[j][t1]+d[t2][i]+d[j][s2]);
		}
	}
	printf("%d\n",m-ans);
    
}






Description



In some country there are exactly n cities and m bidirectional roads connecting the cities. Cities are numbered with integers from 1 to n. If cities a and b are connected by a road, then in an hour you can go along this road either from city a to city b, or from city b to city a. The road network is such that from any city you can get to any other one by moving along the roads.

You want to destroy the largest possible number of roads in the country so that the remaining roads would allow you to get from city s1to city t1 in at most l1 hours and get from city s2 to city t2 in at most l2

Determine what maximum number of roads you need to destroy in order to meet the condition of your plan. If it is impossible to reach the desired result, print -1.



Input


The first line contains two integers nm (1 ≤ n ≤ 3000, 

) — the number of cities and roads in the country, respectively.

Next m lines contain the descriptions of the roads as pairs of integers aibi (1 ≤ ai, bi ≤ nai ≠ bi). It is guaranteed that the roads that are given in the description can transport you from any city to any other one. It is guaranteed that each pair of cities has at most one road between them.

The last two lines contains three integers each, s1t1l1 and s2t2l2, respectively (1 ≤ si, ti ≤ n, 0 ≤ li ≤ n).


Output


Print a single number — the answer to the problem. If the it is impossible to meet the conditions, print -1.


Sample Input


Input


5 41 2 2 3 3 4 4 5 1 3 2 3 5 2


Output


0


Input


5 41 2 2 3 3 4 4 5 1 3 2 2 4 2


Output


1


Input


5 41 2 2 3 3 4 4 5 1 3 2 3 5 1


Output


-1