Problem Description

Jack likes to travel around the world, but he doesn’t like to wait. Now, he is traveling in the Undirected Kingdom. There are n cities and m bidirectional roads connecting the cities. Jack hates waiting too long on the bus, but he can rest at every city. Jack can only stand staying on the bus for a limited time and will go berserk after that. Assuming you know the time it takes to go from one city to another and that the time Jack can stand staying on a bus is x minutes, how many pairs of city (a,b) are there that Jack can travel from city a to b without going berserk?

Input

The first line contains one integer T,T≤5, which represents the number of test case.

For each test case, the first line consists of three integers n,m and q where n≤20000,m≤100000,q≤5000. The Undirected Kingdom has n cities and mbidirectional roads, and there are q queries.

Each of the following m lines consists of three integers a,b and d where a,b∈{1,...,n} and d≤100000. It takes Jack d minutes to travel from city a to city b and vice versa.

Then q lines follow. Each of them is a query consisting of an integer x where x is the time limit before Jack goes berserk.

Output

You should print q lines for each test case. Each of them contains one integer as the number of pair of cities (a,b) which Jack may travel from a to b within the time limit x.

Note that (a,b) and (b,a) are counted as different pairs and a and b must be different cities.

Sample Input

1 5 5 3 2 3 6334 1 5 15724 3 5 5705 4 3 12382 1 3 21726 6000 10000 13000

Sample Output

2 6 12

Source

2015 ACM/ICPC Asia Regional Changchun Online

//time 873MS
//memery 2988K#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#define mem(a) memset(a,0,sizeof(a))
using namespace std;struct node
{int u,v;int w;
}st[110000];struct nod
{int val;int id;friend bool operator<(nod a,nod b){return a.val<b.val;}
}qu[6000];
bool cmp(node a,node b)
{return a.w<b.w;
}
int father[30000];
int num[30000];
void initial(int n)
{int i;for(i=0;i<=n;++i){father[i]=i;num[i]=1;}
}
int find(int x)
{int t=x;while(x!=father[x]){x=father[x];}while(t!=father[t]){int temp=t;t=father[t];father[temp]=x;}return x;
}
bool join(int x,int y)
{x=find(x);y=find(y);if(y<x){swap(x,y);}if(x!=y){father[y]=x;num[x]+=num[y];}
}
int ans[6000];
int main()
{int T;scanf("%d",&T);while(T--){int n,m,q;scanf("%d%d%d",&n,&m,&q);int i;for(i=0;i<m;++i){scanf("%d%d%d",&st[i].u,&st[i].v,&st[i].w);}sort(st,st+m,cmp);for(i=0;i<q;++i){scanf("%d",&qu[i].val);qu[i].id=i;}sort(qu,qu+q);int t=0;initial(n);for(i=0;i<q;++i){int temp;temp=qu[i].val;while(t<m&&st[t].w<=temp){int u=st[t].u;int v=st[t].v;join(u,v);t++;}int ans_temp=0;for(int j=1;j<=n;++j){if(father[j]==j&&num[j]>1){ans_temp+=(num[j]*(num[j]-1));}}ans[qu[i].id]=ans_temp;}for(i=0;i<q;++i){printf("%d\n",ans[i]);}}
}

//time 312MS
//memery 2992K#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#define mem(a) memset(a,0,sizeof(a))
using namespace std;struct node
{int u,v;int w;
}st[110000];struct nod
{int val;int id;friend bool operator<(nod a,nod b){return a.val<b.val;}
}qu[6000];bool cmp(node a,node b)
{return a.w<b.w;
}
int father[30000];
int num[30000];
void initial(int n)
{int i;for(i=0;i<=n;++i){father[i]=i;num[i]=1;}
}
int find(int x)
{int t=x;while(x!=father[x]){x=father[x];}while(t!=father[t]){int temp=t;t=father[t];father[temp]=x;}return x;
}
bool join(int x,int y)
{x=find(x);y=find(y);if(y<x){swap(x,y);}if(x!=y){father[y]=x;num[x]+=num[y];return 1;}return 0;
}
int ans[6000];
int main()
{int T;scanf("%d",&T);while(T--){int n,m,q;scanf("%d%d%d",&n,&m,&q);int i;for(i=0;i<m;++i){scanf("%d%d%d",&st[i].u,&st[i].v,&st[i].w);}sort(st,st+m,cmp);for(i=0;i<q;++i){scanf("%d",&qu[i].val);qu[i].id=i;}sort(qu,qu+q);int t=0;initial(n);int ans_temp=0;for(i=0;i<q;++i){int temp;temp=qu[i].val;while(t<m&&st[t].w<=temp){int u=st[t].u;int v=st[t].v;int u_r=find(u);int v_r=find(v);int num_u=num[u_r];int num_v=num[v_r];if(join(u,v)){ans_temp+=(2*num_u*num_v);}t++;}ans[qu[i].id]=ans_temp;}for(i=0;i<q;++i){printf("%d\n",ans[i]);}}
}