A proper vertex coloring is a labeling of the graph's vertices with colors such that no two vertices sharing the same edge have the same color. A coloring using at most k colors is called a (proper) k-coloring.

Now you are supposed to tell if a given coloring is a proper k-coloring.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N and M (both no more than 1), being the total numbers of vertices and edges, respectively. Then M lines follow, each describes an edge by giving the indices (from 0 to N−1) of the two ends of the edge.

After the graph, a positive integer K (≤ 100) is given, which is the number of colorings you are supposed to check. Then K lines follow, each contains N colors which are represented by non-negative integers in the range of int. The i-th color is the color of the i-th vertex.

Output Specification:

For each coloring, print in a line k-coloring if it is a proper k-coloring for some positive k, or No if not.

Sample Input:

10 11
8 7
6 8
4 5
8 4
8 1
1 2
1 4
9 8
9 1
1 0
2 4
4
0 1 0 1 4 1 0 1 3 0
0 1 0 1 4 1 0 1 0 0
8 1 0 1 4 1 0 5 3 0
1 2 3 4 5 6 7 8 8 9

 

Sample Output:

4-coloring
No
6-coloring
No

#include<bits/stdc++.h>
using namespace std;
const int maxn=100010;
struct Node{
    int x,y;
}node[maxn];
int main(){
    int n,m,k;
    cin>>n>>m;
    for(int i=0;i<m;i++){
        scanf("%d %d",&node[i].x,&node[i].y);
    }
    cin>>k;
    for(int i=0;i<k;i++){
        set<int> s;
        vector<int> v;
        v.resize(n);
        for(int j=0;j<n;j++){
            scanf("%d",&v[j]);
            s.insert(v[j]);
        }
        int len=s.size();
        bool flag=true;
        for(int k=0;k<m;k++){
            if(v[node[k].x]==v[node[k].y]){
                flag=false;
            }
        }
        if(flag==true){
            printf("%d-coloring\n",len);
        }
        else{
            printf("No\n");
        }
    }
    return 0;
}