Problem: We have a connected undirected graph with N vertices and M edges. Edge i in this graph (1 \leq i \leq M) connects Vertex U_i and Vertex V_i bidirectionally. We are additionally given N integers D_1, D_2, ..., D_N.

Determine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph. If the answer is yes, find one such assignment of colors and integers, too.

* There is at least one vertex assigned white and at least one vertex assigned black.
* For each vertex v (1 \leq v \leq N), the following holds.
* The minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.



Here, the cost of traversing the edges is the sum of the weights of the edges traversed.

Constraints

* 2 \leq N \leq 100,000
* 1 \leq M \leq 200,000
* 1 \leq D_i \leq 10^9
* 1 \leq U_i, V_i \leq N
* The given graph is connected and has no self-loops or multiple edges.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
D_1 D_2 ... D_N
U_1 V_1
U_2 V_2
\vdots
U_M V_M


Output

If there is no assignment satisfying the conditions, print a single line containing `-1`.

If such an assignment exists, print one such assignment in the following format:


S
C_1
C_2
\vdots
C_M


Here,

* the first line should contain the string S of length N. Its i-th character (1 \leq i \leq N) should be `W` if Vertex i is assigned white and `B` if it is assigned black.
* The (i + 1)-th line (1 \leq i \leq M) should contain the integer weight C_i assigned to Edge i.

Examples

Input

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5


Output

BWWBB
4
3
1
5
2


Input

5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5


Output

-1


Input

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


Output

BBBW
1
1
1
2
1
1

Solution (in CPP):

Solution:
#include <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <map>
#include <list>
#include <set>
#include <numeric>
#include <queue>
#include <stack>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <cstring>
#include <climits>
#include <cfloat>
#include <ctime>
#include <complex>
#include <cassert>
#include <array>
#include <bitset> 
#include <unordered_map>
using namespace std;
typedef long long LL;
typedef pair<LL,LL> P;


const int L=100*1000+1;
char color[L];
vector<int> edge[L];
bool ok[L];
void solve(long long N, long long M, std::vector<long long> D, std::vector<long long> U, std::vector<long long> V){
	vector<P> order;
	for(int i=0;i<M;i++){
		int u=U[i];
		int v=V[i];
		edge[u].push_back(v);
		edge[v].push_back(u);
		if(D[u]<=D[v]){
			ok[v]=true;
		}
		if(D[u]>=D[v]){
			ok[u]=true;
		}
	}
	for(int i=0;i<N;i++){
		if(!ok[i]){
			cout << -1 << endl;
			return;
		}
		order.push_back(P(D[i],i));
	}
	sort(order.begin(),order.end());
	for(auto p:order){
		int r=p.second;
		bool hasB=false;
		bool hasW=false;
		for(auto s:edge[r]){
			if(color[s]=='B'){
				hasB=true;
			}
			else if(color[s]=='W'){
				hasW=true;
			}
		}
		if(hasB){
			color[r]='W';
		}
		else {
			color[r]='B';
		}
	}
	printf("%s\n",color);
	for(auto i=0;i<M;i++){
		printf("%lld\n",max(D[U[i]],D[V[i]]));
	}
}

int main(){
    long long N;
    scanf("%lld",&N);
    long long M;
    scanf("%lld",&M);
    std::vector<long long> D(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&D[i]);
    }
    std::vector<long long> U(M);
    std::vector<long long> V(M);
    for(int i = 0 ; i < M ; i++){
        scanf("%lld",&U[i]);
		U[i]--;
        scanf("%lld",&V[i]);
		V[i]--;
    }
    solve(N, M, std::move(D), std::move(U), std::move(V));
    return 0;
}