Problem: Constraints

* 1 ≤ |V| ≤ 1000
* 0 ≤ |E| ≤ 2000
* -10000 ≤ di ≤ 10000
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E) and the source r.


|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which is reachable from the source r, print


NEGATIVE CYCLE


in a line.

Otherwise, print


c0
c1
:
c|V|-1


The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print "INF".

Examples

Input

4 5 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

0
2
-3
-1


Input

4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0


Output

NEGATIVE CYCLE


Input

4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2


Output

INF
0
-5
-3

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<algorithm>
#include<cmath>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
#define reg(i,a,b) for(int i=(a);i<=(b);i++)
typedef long long int lli;
typedef pair<int,int> mp;
#define fir first
#define sec second


bool belfo(int n,int s,vector<mp>* vs,int* dist,int* gone){
	memset(gone,-1,sizeof(int)*n);
	gone[s]=1;
	dist[s]=0;
	
	rep(k,n+1){
		if(k==n)return false;
		bool ch=false;
		rep(no,n){
			if(gone[no]==-1)continue;
			int nc=dist[no];
			rep(i,vs[no].size()){
				int to=vs[no][i].fir,
					co=vs[no][i].sec;
				if(gone[to]==-1 || dist[to]>nc+co){
					dist[to]=nc+co;
					gone[to]=1;
					ch=true;
				}
			}
		}
		if(!ch)break;
	}
	return true;
}



	
	
	
int n,m;

vector<mp> vs[100005];


int dist[100005];
int gone[100005];




int main(void){
	int n,m,s;
	scanf("%d%d%d",&n,&m,&s);
	rep(i,m){
		int a,b,c;
		scanf("%d%d%d",&a,&b,&c);
		vs[a].push_back(mp(b,c));
		//vs[b].push_back(mp(a,c));
	}
	if(belfo(n,s,vs,dist,gone)){
		rep(i,n){
			if(gone[i]!=-1)printf("%d\n",dist[i]);
			else printf("INF\n");
		}
	}
	else printf("NEGATIVE CYCLE\n");
	return 0;
	
}