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<iostream>
#include<bits/stdc++.h>
using namespace std;
const long long int inf=INT_MAX;
const int MAX =1e5+6;
long long int dis[MAX];
vector<long long int>adj[MAX];
void intit(int n){
	for(int i=0;i<n;i++){
		dis[i]=inf;
	}
}
int main(){
	long long 	int i,j,k,n,m,s;
	scanf("%lld %lld %lld" , &n , &m , &s);
	for(i=0;i<m;i++){
		long long int x,y,z;
		scanf("%lld %lld %lld" , &x , &y, &z);
		adj[i].push_back(x);
		adj[i].push_back(y);
		adj[i].push_back(z);
	}
	intit(n);
	dis[s]=0;
	for(i=0;i<n-1;i++){
		int j=0;
		while(adj[j].size()!=0){
			if((dis[adj[j][1]]>dis[adj[j][0]]+adj[j][2])&&dis[adj[j][0]]!=inf){
				dis[adj[j][1]]=dis[adj[j][0]]+adj[j][2];
				
			}
			j++;
		}
	}
	int f=0;
	for(int i=0;i<n-1;i++){
		int j=0;
		while(adj[j].size()!=0){
			if((dis[adj[j][1]]>dis[adj[j][0]]+adj[j][2])&&dis[adj[j][0]]!=inf){
				f=1;
				break;
			}
			j++;
		}
	}
	if(f){
		cout<<"NEGATIVE CYCLE"<<"\n";
	}
	else{
	for(i=0;i<n;i++){
		if(dis[i]>=inf)
			cout<<"INF"<<"\n";
		else
		printf("%lld\n", dis[i] );
	}
}
}