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<bits/stdc++.h>
#define to first
#define wgt second 

using namespace std;

const int MAXN=1010;

typedef pair<int,int> pii;
typedef vector<pii> vec;
typedef vector<vec> Graph;

Graph G(MAXN);
int n,d[MAXN],times[MAXN];
bool negative_cycle; 

void SPFA(int s)
{
	queue<int> que;
	negative_cycle=false;
	memset(times,0,sizeof(times));
	fill(d,d+n,INT_MAX);
	d[s]=0;
	times[s]=1;
	que.push(s);
	while(!que.empty())
	{
		int u=que.front();que.pop();
		for(int i=0;i<G[u].size();i++)
			if(d[G[u][i].to]>d[u]+G[u][i].wgt)
			{
				d[G[u][i].to]=d[u]+G[u][i].wgt;
				que.push(G[u][i].to);
				times[G[u][i].to]++;
				if(times[G[u][i].to]>n)
				{
					negative_cycle=true;
					while(que.empty()) que.pop();
					return ;
				}
			}
	}
}

int main()
{
	int e,r;
	scanf("%d%d%d",&n,&e,&r);
	for(int i=0;i<e;i++)
	{
		int s,t,d;
		scanf("%d%d%d",&s,&t,&d);
		G[s].push_back(make_pair(t,d));
	}
	SPFA(r);
	if(negative_cycle)
		printf("NEGATIVE CYCLE\n");
	else
		for(int i=0;i<n;i++)
			if(d[i]==INT_MAX)
				printf("INF\n");
			else
				printf("%d\n",d[i]);
	return 0;
}