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>
using namespace std;
const int inf = 1012345678;
int V, E, s, a[2009], b[2009], c[2009], dist[2009];
int main() {
	scanf("%d%d%d", &V, &E, &s);
	for(int i = 0; i < E; i++) scanf("%d%d%d", &a[i], &b[i], &c[i]);
	fill(dist, dist + V, inf); dist[s] = 0;
	for(int i = 0; i < V; i++) {
		for(int j = 0; j < E; j++) {
			dist[b[j]] = min(dist[b[j]], dist[a[j]] + c[j]);
		}
	}
	bool flag = false;
	for(int i = 0; i < E; i++) {
		if(dist[b[i]] < inf / 2 && dist[a[i]] + c[i] < dist[b[i]]) flag = true;
	}
	if(flag) puts("NEGATIVE CYCLE");
	else for(int i = 0; i < V; i++) {
		if(dist[i] >= inf / 2) puts("INF");
		else printf("%d\n", dist[i]);
	}
	return 0;
}