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 INF 0x3f3f3f3f
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;

struct st {
	int from, to, c;
};
vector<st>E;
int d[1000];
int main() {
	int v, e, r; scanf("%d%d%d", &v, &e, &r);
	rep(i, e) {
		int s, t, d; scanf("%d%d%d", &s, &t, &d);
		E.push_back({ s,t,d });
	}
	memset(d, 0x3f, sizeof(d));
	d[r] = 0;
	rep(i, v)rep(j, e) {
		st s = E[j];
		if (d[s.from] != INF&&d[s.to] > d[s.from] + s.c) {
			d[s.to] = d[s.from] + s.c;
			if (i == v - 1) {
				puts("NEGATIVE CYCLE"); return 0;
			}
		}
	}
	rep(i, v) {
		if (d[i] == INF)puts("INF");
		else printf("%d\n", d[i]);
	}
}