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 <algorithm>

#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

const int inf = 1e7;

struct E{
	E(){}
	E(int f, int t, int c): f(f), t(t), c(c){}

	int f, t, c;
};

int n, m, r;
E g[2000];
int d[1000];

int main(){
	scanf("%d%d%d", &n, &m, &r);
	rep(i, m){
		int f, t, c;
		scanf("%d%d%d", &f, &t, &c);
		g[i] = E(f, t, c);
	}

	fill_n(d, n, inf);

	d[r] = 0;
	rep(a, n){
		bool update = false;
		rep(i, m){
			E e = g[i];
			if(d[e.f] != inf && d[e.t] > d[e.f] + e.c){
				d[e.t] = d[e.f] + e.c;
				update = true;
			}
		}
		if(!update){
			break;
		}
		if(a == n - 1){
			puts("NEGATIVE CYCLE");
			return 0;
		}
	}

	rep(i, n){
		if(d[i] == inf){
			puts("INF");
		}
		else{
			printf("%d\n", d[i]);
		}
	}
	return 0;
}