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;
#define INF INT_MAX
typedef pair<int, int> P;
int main(void){
	int v, e, r;
	cin >> v >> e >> r;
	int from[e], to[e], cost[e], sum = 0;
	for(int i = 0; i < e; i++) cin >> from[i] >> to[i] >> cost[i];
	int leng[v];
	fill(leng, leng + v, INF);
	leng[r] = 0;
	int i, upd;
	for(i = 0; i < v; i++){
		upd = 0;
		for(int j = 0; j < e; j++){
			int f = from[j], t = to[j], c = cost[j];
			if(leng[f] != INF && leng[t] > leng[f] + c) leng[t] = leng[f] + c, upd = 1;
		}
		if(!upd) break;
	}
	if(i == v && upd) cout << "NEGATIVE CYCLE" << endl;
	else {
		for(int i = 0; i < v; i++){
			if(leng[i] == INF) cout << "INF" << endl;
			else cout << leng[i] << endl;
		}
	}
	return 0;
}