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 1000000000
#define MAX_V 1000
#define MAX_E 2000
using namespace std;

struct edge { int from, to, cost; };
int V, E, r;
int d[MAX_V];

edge es[MAX_E];

bool Bellman_Ford(int start) {
	fill(d, d + V, INF);
	d[start] = 0;
	bool update;
	for (int i = 0; i < V; i++) {
		update = false;
		for (int j = 0; j < E; j++) {
			edge e = es[j];
			if (d[e.from] != INF && d[e.to] > d[e.from] + e.cost) {
				d[e.to] = d[e.from] + e.cost;
				update = true;
			}
		}
		if (!update) return false;
	}
	return true;
}

int main()
{
	int r;
	cin >> V >> E >> r;
	for (int i = 0; i < E; i++)
		cin >> es[i].from >> es[i].to >> es[i].cost;

	if (!Bellman_Ford(r)) {
		for (int i = 0; i < V; i++) {
			if (d[i] == INF)
				cout << "INF" << endl;
			else
				cout << d[i] << endl;
		}
	}
	else {
		cout << "NEGATIVE CYCLE" << endl;
	}
	return 0;
}