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 rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

struct Edge {
	int s, t, d;
};

const int INF = 1 << 30;

int main() {
  int V, E, r;
	cin >> V >> E >> r;
	vector<Edge> g(E);
	rep(i, E) {
		cin >> g[i].s >> g[i].t >> g[i].d;
	}
	vector<int> ans(V, INF);
	ans[r] = 0;
	for (int i = 0; i < V; i++) {
		for (int j = 0; j < E; j++) {
			if (ans[g[j].s] == INF) continue;
			if (ans[g[j].s] + g[j].d < ans[g[j].t]) {
				ans[g[j].t] = ans[g[j].s] + g[j].d;
				if (i == V - 1) {
					cout << "NEGATIVE CYCLE" << endl;
					return 0;
				}
			}
		}
	}
	rep(i, V) {
		if (ans[i] != INF) cout << ans[i] << endl;
		else cout << "INF" << endl;
	}
	return 0;
}