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 fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair <int, int> pii;
typedef pair <pii, int> ppiii;

const int INF = 0x3f3f3f3f;
int n, m, r, t1, t2, t3, d[100005];
vector <ppiii> e;

int main() {
	cin >> n >> m >> r;
	for (int i = 0; i < n; i++) d[i] = INF;
	for (int i = 0; i < m; i++) {
		cin >> t1 >> t2 >> t3;
		e.pb(mp(mp(t1, t2), t3));
	}
	d[r] = 0;
	for (int i = 0; i < n - 1; i++) {
		for (ppiii j : e) {
			int &u = j.fi.fi, &v = j.fi.se, &w = j.se;
			if (d[u] != INF && d[u] + w < d[v]) {
				d[v] = d[u] + w;
			}
		}
	}
	for (ppiii i : e) {
		int &u = i.fi.fi, &v = i.fi.se, &w = i.se;
		if (d[u] != INF && d[u] + w < d[v]) {
			cout << "NEGATIVE CYCLE" << endl;
			return 0;
		}
	}
	for (int i = 0; i < n; i++) {
		if (d[i] == INF) cout << "INF" << endl;
		else cout << d[i] << endl;
	}
}