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 <iostream>
#include <string>
#include <vector>
using namespace std;
constexpr long long INF = (long long)1<<60;
int main() {
	struct edge { long long from, to, cost; };
	int V, E, r;
	cin>>V>>E>>r;
	vector<edge> es(E);
	for (auto i = 0; i < E; i++) {
		int s, t, d;
		cin>>s>>t>>d;
		es[i] = {s,t,d};
	}
	vector<long long> d(V, INF);
	d[r] = 0;
	int cnt = V;
	bool neg_loop = false;
	while (true) {
		if (!cnt--) {
			neg_loop = true;
			break;
		}
		bool flag = false;
		for (auto& i : es) {
			if (d[i.from] != INF && d[i.to] > d[i.from]+i.cost) {
				flag = true;
				d[i.to] = d[i.from]+i.cost;
			}
		}
		if (!flag) break;
	}
	if (neg_loop) cout << "NEGATIVE CYCLE" << endl;
	else {
		for (auto& i : d)
			cout << (i == INF ? "INF" : to_string(i)) << endl;
	}
	return 0;
}