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>
#include <array>
using namespace std;
using ULL = unsigned long long;
using UL = unsigned;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

	void Solve() {
		UL V, E, r; cin >> V >> E >> r;
		vector<pair<pair<UL, UL>, LL>> G(E);
		rep(i, E) {
			UL a, b; LL d; cin >> a >> b >> d;
			G[i] = { { a, b }, d };
		}
		const LL INF = 1000000000000;
		vector<LL> ans(V, INF);
		ans[r] = 0;
		rep(i, V - 1) {
			for (auto e : G) {
				UL u = e.first.first, v = e.first.second;
				LL d = e.second;
				if (ans[u] == INF) continue;
				ans[v] = min(ans[v], ans[u] + d);
			}
		}
		for (auto e : G) {
			UL u = e.first.first, v = e.first.second;
			LL d = e.second;
			if (ans[u] == INF) continue;
			if (ans[v] > ans[u] + d) { cout << "NEGATIVE CYCLE" << endl; return; }
		}
		rep(i, V) {
			if (ans[i] == INF) cout << "INF" << endl;
			else cout << ans[i] << endl;
		}
	}


	Problem();
};
int main() {
	unique_ptr<Problem> p(new Problem());
	p->Solve();
	return 0;
}
Problem::Problem() {
	cout << fixed << setprecision(10);
}