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 debug(x) cerr << #x << ": " << x << '\n';
using namespace std;
using ll = long long;
using P = pair<int, int>;

struct edge{
	int from, to, cost;
};

const int MAX_V = 1000;

// bool used[MAX_V];
int d[MAX_V];
int r, V, E;
vector<edge> G;


int main(void){
	cin >> V >> E >> r;
	for(int i = 0; i < E; i++){
		int s, t, d; cin >> s >> t >> d;
		edge e = {s, t, d};
		G.push_back(e);
	}

	fill(d, d+V, INF);
	d[r] = 0;

	bool updated = true;
	for(int i = 0; i < V and updated; i++){
		updated = false;
		for(auto e: G){
			if(d[e.from] < INF and d[e.to] > d[e.from] + e.cost){
				updated = true;
				d[e.to] = d[e.from] + e.cost;
				if(i == V-1){
					cout << "NEGATIVE CYCLE" << '\n';
					return 0;
				}
			}
		}
	}

	for(int i = 0; i < V; i++){
		if(d[i] == INF) cout << "INF" << '\n';
		else cout << d[i] << '\n';
	}

	return 0;
}