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<queue>
#include<vector>
#include<functional>
using namespace std;
typedef long long ll;
ll INF = 1e15;
struct Edge {
	ll from;
	ll to;
	ll cost;
};
using P = pair<ll, ll>;
vector<Edge>G[100005];
ll d[100005];
Edge es[200005];

int main() {
	int r;
	int V;
	int E;
	cin >> V >> E >> r;
	for (int i = 0; i < E; i++) {
		d[i] = INF;
	}
	for (int i = 0; i < E; i++) {
		cin >> es[i].from >> es[i].to >> es[i].cost;
	}
	d[r] = 0;
	bool update = true;
	int count = 0;
	while (update) {
		update = false;
		for (int i = 0; i < E; i++) {
			Edge e = es[i];
			if (d[e.from] != INF && d[e.to] > d[e.from] + e.cost) {
				d[e.to] = d[e.from] + e.cost;
				update = true;
			}
		}
		
		if (count == V) {
			cout << "NEGATIVE CYCLE" << endl;
			return 0;
		}
		if (!update)break;
		count++;
	}
	for (int i = 0; i < V; i++) {
		if (d[i] == INF) {
			cout << "INF" << endl;
		}
		else {
			cout << d[i] << endl;
		}
	}
	return 0;
}