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 <vector>
#include <iostream>
using namespace std;
#define MAX 100000
#define INF __INT_MAX__

struct edge{
    // 始点,終点,重み
    int s,t,w;
};

vector<edge> edges;
int d[MAX];

void BellmanFord(int startVertex,int vNum,int eNum){
	fill(d,d + MAX,INF);
	d[startVertex] = 0;
	
	// 頂点分回すことで、最後のサイクルは負のサイクルを確認するプロセスになる
	for(int i=0;i < vNum;++i){
		bool update = false;
		for(int j = 0;j < eNum;++j){
			edge e = edges[j];
			if(d[e.s] != INF && d[e.t] > d[e.s] + e.w){
				d[e.t] = d[e.s] + e.w;
				update = true;
				// 頂点分更新されていれば、負のサイクルがあることがわかる
				if(i == vNum - 1){
					cout << "NEGATIVE CYCLE" << endl;
					return;
				}
			}
		}
		if(!update)break;
	}

	for(int i = 0;i < vNum;++i){
		if(d[i] == INF){
		    cout << "INF"<< endl;
		}
		else cout<< d[i] << endl;
	}
}

int main(){
    int v,e,r;
	cin >> v >> e >> r;
	for(int i = 0;i < e;++i){
		int s,t,w;
		cin >> s >> t >> w;
		edges.push_back({s,t,w});
	}
	BellmanFord(r,v,e);
}