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>
using namespace std;
using ll = long long;
const int INF = 1e9;

int main()
{
	int V,E,R;
	cin >> V >> E >> R;
	vector<vector<pair<int,int>>> G(V);
	vector<ll> D(V,INF);
	for(int i = 0;i<E;i++)
	{
		int s,t,d;
		cin >> s >> t >> d;
		G[s].emplace_back(t,d);
	}

	D[R] = 0;
	for(int i = 0;i<V;i++)
	{
		bool update = false;
		for(int j = 0;j<V;j++)
		{
			//if(update == false)break;
			for(auto k:G[j])
			{
				if(D[k.first]>D[j]+k.second&&D[j]!=INF)
				{
					update = true;
					D[k.first] = D[j] + k.second;
				}
			}
		}
		if(update==false)break;
		if(i==V-3)
		{
			cout<<"NEGATIVE CYCLE"<<endl;
			return 0;
		}
	}
	for(auto i:D)
	{
		if(i==INF)
		{
			cout<<"INF"<<endl;
		}
		else
		{
			cout<<i<<endl;
		}
		
	}
}