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 rep(i,n) for(int (i)=0;(i)<(n);(i)++)
using namespace std;

const int vmax=1010;
const int inf=1023456789;

int N,M,S;
struct node{int to,cost;};
vector<node> graph[vmax];

int dist[vmax];

bool bellman_ford(){
	rep(i,N)dist[i]=inf;
	dist[S]=0;
	rep(loop,N){
		rep(i,N)for(auto &e:graph[i]){
			if(dist[i]==inf) continue;
			if(dist[e.to]>dist[i]+e.cost){
				dist[e.to]=min(dist[e.to],dist[i]+e.cost);
				if(loop==N-1) return true;
			}
		}
	}
	return false;
}

int main(void){
	cin >> N >> M >> S;
	rep(i,M){
		int a,b,c;
		cin >> a >> b >> c;
		graph[a].push_back({b,c});
	}
	if(bellman_ford())
		cout << "NEGATIVE CYCLE" << endl;
	else{
		rep(i,N){
			if(dist[i]==inf)
				cout << "INF" << endl;
			else
				cout << dist[i] << endl;
		}
	}
	return 0;
}