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<algorithm>
#include<vector>
#include<utility>
#include<queue>
#include<functional>
using namespace std;
#define LL long long
#define MOD 1000000007

int v,e,r,vc[1002],edge[2002][3];//s,t,d
bool NC = false, END;

int main(){
	cin >> v >> e >> r;
	for(int i=0; i<v; i++) vc[i] = MOD;
	for(int i=0; i<e; i++) cin >> edge[i][0] >> edge[i][1] >> edge[i][2];		
	
	vc[r] = 0;
	for(int i=0; i<v; i++){
		if(END)break;
		if(i == v-1){
			NC = true;
			break;
		}
		END = true;
		for(int j=0; j<e; j++){
			if((vc[edge[j][1]] > vc[edge[j][0]] + edge[j][2]) && vc[edge[j][0]] != MOD){
				END = false;
				vc[edge[j][1]] = vc[edge[j][0]] + edge[j][2];
			}
		}
	}

	if(NC && e)cout << "NEGATIVE CYCLE" << endl;
	else{
		for(int i=0; i<v; i++){
			if(vc[i] == MOD) cout << "INF" <<endl;
			else cout << vc[i] << endl;
		}
	}
	return 0;
}