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<cstdio>
#include<vector>

#define INF 999999999
#define ll long long

using namespace std;

const int MAX_N = 1000;
const int MAX_M = 2000;

struct edge
{
	int from;  //?????????
	int to;    //??°??????
	int cost;  //??????
};

int d[MAX_N];
edge es[MAX_M];
bool flag;	//???????????????????????????

void shortest_path(int n,int m,int s)	//s???????????????????????????????????????????????¢????±???????
{
	int cnt = 0;
	fill(d,d+n,INF);
	d[s] = 0;
	while(true && cnt < n){
		bool update = false;
		for(int i=0;i<m;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(!update) break;
		cnt++;
	}
	if(cnt == n){
		flag = true;
	}
}

int main()
{
	int i,n,m,s;
	cin >> n;  //????????°
	cin >> m;  //?????°
	cin >> s;  //???????????????
	for(int i=0;i<m;i++){
		scanf("%d",&es[i].from);
		scanf("%d",&es[i].to);
		scanf("%d",&es[i].cost);
	}
	flag = false;
	shortest_path(n,m,s);
	if(!flag){
		for(int i=0;i<n;i++){
			if(d[i] == INF){
				cout << "INF\n";
			}else{
				cout << d[i] << "\n";
			}
		}
	}else{
		cout << "NEGATIVE CYCLE\n";
	}
}