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;
typedef long long int ll;
typedef pair<ll,ll> mp;
#define inf 1e9
struct edge{
	int from,to,cost;
};
bool  find_negative_loop(vector<edge> &e,int s,int v,vector<ll> &res ){//bellmanford
	res = vector<ll>(v,inf);
	res[s] = 0;
	int E = e.size();
	for(int i=0;i<v;i++){
		for(int j=0;j<E;j++){
			if(res[e[j].from] != inf &&res[e[j].to]  > res[e[j].from] + e[j].cost){
				res[e[j].to] = res[e[j].from] + e[j].cost;
				if(i==v-1)return true;
			}
		}
	}
	return false;
}

int main(){
	int v,E,r;
	cin>>v>>E>>r;
	vector<edge> e(E);
	for(int i=0;i<E;i++){
		cin>>e[i].from>>e[i].to>>e[i].cost;
	}
	vector<ll> res;
	if(find_negative_loop(e,r,v,res)){
		cout<<"NEGATIVE CYCLE"<<endl;
	}else{
		for(int i=0;i<v;i++)if(res[i] == inf){
			cout<<"INF"<<endl;
		}else{
			cout<<res[i]<<endl;
		}
	}

	return 0;
}