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:
//
//  single_source_shortest_path.cpp
//  
//
//  Created by Yoshida Satoshi on 2018/11/10.
//

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <vector>

#define MAX 3000
#define INF 20000000

using namespace std;

typedef long long ll;

int main()
{
    int V,E,r;
    ll s[MAX],t[MAX],d[MAX];
    cin>>V>>E>>r;
    for(int i=0;i<E;i++) cin>>s[i]>>t[i]>>d[i];
    
    ll min[MAX];
    for(int i=0;i<V;i++) if(i!=r) min[i]=INF;
    
    min[r]=0;
    
    bool flag;
    for(int cnt=0;cnt<V;cnt++)
    {
        flag=false;
        for(int i=0;i<E;i++)
        {
            if(min[s[i]]!=INF&&min[t[i]]>min[s[i]]+d[i])
            {
                min[t[i]]=min[s[i]]+d[i];
                flag=true;
            }
        }
    }
    
    if(flag) cout<<"NEGATIVE CYCLE"<<endl;
    else
    {
        for(int i=0;i<V;i++)
        {
            if(min[i]==INF) cout<<"INF"<<endl;
            else            cout<<min[i]<<endl;
        }
    }
    
    return 0;
}