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;
int main()
{
    int a,b,r;
    cin >> a >> b >> r;
    int u[b],v[b],d[b];
    for(int i=0;i<b;i++)
    {
        cin >> u[i] >> v[i] >> d[i];
    }
    int dis[a];
    for(int i=0;i<a;i++)
    {
        dis[i]=INT_MAX;
    }
    dis[r]=0;
    for(int j=1;j<a;j++)
    {
        for(int i=0;i<b;i++)
        {
            if(dis[u[i]]!=INT_MAX)
            {
                if(dis[v[i]]>dis[u[i]]+d[i])
                    dis[v[i]]=dis[u[i]]+d[i];
            }
        }
    }
    int g=0;
    for(int i=0;i<b;i++)
    {
        if(dis[u[i]]!=INT_MAX)
        {
            if(dis[v[i]]>dis[u[i]]+d[i])
            {
                g++;
            }
        }
    }
    if(g>0)
        cout << "NEGATIVE CYCLE" << endl;
    else
    {
        for(int i=0;i<a;i++)
        {
            if(dis[i]==INT_MAX)
                cout << "INF" << endl;
            else
                cout << dis[i] << endl;
        }
    }
}