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>
#define inf 2147483647
#define ll long long
using namespace std;
struct node{
    int u,v;
    ll cost;
}edge[500005];
ll dis[10005];
int n,m,s;
void init()
{
    for(int i=0;i<n;i++) dis[i]=(i==s?0:inf);
}
bool Bellman_Ford()
{
    init();
    bool flag=true;
    for(int i=0;i<n;i++)
    {
        flag=true;
        for(int j=0;j<m;j++)
        if(dis[edge[j].v]>dis[edge[j].u]+edge[j].cost&&dis[edge[j].u]!=inf)
        {
            dis[edge[j].v]=dis[edge[j].u]+edge[j].cost;
            flag=false;
        }
        if(flag) return true;
    }
    for(int j=0;j<m;j++)
    if(dis[edge[j].v]>dis[edge[j].u]+edge[j].cost&&dis[edge[j].u]!=inf) return false;
    return true;
}
int main()
{
    cin>>n>>m>>s;
    for(int i=0;i<m;i++) cin>>edge[i].u>>edge[i].v>>edge[i].cost;
    if(Bellman_Ford())
    for(int i=0;i<n;i++)
	if(dis[i]!=inf) cout<<dis[i]<<endl;
	else cout<<"INF"<<endl;
    else cout<<"NEGATIVE CYCLE"<<endl;
    return 0;
}