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<bits/stdc++.h>
#define F first
#define S second
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<P,ll> PP;
ll n,m,r,a,b,c,dp[100000],INF=(1LL<<60);
vector<PP> v;
bool Bell(void){
    for(int i=0;i<n;i++){
        for(int j=0;j<m;j++){
            if(dp[v[j].F.F]!=INF&&dp[v[j].F.S]>dp[v[j].F.F]+v[j].S){
                dp[v[j].F.S]=dp[v[j].F.F]+v[j].S;
                if(i==n-1)return false;
            }
        }
    }
    return true;
}
int main(void){
    cin>>n>>m>>r;
    for(int i=0;i<100000;i++)dp[i]=INF;
    dp[r]=0;
    for(int i=0;i<m;i++){
        cin>>a>>b>>c;
        v.push_back({{a,b},c});
    }
    if(!Bell()){
        cout<<"NEGATIVE CYCLE"<<endl;
        return 0;
    }
    for(int i=0;i<n;i++){
        if(dp[i]==INF)cout<<"INF"<<endl;
        else cout<<dp[i]<<endl;
    }
}