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<vector>
#include<queue>
#include<climits>
using namespace std;

struct edge{
    int s, t, d;
};

int main(){
    int n, m, s;
    cin >> n >> m >> s;
    vector<edge> v;
    for(int i = 0; i < m; i++){
        int s, t, d;
        cin >> s >> t >> d;
        v.push_back(edge({s,t,d}));
    }
    vector<int> dp(n, INT_MAX);
    dp[s] = 0;
    for(int i = 1; i < n; i++){
        vector<int> next(n, INT_MAX);
        for(int j = 0; j < m; j++){
            edge e = v[j];
            if(dp[e.s] != INT_MAX)  next[e.t] = min(next[e.t], dp[e.s] + e.d);
        }
        for(int j = 0; j < n; j++)  next[j] = min(next[j], dp[j]);
        dp = next;
    }
    for(int j = 0; j < m; j++){
        edge e = v[j];
        if(dp[e.s] != INT_MAX && dp[e.t] > dp[e.s] + e.d){
            cout << "NEGATIVE CYCLE" << endl;
            return 0;
        }
    }
    for(int i = 0; i < n; i++){
        if(dp[i] != INT_MAX)    cout << dp[i] << endl;
        else                    cout << "INF" << endl;
    }
    return 0;
}