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;

#define MAX_N 1000
#define MAX_M 2000

struct Edge{
    int v[2], cost;
    Edge(){}
    Edge(int a, int b, int c) {
        v[0] = a; v[1] = b; cost = c;
    }
};

int n, m, r, d[MAX_N];
Edge E[MAX_M];

void shortest_path(){
    fill(d, d + n, INT_MAX);
    d[r] = 0;
    for(int cnt = 0; ; cnt++){
        if(cnt == n){
            cout << "NEGATIVE CYCLE" << endl;
            return;
        }
        bool update = true;
        for(int j = 0; j < m; j++){
            int s = E[j].v[0], t = E[j].v[1], w = E[j].cost;
            if(d[s] != INT_MAX && d[s] + w < d[t]){
                d[t] = d[s] + w;
                update = false;
            }
        }
        if(update) break;
    }
    for(int i = 0; i < n; i++){
        cout << (d[i] == INT_MAX ? "INF" : to_string(d[i])) << endl;
    }
    return;
}

int main(){
    cin >> n >> m >> r;
    for(int i = 0; i < m; i++){
        int s, t, d;
        cin >> s >> t >> d;
        E[i] = Edge(s, t, d);
    }
    shortest_path();
    return 0;
}