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 <stdio.h>
#include <iostream>
using namespace std;

#define V_MAX 1000
#define E_MAX 2000
#define INF 1000000000

typedef struct Edge{
    int v1;
    int v2;
    int w;
}Edge;

Edge Es[E_MAX];
int A[V_MAX];

void init(void){
    for(int i = 0; i < V_MAX; i++){
        A[i] = INF;
    }
}


int main(void){
    init();

    int V, E, r;
    scanf("%d %d %d", &V, &E, &r);

    for(int i = 0; i < E; i++){
        scanf("%d %d %d", &Es[i].v1, &Es[i].v2, &Es[i].w);
    }

    A[r] = 0;

    bool is_updated;
    for(int i = 0; i < V; i++){
        is_updated = false;
        for(int j = 0; j < E; j++){
            if(A[Es[j].v2] > A[Es[j].v1] + Es[j].w && A[Es[j].v1] != INF){
                A[Es[j].v2] = A[Es[j].v1] + Es[j].w;
                is_updated = true;
            }
        }
    }

    if(is_updated){
        printf("NEGATIVE CYCLE\n");
        return 0;
    }

    for(int i = 0; i < V; i++){
        if(A[i] == INF){
            printf("INF\n");
        }else{
            printf("%d\n", A[i]);
        }
    }

}