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 rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
#define int long long
using P = pair<int,int>;
struct edge{int from, to, cost;};
edge graph[2200];
int dist[1100];
const int INF = 1001001001001ll;
bool ng = false;
signed main(){
    int v,e,r;cin >> v >>e >> r;
    rep(i,e){
        cin >> graph[i].from >> graph[i].to >> graph[i].cost;
    }
    rep(i,v)dist[i] = INF;
    dist[r] = 0;
    int cnt = 0;
    while(1){
        cnt++;
        bool update = false;
        rep(i,e){
            auto e = graph[i];
            if(dist[e.from] != INF && dist[e.to] > dist[e.from] + e.cost){
                dist[e.to] = dist[e.from] + e.cost;
                update = true;
            }
        }
        if(!update)break;
        if(cnt > v){
            ng = true;
            break;
        }
        

        
    }
    if(ng){
        cout << "NEGATIVE CYCLE" << endl;
        return 0;
    }
    rep(i,v){
        if(dist[i] == INF)cout << "INF" << endl;
        else cout << dist[i] << endl;
    }

    return 0;
}