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) repi(i,0,n)
#define repi(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define pb push_back 
#define MAX_E 2017
#define MAX_V 1145
#define INF INT_MAX / 3

// make_pair ??????????????§
struct edge{int from, to, cost; };
edge es[MAX_E]; // ???
int d[MAX_V]; // ???????????¢
int V, E; // V???????????°???E????????°
//?§????s????????????????????????????????¢????±???????
bool find_negative_loop(int s){ 
    rep(i, V) d[i] = INF;
    d[s] = 0;
    rep(i, V){
        rep(j, E){
            edge e = es[j];
            if(d[e.from] != INF && d[e.to] > d[e.from] + e.cost){
                d[e.to] = d[e.from] + e.cost;
                if(i == V - 1) return true;
            }
        }
    }
    return false;
}
int main(){
	int r;
	cin >> V >> E >> r;
	int s, t, w;
	rep(i, E)
	{
		cin >> s >> t >> w;
		es[i] = {s, t, w};
	}
	if(!find_negative_loop(r))
	{
		rep(i, V)
		{
			if(d[i] == INF) cout << "INF" << endl;
			else cout << d[i] << endl;
		}
	}
	else
	{
		cout << "NEGATIVE CYCLE" << endl;
	}
}