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;

typedef long long ll;
typedef pair<ll, ll> pll;

#define REP(i, n) for(int i=0; i < (n); ++i)
#define mp make_pair
#define fi first
#define se second
#define pb push_back

const int MAX_V = 1e4;
const int MAX_E = 1e4;
ll INF = 1e16;

struct Edge {
    int from, to, w;
};

vector<Edge> w(MAX_E);
ll d[MAX_V];
int V, E;

bool bellman_ford(int s) {
    REP(i, V) d[i] = INF;
    d[s] = 0;

    REP(i, V) {
        REP(j, E) {
            Edge e = w[j];
            if (d[e.from] != INF && d[e.to] > d[e.from] + e.w) {
                d[e.to] = d[e.from] + e.w;

                if (i == V - 1) {
                    return true; // detect negative loop.
                }
            }
        }
    }

    return false; // no negative loops.
}

int main() {
    int r;
    cin >> V >> E >> r;

    REP(i, E) {
        int a, b, c;
        cin >> a >> b >> c;
        w[i] = {a, b, c};
    }


    if (bellman_ford(r)) {
        cout << "NEGATIVE CYCLE" << endl;
    } else {
        REP(i, V) {
            if (d[i] == INF) cout << "INF" << endl;
            else cout << d[i] << endl;
        }
    }
}