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>
#define REP(i, n) for(int i = 0; i < n; ++i)
using namespace std;

template<typename T>
struct edge {
    int from;
    int to;
    T cost;
};

template<typename T>
vector<T> BellmanFord(int s, int v, const vector<edge<T>> &g) {
    const T INF = numeric_limits<T>::max();
    vector<T> dist(v,INF);
    dist[s] = 0;
    for(int i = 0; i < v-1; ++i) {
        for(auto& e : g) if(dist[e.from]!=INF) {
            dist[e.to] = min(dist[e.to],  dist[e.from]+e.cost);
        }
    }
    for(auto &e : g) if(dist[e.from]!=INF) {
        if(dist[e.from] + e.cost < dist[e.to]) return vector<T>();
    }
    return dist;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int v,e,r; cin >>  v >> e >>  r;
    vector<edge<int>> g;
    REP(i,e) {
        int s,t,d; cin >> s >> t >> d;
        g.push_back({s,t,d});
    }
    vector<int> dist = BellmanFord(r,v,g);
    if(dist.empty()) cout << "NEGATIVE CYCLE" << endl;
    for(auto x : dist) {
        if(x==numeric_limits<int>::max()) cout << "INF" << '\n';
        else cout << x << '\n';
    }
    return 0;
}