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

#define FOR(i, n, m) for(ll (i)=(m);(i)<(n);++(i))
#define REP(i, n) FOR(i,n,0)
#define OF64 std::setprecision(10)

const ll MOD = 1000000007;
const ll INF = (ll) 1e15;

struct Edge {
    ll from;
    ll to;
    ll cost;
};

Edge E[2005];
ll C[1005];

int main() {
    ll N, M, R;
    cin >> N >> M >> R;
    REP(i, M) {
        cin >> E[i].from >> E[i].to >> E[i].cost;
    }
    REP(i, N) {
        C[i] = INF;
    }
    C[R] = 0;

    bool cycle = false;
    REP(i, N + 1) {
        bool update = false;
        REP(e, M) {
            if (C[E[e].from] == INF)
                continue;
            ll c = C[E[e].from] + E[e].cost;
            if (C[E[e].to] > c) {
                C[E[e].to] = c;
                update = true;
            }
        }
        cycle = update;
        if (!update)
            break;
    }

    if (cycle)
        cout << "NEGATIVE CYCLE" << endl;
    else {
        REP(i, N) {
            if (C[i] == INF)
                cout << "INF" << endl;
            else
                cout << C[i] << endl;
        }
    }
    return 0;
}