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)
typedef long long int_t;

const int v_size = 1000;
const int e_size = 2000;
int_t v, e, r;
int_t s[e_size];
int_t t[e_size];
int_t d[e_size];

bool input() {
  if (cin >> v >> e >> r) {
    rep (i, e) cin >> s[i] >> t[i] >> d[i];
    return true;
  }
  return false;
}

const int_t inf = numeric_limits<int_t>::max();
int_t mc[v_size];

void solve() {
  fill(mc, mc+v_size, inf);
  mc[r] = 0;

  int cnt = 0;
  bool updated = true;
  while (updated) {
    updated = false;

    rep (i, e) {
      if (mc[s[i]] == inf) continue;
      if (mc[t[i]] <= mc[s[i]] + d[i]) continue;
      mc[t[i]] = mc[s[i]] + d[i];
      updated = true;
    }

    cnt++;
    if (cnt > v) break;
  }

  if (cnt > v) {
    cout << "NEGATIVE CYCLE" << endl;
  } else {
    rep (i, v) {
      if (mc[i] == inf) {
        cout << "INF" << endl;
      } else {
        cout << mc[i] << endl;
      }
    }
  }
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  while (input()) {
    solve();
  }
  return 0;
}