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 Int = int64_t;
using UInt = uint64_t;
using C = std::complex<double>;
#define rep(i, n) for(Int i = 0; i < (Int)(n); ++i)

int main() {
   Int v, e, r;
   std::cin >> v >> e >> r;
   std::vector<Int> ss(e), ts(e), ds(e);
   rep(i, e) std::cin >> ss[i] >> ts[i] >> ds[i];
   const Int inf = (Int)1 << 53;
   std::vector<Int> xs(v, inf);
   xs[r] = 0;
   std::vector<bool> ys(v, false);
   ys[r] = true;
   for(Int i = 0; i < v; ++i) {
      for(Int k = 0; k < e; ++k) {
         Int s = ss[k], t = ts[k], d = ds[k];
         xs[t] = std::min(xs[t], xs[s] + d);
         if( ys[s] ) ys[t] = true;
      }
   }
   bool negativeCycle = false;
   rep(k, e) {
      Int s = ss[k], t = ts[k], d = ds[k];
      if( ys[s] and ys[t] and xs[s] + d < xs[t] ) negativeCycle = true;
   }
   if( negativeCycle ) {
      puts("NEGATIVE CYCLE");
   }
   else {
      rep(i, v) {
         if( ys[i] ) {
            printf("%ld\n", xs[i]);
         }
         else {
            puts("INF");
         }
      }
   }
}