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 <cmath>
#include <vector>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>

using namespace std;

const long long lim = 40000000;
const long long inf = 0x3f3f3f3f3f3f3f3f;

signed main(void)
{
	int n, m, s; cin >> n >> m >> s;

	vector<pair<pair<int, int>, int > > edge;

	for (int i = 0, u, v, w; i < m; ++i)
	{
		cin >> u >> v >> w;
		edge.push_back(make_pair(make_pair(u, v), w));
	}

	vector<long long> dis(n); for (auto &i : dis)i = inf; dis[s] = 0;

	for (int i = 0; i < n; ++i)for (auto j : edge)
		if (dis[j.first.second] > dis[j.first.first] + j.second)
			dis[j.first.second] = dis[j.first.first] + j.second;

	for (auto i : edge)if (dis[i.first.second] > dis[i.first.first] + i.second)
		if (dis[i.first.second] <= lim)return cout << "NEGATIVE CYCLE" << endl, 0;

	for (auto i : dis)if (i < lim)cout << i << endl; else cout << "INF" << endl;
}