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<stdio.h>
#include<algorithm>
#include <map>
#include <list>
#include <stack>
#include <queue>
#include <vector>
#include <iostream>
#include <functional>
#include <time.h>
using namespace std;
clock_t fi, endtime;
const int r_c = 0;
const int r_t = 1;
const int MAX_V = 100000;
const int MAX_d = 100000;
const int MAX_E = 500000;
long long int INF = 10000 * 50000;

int n, m, a, b, c, t;
int k, p, q, r;
long long int wf[MAX_V];

struct edge { int from, to, ct; };
edge edg[MAX_E];

int main()
{
	int cou = 0;
	scanf("%d %d %d", &n, &m, &r);
	for (int i = 0; i < m; ++i) {
		scanf("%d %d %d", &a, &b, &c);
		edg[i].from = a; edg[i].to = b; edg[i].ct = c;
	}
	for (int i = 0; i < n; ++i) {
		wf[i] = INF;
	}
	wf[r] = 0;
	while (1) {
		bool bo = false;
		for (int i = 0; i < m; ++i) {
			edge e = edg[i];
			if (wf[e.from] != INF && wf[e.to] > wf[e.from] + e.ct) {
				wf[e.to] = wf[e.from] + e.ct;
				bo = true;
			}
		}
		if (!bo) break;
		++cou;
		if (cou > n) break;
	}
	if (cou > n) printf("NEGATIVE CYCLE\n");
	else {
		for (int i = 0; i < n; ++i) {
			if (wf[i] == INF) printf("INF\n");
			else printf("%lld\n", wf[i]);
		}
	}
}