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 PYTHON3):

Solution:
import sys
from math import isinf
# どれが終点の時に負の閉路があるかをnegative[v]にいれる
# dists = [float('inf')] * V # 到達不能はinf
# negatives = [False] * V

def bellman_ford(start:int)->bool:
    """ ベルマンフォード O(|V|*|E|)
    :param V:      頂点数
    :param edges:  辺 [(始点，終点，重み)]
    :param start:  始点
    """
    global dists, negatives
    global edges
    dists[start] = 0
    V = len(dists)
    for i in range(V):
        for (s, t, w) in edges:
            if isinf(dists[s]): continue
            if dists[t] > dists[s] + w:
                dists[t] = dists[s] + w
                if i==V-1:
                    negatives[t] = True


if __name__ == "__main__":
    V,E,start = map(int, input().split())
    edges = []
    for _ in range(E):
        s,t,d = map(int, input().split())
        edges.append((s,t,d))

    dists = [float('inf')] * V # 到達不能はinf
    negatives = [False] * V
    bellman_ford(start)
    if any(neg for neg in negatives)==True:
        print("NEGATIVE CYCLE")
        exit()
    for di in dists:
        if di==float('inf'):
            print("INF")
        else:
            print(di)