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:
# -*- coding: utf-8 -*-

import sys

sys.setrecursionlimit(10 ** 9)
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
INF=float('inf')

# ベルマンフォード(頂点数, 辺集合(0-indexed), 始点)
def bellman_ford(N: int, edges: list, src: int) -> list:
    # 頂点[ある始点からの最短距離]
    # (経路自体を知りたい時はここに前の頂点も持たせる)
    res = [INF] * N
    res[src] = 0
    # 各辺によるコストの置き換えを頂点数N-1回繰り返す
    for i in range(N-1):
        for src, dest, cost in edges:
            if res[dest] > res[src] + cost:
                res[dest] = res[src] + cost
    # 負の閉路(いくらでもコストを減らせてしまう場所)がないかチェックする
    for src, dest, cost in edges:
        if res[dest] > res[src] + cost:
            # あったら空リストを返却
            return []
    # 問題なければ頂点リストを返却
    return res

N,M,r=MAP()
edges=[None]*M
for i in range(M):
    s,t,d=MAP()
    edges[i]=(s, t, d)

ans=bellman_ford(N, edges, r)

if not len(ans):
    print('NEGATIVE CYCLE')
    exit()

for i in range(N):
    if ans[i]==INF:
        ans[i]='INF'
for i in range(N):
    print(ans[i])