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:
def shortest_path_faster_algorithm(E, start):
    # ベルマンフォードの更新があるところだけ更新する感じのやつ
    # O(VE) だが実用上高速
    # E は隣接リスト
    # 検証: http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=4005805#1
    from collections import deque
    inf = float("inf")  # 10**18 は良くない
    N = len(E)
    q = deque([start])  # スタックにするとコーナーケースがあるっぽい
    distance = [inf] * N;  distance[start] = 0
    in_q = [0] * N;        in_q[start] = True
    times = [0] * N;       times[start] = 1
    while q:
        v = q.popleft()
        in_q[v] = False
        dist_v = distance[v]
        for u, cost in E[v]:
            new_dist_u = dist_v + cost
            if distance[u] > new_dist_u:
                times[u] += 1
                if times[u] >= N:  # 負閉路検出
                    print("NEGATIVE CYCLE"); exit()
                    distance[u] = -inf
                else:
                    distance[u] = new_dist_u
                if not in_q[u]:
                    in_q[u] = True
                    q.append(u)
    return distance

import sys
def main():
    N, M, r = map(int, sys.stdin.readline().split())
    E = [[] for _ in range(N)]
    for s, t, d in zip(*[iter(map(int, sys.stdin.read().split()))]*3):
        E[s].append((t, d))
    distance = shortest_path_faster_algorithm(E, r)
    for d in distance:
        if d == float("inf"):
            print("INF")
        else:
            print(d)

main()