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
input = sys.stdin.readline
from collections import deque
def main():
    N, M, r = map( int, input().split())
    d = dict()
    E = [[] for _ in range(N)]
    for _ in range(M):
        a, b, c = map( int, input().split())
        d[(a,b)] = c
        E[a].append(b)
    INF = 10**14*2
    V = [INF]*N
    V[r] = 0
    for _ in range(N-1):
        for e in d:
            s, t = e
            if V[s] + d[e] < V[t]:
                V[t] = V[s] + d[e]
    q = deque([r])
    W = [False]*N
    while q:
        v = q.pop()
        for w in E[v]:
            if W[w] == False:
                W[w] = True
                q.append(w)
    for e in d:
        s, t = e
        if V[s] + d[e] < V[t] and (W[s] == True or W[t] == True):
            print("NEGATIVE CYCLE")
            return
    for i in range(N):
        if V[i] >= 10**14:
            print("INF")
            continue
        print(V[i])
    # #if you want to know whether its path has negative cycle, we need followings.
    # E = [ V[i] for i in range(N)]
    # for _ in range(N-1):#probably OK, maybe N
    #     for e in d:
    #         s, t = e
    #         if E[s] + d[e] < E[t]:
    #             E[t] = E[s] + d[e]
    # #if you want to know whether its path has negative cycle, we need followings.
    # for i in range(N):
    #     if V[i] == E[i]:
    #         print(V[i])
    #     else:
    #         print("NEGATIVE CYCLE")
        
if __name__ == '__main__':
    main()