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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
import time,random

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
mod2 = 998244353
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)

class BellmanFord:
    def __init__(self, n):
        self.N = n
        self.e = collections.defaultdict(list)

    def add(self, u, v, d):
        self.e[u].append((v,d))

    def delete(self, u, v):
        self.e[u] = [_ for _ in self.e[u] if _[0] != v]

    def search(self, s):
        d = collections.defaultdict(lambda: inf)
        d[s] = 0
        update = True
        cnt = 0
        while update:
            cnt += 1
            if cnt > self.N:
                return d,True
            update = False
            for k,v in self.e.items():
                if d[k] == inf:
                    continue
                dk = d[k]
                for n,nd in v:
                    if d[n] > dk + nd:
                        update = True
                        d[n] = dk + nd

        return d,False

    # 繝｡繧ｽ繝・ラ縺ｮ縺ｿ迚・
    def search(s, N):
        d = collections.defaultdict(lambda: inf)
        d[s] = 0
        update = True
        cnt = 0
        while update:
            cnt += 1
            if cnt > N:
                return d,True
            update = False
            for k,v in e.items():
                if d[k] == inf:
                    continue
                dk = d[k]
                for n,nd in v:
                    if d[n] > dk + nd:
                        update = True
                        d[n] = dk + nd

        return d,False


def main():
    v,e,r = LI()
    std = [LI() for _ in range(e)]

    e = collections.defaultdict(list)
    for s,t,d in std:
        e[s].append((t,d))

    def search(s, N):
        d = collections.defaultdict(lambda: inf)
        d[s] = 0
        us = set([s])
        cnt = 0
        while us:
            cnt += 1
            if cnt > N:
                return d,True
            ns = set()
            for k,v in e.items():
                if d[k] == inf:
                    continue
                dk = d[k]
                for n,nd in v:
                    if d[n] > dk + nd:
                        ns.add(n)
                        d[n] = dk + nd
            us = ns

        return d,False

    d,f = search(r,v)
    if f:
        return "NEGATIVE CYCLE"

    r = []
    for i in range(v):
        t = d[i]
        if t == inf:
            r.append("INF")
        else:
            r.append(t)


    return JA(r, "\n")

print(main())