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
# Your code here!
"""
Bellman_Ford
単一始点最短経路を求める
g: グラフの隣接リスト
start: 始点
返り値: dist, is_OK (負回路なしならTrue)
"""
def Bellman_Ford(g,start):
    n = len(g)    
    dist = [float("inf")]*n
    dist[start] = 0
    
    for i in [0]*(n):
        updated = False
        for v in range(n):
            for to, cost in g[v]:
                if dist[to] <= dist[v] + cost: continue
                dist[to] = dist[v] + cost
                updated = True
        if not updated: break
    else: return None, False #n周更新された場合
    return dist, True        
    

"""
###############################################################
AOJ: GRL_1_B http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_B

##############################################################
"""

v,e,r = [int(i) for i in input().split()]
std = [[int(i) for i in input().split()] for _ in range(e)]

g = [[] for _ in range(v)]
for s,t,d in std:
    g[s].append((t,d))


dist, tf = Bellman_Ford(g,r)
if tf:
    for i in dist:
        print(i if i != float("inf") else "INF")
else: print("NEGATIVE CYCLE")