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:
from collections import defaultdict
v_num, e_num, source = (int(n) for n in input().split(" "))
conn = []
cost = [float("inf") for n in range(v_num)]
cost[source] = 0
for _ in range(e_num):
    s1, t1, weight = (int(n) for n in input().split(" "))
    conn.append([s1, t1, weight])

def bellman_ford(source, conn, v_num, cost):
    for i in range(v_num):
        for s, t, weight in conn:
            if cost[t] > cost[s] + weight:
                if i == v_num - 1:
                    return True
                cost[t] = cost[s] + weight
    return False

if bellman_ford(source, conn, v_num, cost):
    print("NEGATIVE CYCLE")
else:
    cost = ["INF" if n == float("inf") else n for n in cost]
    for c in cost:
        print(c)