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
inf = math.inf
negative_cycle_flag = False

def INITSS (G, s): # s means start
    # for u in G.V:
    #      u.d = inf
    #      u.pi = None
    G.V_d[s] = 0


def RELAX(u, v, w, V_d, V_pi):
    if V_d[v] > V_d[u] + w[u][v]:
        V_d[v] = V_d[u] + w[u][v]
        V_pi[v] = u


def BELLMANFORD (G, s, w):# w is weight matrix
    global negative_cycle_flag
    INITSS(G, s)
    for i in range(1,len(G.V_d)):
        for u, v in G.E:
            RELAX(u, v, w, G.V_d, G.V_pi)

    for u, v in G.E:
        if G.V_d[u] + w[u][v] < G.V_d[v]:
            negative_cycle_flag = True
            break

class Graph:
    def __init__(self, v_num, e_num, E):
        self.V_d = [inf for _ in range(v_num)]
        self.V_pi = [None for _ in range(v_num)]
        self.E = E

v_num, e_num, s = map(int, input().split())
E =[]
w = [[inf for _ in range(v_num)] for _ in range(v_num)]
for _ in range(e_num):
    u, v, weight = map(int, input().split())
    w[u][v] = weight
    E.append((u, v))

G = Graph(v_num, e_num, E)

BELLMANFORD(G, s, w)
if negative_cycle_flag == True:
    print("NEGATIVE CYCLE")
else:
    for k in range(v_num):
        if(G.V_d[k]==inf):
            print("INF")
        else:
            print(G.V_d[k])