Problem: You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:

  * Every label is an integer between 0 and n-2 inclusive. 
  * All the written labels are distinct. 
  * The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. 



Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.

Input

The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).

Examples

Input


3
1 2
1 3


Output


0
1


Input


6
1 2
1 3
2 4
2 5
5 6


Output


0
3
2
4
1

Note

The tree from the second sample:

<image>

Solution (in PYTHON3):

Solution:
from collections import deque
El = []
Er = []
En = []
# g = defaultdict(lambda: [])
N = int(input())
# N = 10**5
g = [[0] for _ in range(N+1)]
dist = [2**20 for _ in range(N+1)]
visited = [0] * (N+1)
# print(time.time() - start)
for num in range(N-1):
    u, v = list(map(int, input().split()))
    # u, v = num+1, num+2
    g[u][0] += 1
    g[u].append(v)
    g[v][0] += 1
    g[v].append(u)
    El.append(v)
    Er.append(u)
    En.append(num)
    # E.append( [v, u, num] )
# print(time.time() - start)

order = []
# dst(1)
s = deque([1])
while s:
    v = s.pop()
    visited[v] = 1
    order.append(v)
    for i in g[v][1:]:
        if not visited[i]:
            s.append(i)
# print(time.time() - start)

for u in reversed(order):
    if g[u][0] == 1:
        dist[u] = 0
    else:
        dist[u] = min([dist[u]] + [dist[v]+1 for v in g[u][1:]])

# print(time.time() - start)
for u in order:
    if g[u][0] == 1:
        dist[u] = 0
    else:
        prdist = dist[u]
        dist[u] = min([dist[u]] + [dist[v]+1 for v in g[u][1:]])
        if dist[u] == prdist:
            break
# print(time.time() - start)

keys = [dist[el]+dist[er] for el, er in zip(El, Er)]
X = [(e, n) for n, e in enumerate(sorted(En, key=lambda x: keys[x]))]

# print(time.time() - start)

print('\n'.join([str(i) for _, i in sorted(X)]))