1325_C. Ehab and Path-etic MEXs
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>
```python
n = int(input())
occ = [0 for i in range(n)]
graph = [[0,0] for i in range(n-1)]
for i in range(n-1):
    x, y = map(int,input().split())
    occ[x-1]+=1
    occ[y-1]+=1
    graph[i][0] = x-1
    graph[i][1] = y-1
    
fin = [-1 for i in range(n-1)]
for i in range(n):
    if occ[i] >= 3 :
        var = 0
        for j in range(n-1):
            if graph[j][0] == i or graph[j][1] == i:
                fin[j] = var
                var += 1
        break
else:
    var = 0
    for i in range(n):
        if var > 1:
            break
        if occ[i] == 1:
            for j in range(n-1):
                if graph[j][0] == i or graph[j][1] == i:
                    fin[j] = var
                    var += 1
                    break
for i in fin:
    if n == 2:
        print(0)
        break
    if i == -1:
        print(var)
        var += 1
    else:
        print(i)
```