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:

inputFormat

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.

outputFormat

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:

样例

6
1 2
1 3
2 4
2 5
5 6

0
3
1
2
4

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