CodeForces - 1325C Ehab and Path-etic MEXs

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

Every label is an integer between 00 and n−2n−2 inclusive.
All the written labels are distinct.
The largest value among MEX(u,v)MEX(u,v) over all pairs of nodes (u,v)(u,v) is as small as possible.

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

Input

The first line contains the integer nn (2≤n≤1052≤n≤105) — the number of nodes in the tree.

Each of the next n−1n−1 lines contains two space-separated integers uu and vv (1≤u,v≤n1≤u,v≤n) that mean there's an edge between nodes uu and vv. It's guaranteed that the given graph is a tree.

Output

Output n−1n−1 integers. The ithith of them will be the number written on the ithith edge (in the input order).

Examples

Input

3
1 2
1 3

Output

0
1

Input

Output

Note

The tree from the second sample:

Sponsor

贪心就行只要是叶节点就从0往后递增

不是根节点就从n-2往前递减

#include<bits/stdc++.h>
const int maxn = 1e5 + 5;
int degree[maxn];
int a[maxn];
int b[maxn];
using namespace std;
int main(){int n;cin >> n;for(int i = 1; i < n; i++){cin >> a[i] >> b[i];degree[a[i]]++;degree[b[i]]++;}int cnt = 0;int cnt2 = n - 2;for(int i = 1; i < n; i++){if(degree[a[i]] == 1 || degree[b[i]] == 1){cout << cnt << endl;cnt++;}else{cout << cnt2 << endl;cnt2--;}}
}

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