We will recursively define uninity of a tree, as follows: (Uni is a Japanese word for sea urchins.)

* A tree consisting of one vertex is a tree of uninity 0.
* Suppose there are zero or more trees of uninity k, and a vertex v. If a vertex is selected from each tree of uninity k and connected to v with an edge, the resulting tree is a tree of uninity k+1.



It can be shown that a tree of uninity k is also a tree of uninity k+1,k+2,..., and so forth.

You are given a tree consisting of N vertices. The vertices of the tree are numbered 1 through N, and the i-th of the N-1 edges connects vertices a_i and b_i.

Find the minimum k such that the given tree is a tree of uninity k.

Constraints

* 2 ≦ N ≦ 10^5
* 1 ≦ a_i, b_i ≦ N(1 ≦ i ≦ N-1)
* The given graph is a tree.

Input

The input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

Print the minimum k such that the given tree is a tree of uninity k.

Examples

Input

7
1 2
2 3
2 4
4 6
6 7
7 5


Output

2


Input

12
1 2
2 3
2 4
4 5
5 6
6 7
7 8
5 9
9 10
10 11
11 12


Output

3
#include <algorithm>
#include <bitset>
#include <cstdio>
#include <iostream>
#include <vector>

const int N = 100000;

std::vector<int> tree[N];

int dfs(int p, int u)
{
    int ban = 0;
    int k = 0;
    for (auto&& v : tree[u]) {
        if (v != p) {
            int ret = dfs(u, v);
            int high = 31 - (int)__builtin_clz(ban & ret);
            k = std::max(k, high);
            ban |= ret;
        }
    }
    while (ban >> k & 1) {
        k ++;
    }
    return (ban | (1 << k)) & ~((1 << k) - 1);
}

int main()
{
#ifdef LOCAL_JUDGE
    freopen("D.in", "r", stdin);
#endif
    int n;
    while (scanf("%d", &n) == 1) {
        for (int i = 0; i < n; ++ i) {
            tree[i].clear();
        }
        for (int i = 1; i < n; ++ i) {
            int a, b;
            scanf("%d%d", &a, &b);
            a --;
            b --;
            tree[a].push_back(b);
            tree[b].push_back(a);
        }
        auto result = dfs(-1, 0);
        printf("%d\n", 31 - __builtin_clz(result));
    }
}