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<iostream>
#include<algorithm>
#include<vector>

using namespace std;

#define sz(x) (int)(x.size())
#define rep(i,a,b) for(int i=a;i<b;++i)
#define pb push_back
///////////////////////

int const N = 3e5 + 41;
int const M = 25;

int n;
int d[N];
vector<int> e[N];

int dfs(int u, int p){
	int atleastOne = 0;
	int atleastTwo = 0;
	rep(i, 0, sz(e[u])){
		int to = e[u][i];
		if(to == p) continue;
		int res = dfs(to, u);
		atleastTwo|= (atleastOne & res);
		atleastOne |= res;
	}
	int ret;
	rep(i, 0, M){
		if( ((1<<i) > atleastTwo) && !(atleastOne&(1<<i)) ){
			ret = i;
			break;
		}
	}
	
	int result = (1 << ret);
	rep(i, ret, M){
		result |= ((1 << i) & atleastOne);
	}

	return d[u] = result;
}

void solve(){
	cin >> n;
	rep(i, 0, n-1){
		int u, v;
		cin >> u >> v;
		--u;--v;
		e[u].pb(v);
		e[v].pb(u);
	}
	int ansMask = dfs(0, 0);
	int ans = -1;
	while(ansMask){
		++ans;
		ansMask /= 2;
	}
	cout << ans << endl;
}

int main(){
#ifdef _DEBUG
	freopen("input.txt","r",stdin);
	freopen("output.txt","w",stdout);
#endif

	solve();

	return 0;
}