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 <bits/stdc++.h>

#define FI(i,a,b) for(int i=(a);i<=(b);i++)
#define FD(i,a,b) for(int i=(a);i>=(b);i--)

#define LL long long
#define Ldouble long double
#define PI 3.1415926535897932384626

#define PII pair<int,int>
#define PLL pair<LL,LL>
#define mp make_pair
#define fi first
#define se second

using namespace std;

#define M 300003

int n, ans;
vector<int> v[M];
int lab[M];

void dfs(int id, int pv){
	int bitcnt[19];
	memset(bitcnt, 0, sizeof(bitcnt));
	for(auto to: v[id]) if(to != pv){
		dfs(to, id);
		FI(j, 0, 18) if(lab[to] & (1 << j)) bitcnt[j]++;
	}
	FD(i, 18, 0) if(bitcnt[i] > 1){
		FD(j, i, 0) bitcnt[j] = 1;
		break;
	}
	FI(i, 0, 18) lab[id] += bitcnt[i] * (1 << i);
	lab[id]++;
//	printf("%d: %d\n", id, lab[id]);
}

int main(){
	scanf("%d", &n);
	FI(i, 2, n){
		int a, b;
		scanf("%d %d", &a, &b);
		v[a].push_back(b);
		v[b].push_back(a);
	}
	dfs(1, 0);
	int ans = 0;
	while(lab[1]){
		ans++;
		lab[1] >>= 1;
	}
	printf("%d\n", ans - 1);
	return 0;
}