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 <cstdio>
const int M=101000;
#define A(a,b) y[++t]=b,N[t]=F[a],F[a]=t
int n,i,u,v,x,t,y[2*M],N[2*M],F[2*M],Q[2*M];
inline int DFS(int u,int f) {
	int K=0,P=0,S=0;
	for (int j=F[u];j;j=N[j])if(y[j]!=f)S|=((K=DFS(y[j],u))&P),P|=K;
	return(P|((1<<Q[S]+1)-1))+1;
}
int main() {
	scanf("%d",&n);
	for (i=0;i<n-1;i++) scanf("%d%d",&u,&v),A(u,v),A(v,u);
	for (Q[0]=-1,i=2;!(i>>17);i++) Q[i]=Q[i>>1]+1;
	printf("%d\n",Q[DFS(1,0)]);
}
