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 <cstring>
#include <cstdio>
int lst[100005], to[200005], pre[200005], app[100005][25], tot, ans;
inline void add_edge(int u, int v)
{
	to[tot] = v; 
	pre[tot] = lst[u];
	lst[u] = tot++;
}
void dfs(int u, int fa = -1)
{
	for (int i = lst[u]; ~i; i = pre[i])
	{
		if (to[i] != fa)
		{
			dfs(to[i], u);
			for (int j = 0; j < 20; j++)
				app[u][j] += app[to[i]][j];
		}
	}
	int res = 0;
	for (int i = 19; i >= 0; i--)
	{
		if (app[u][i] > 1)
		{
			res = i + 1;
			break;
		}
	}
	while (app[u][res])
		res++;
	for (int j = 0; j < res; j++)
		app[u][j] = 0;
	app[u][res]++;
	if (res > ans)
		ans = res;
}
int main()
{
	// freopen("AGC009-D.in", "r", stdin);
	memset(lst, -1, sizeof(lst));
	int n;
	scanf("%d", &n);
	for (int i = 1; i < n; i++)
	{
		int u, v;
		scanf("%d%d", &u, &v);
		add_edge(--u, --v);
		add_edge(v, u);
	}
	dfs(0);
	printf("%d\n", ans);
	return 0;
}
