There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.

At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the minimum possible number of different characters contained in the strings.

Examples

Input

3
3 2 1


Output

2


Input

5
2 3 2 1 2


Output

2
#include<bits/stdc++.h>
using namespace std;
const int N=200005;
int a[N],n;
map<int,int>m;
inline int check(int mid)
{
	if(mid==1)
	{
		for(int i=1;i<n;i++)
			if(a[i]>=a[i+1])
				return 0;
		return 1;
	}
	m.clear();
	for(int i=2;i<=n;i++)
	{
		if(a[i]<=a[i-1])
		{
			m.erase(m.upper_bound(a[i]),m.end());
			int k=a[i];
			m[k]++;
			for(;k&&m[k]==mid;)
			{
				m.erase(k);
				k--;
				m[k]++;
			}
			if(!k)
				return 0;
		}
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",a+i);
	int l=1,r=n,mid;
	while(l<r)
	{
		mid=l+r>>1;
		if(check(mid))
			r=mid;
		else
			l=mid+1;
	}
	printf("%d\n",l);
	return 0;
}
