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<iostream>
#include<map>
#include<algorithm>
using namespace std;

int a[1000000],n;

int check(int m)
{
	int i;
	if(m==1)
	{
		for(i=1; i<n; ++i)
			if(a[i]>=a[i+1])
				return 0;
		return 1;
	}
	map<int,int> f;
	for(i=2; i<=n; ++i)
		if(a[i]<=a[i-1])
		{
			f.erase(f.upper_bound(a[i]),f.end());
			int k=a[i];
			++f[k];
			while(k>0&&f[k]==m)
				f.erase(k),++f[--k];
			if(!k)
				return 0;
		}
	return 1;
}

int main()
{
	cin>>n;
	int i;
	for(i=1; i<=n; ++i)
		scanf("%d",&a[i]);
	int l=1,r=n,m;
	while(l<r)
	{
		m=l+r>>1;
		if(check(m))
			r=m;
		else
			l=m+1;
	}
	cout<<l;
}
