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>
#define rep(i,n) for ((i)=1;(i)<=(n);(i)++)
using namespace std;
int a[500005],b[500005],c[500005],n,i,j,l,r,mid,ans,aa[500005];
bool check(int x)
{
	int i,tp=0,j;
	rep(i,n)
	{
		if (aa[i]>aa[i-1])
		{
			tp++;
			a[tp]=b[tp-1]+1;
			b[tp]=aa[i];
			c[tp]=1;
		}
		if (aa[i]<aa[i-1])
		{
			while (b[tp]>aa[i])
			{
				if (a[tp]<=aa[i]) b[tp]=aa[i]; else tp--;
			}
		}
		if (aa[i]<=aa[i-1])
		{
			int f=aa[i]+1;
			for (j=tp;j;j--)
			{
				if (c[j]==x)
				{
					f=a[j];
				}
				else break;
			}
			if (j<1) return 0;
			if (a[j]==b[j]) c[j]++; else
			{
				b[j]--;
				j++;
				a[j]=b[j]=b[j-1]+1;
				c[j]=c[j-1]+1;
			}
			tp=j;
			if (f<=aa[i])
			{
				tp++;
				a[tp]=f;
				b[tp]=aa[i];
				c[tp]=1;
			}
		}
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	rep(i,n)
	{
		scanf("%d",&aa[i]);
	}
	l=0;r=ans=n;
	while (l<r)
	{
		mid=(l+r+1)/2;
		if (check(mid))
		{
			r=mid-1;
			ans=mid;
		}
		else l=mid;
	}
	cout<<ans<<endl;
	return 0;
}