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<cstdio>
#include<cstring>
using namespace std;
int n,a[210000];
struct node
{
	int x,p;
}sta[210000];int top;
bool pand(int x)
{
	sta[0].p=0;top=1;
	sta[1].x=1;sta[1].p=a[1];
	for(int i=2;i<=n;i++)
	{
		if(sta[top].p<a[i])
		{
			if(sta[top].x==1)sta[top].p=a[i];
			else sta[++top]=(node){1,a[i]};
		}
		else
		{
			while(top>0&&sta[top].p>a[i])top--;
			if(sta[top].p!=a[i])sta[++top]=(node){1,a[i]};
			sta[top].x++;
			while(sta[top].x==x)
			{
				if(sta[top-1].p!=sta[top].p-1)
				{
					sta[top].x=2;
					sta[top].p=sta[top].p-1;
				}
				else
				{
					top--;
					if(top==0)return false;
					sta[top].x++;
				}
			}
			if(sta[top].p!=a[i])sta[++top]=(node){1,a[i]};
		}
	}
	return true;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	int l=2,r=n+1;
	while(l<r)
	{
		int mid=(l+r)/2;
		if(pand(mid))r=mid;
		else l=mid+1;
	}
	printf("%d\n",r-1);
	return 0;
}