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>
#define N 200001
int a[N],i,l,n,r,o[N],p[N],q;
inline bool check(int s)
{
	if(s==1)
	{
		for(i=1;i<n;i++)if(a[i]>=a[i+1])return false;
		return true;
	}
	for(i=1,q=0;i<=n;i++)
	if(o[q]<a[i])o[++q]=a[i],p[q]=1;
	else
	{
		while(a[i]<o[q])q--;
		if(o[q]!=a[i])o[++q]=a[i],p[q]=2;
		else if(p[q]!=s)p[q]++;
		else
		{
			for(;o[q-1]+1==o[q]&&p[q-1]==s;q--);
			if(o[q-1]+1==o[q]&&q==1)return false;
			else if(o[q]==o[q-1]+1)p[q-1]++,o[q]=a[i],p[q]=1;
			else o[q]--,p[q]=2,o[++q]=a[i],p[q]=1;
		}
	}
	return true;
}
int main()
{
	scanf("%d",&n),l=1,r=n;
	for(i=1;i<=n;i++)scanf("%d",a+i);
	while(l<r)check(l+r>>1)?r=l+r>>1:l=l+r+2>>1;
	return 0*printf("%d\n",l);
}