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>
#include<algorithm>
#include<map>
using namespace std;
int n,a[200020];
bool check(int w)
{
	map<int,int>s;
	int len=0;
	for(int i=1;i<=n;++i)
	{
		if(a[i]>a[i-1])len=a[i];
		else
		{
			while(s.size()&&s.rbegin()->first>a[i])s.erase(s.rbegin()->first);
			len=a[i];++s[len];
			int x=len;
			while(s[x]==w)
			{
				if(x==1)return 0;
				s[x]-=w;
				++s[x-1];
				--x;
			}
		}
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]);
	bool flag=0;
	for(int i=1;i<n;++i)if(a[i]>=a[i+1])flag=1;
	if(!flag)return printf("1"),0;
	int l=2,r=n,mid;
	while(l<r)
	{
		mid=l+r>>1;
		if(check(mid))r=mid;
		else l=mid+1;
	}
	printf("%d",l);
	return 0;
}
