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>
using namespace std;
int n,a[300001];
bool add1(list<pair<int,int>> &v,int base)
{
	if(base==1)return 0;
	auto it=--v.end();
	for(;;)
	{
		if(it->first>1)v.insert(it,{it->first-1,it->second}),it->first=1;
		if(++it->second<base)break;
		if(it==v.begin())return 0;
		it-- ->second=0;
	}
	return 1;
}
bool check(int base)
{
	list<pair<int,int>> v;
	v.push_back({a[1],0});
	for(int i=2;i<=n;i++)
		if(a[i-1]<a[i])v.push_back({a[i]-a[i-1],0});
		else
		{
			int x=a[i-1]-a[i];
			while(x)
				if(v.back().first<=x)x-=v.back().first,v.pop_back();
				else v.back().first-=x,x=0;
			if(!add1(v,base))return 0;
		}
	return 1;
}
int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i];
	int l=1,r=n,ans=n;
	while(l<=r)
	{
		int m=(l+r)/2;
		if(check(m))ans=m,r=m-1;
		else l=m+1;
	}
	cout<<ans<<'\n';
}
