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;
#define mod 998244353
#define nn 200008
#define ll long long
int len[nn];int n;
map<int,int> m;
int tms=0;
int add(int x,int A)
{
	int y=x;
	while(m[x]>=A-1 and x>0) x--,tms++;
	if(!x) return 0;
	map<int,int>::iterator it=m.upper_bound(x),itt;
	while(it!=m.end()) itt=it,++it,m.erase(itt),tms++;
	m[x]++;return 1;
}
int check(int A)
{
	m.clear();tms=0;
	if(A==1)
	{
		for(int i=2;i<=n;i++)
		{
			if(len[i]<len[i-1]) return 0; 
		}return 1;
	}
	for(int i=2;i<=n;i++)
	{
		if(len[i]>len[i-1]) continue;
		else 
		{
			if(add(len[i],A)==0) return 0;
		}
	}
	return 1;
}
int main()
{	
	cin>>n;for(int i=1;i<=n;i++) scanf("%d",&len[i]);
	int l=1,r=n;int ans=0;
	while(l<=r)
	{
		int mid=(l+r)/2;
		if(check(mid))
			ans=mid,r=mid-1;
		else l=mid+1;
		//if(tms>n*4) assert(0);
	}
	cout<<ans;
    return 0;
}