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 <iostream>
#include <algorithm>
#define ll long long
template <class T>
inline void read(T &x)
{
   x=0; char c=getchar(); int f=1;
   while(!isdigit(c)){if(c=='-')f=-1; c=getchar();}
   while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int N=2e5+10;
int a[N];
int pos[N],num[N],top,n;
bool che(int b)
{
	top=0;
	for(int i=2;i<=n;i++)
	if(a[i]<=a[i-1])
	{
		int tmp=a[i];
		while(top&&pos[top]>tmp) top--;
		while(top&&tmp&&pos[top]==tmp&&num[top]==b-1) tmp--,top--;
		if(tmp==0) return 0;
		if(pos[top]<tmp){ pos[++top]=tmp,num[top]=1; if(b<2) return 0;}
		else num[top]++;
	}
	return 1;
}
int main()
{
	read(n);
	for(int i=1;i<=n;i++) read(a[i]);
	int l=1,r=n;
	while(l<r)
	{
		int mid=l+r>>1;
		if(che(mid)) r=mid;
		else l=mid+1;
	}
	printf("%d",r);
	return 0;
}