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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<string>
#include<algorithm>
#define N 200005
using namespace std;
int n,top;
int s[N],st1[N],st2[N];
bool check(int a){
	top=0;
	for(int i=1;i<=n;i++){
		if(s[i]<=s[i-1]){
			if(a==1) return 0;
			while(top>0&&st1[top]>s[i]) top--;
			if(st1[top]==s[i]) st2[top]++;
			else top++,st1[top]=s[i],st2[top]=1;
			while(st2[top]>=a&&top!=0){
				if(st1[top]-st1[top-1]==1) st2[top-1]++,top--;
				else{st1[top]--;st2[top]=1;break;}
			}
			if(top==0&&st2[top]!=0) return 0;
		}
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&s[i]);
	int l=1,r=n;
	while(l+1<r){
		int mid=(l+r)>>1;
		if(check(mid)) r=mid;
		else l=mid;
	}
	if(check(l)) printf("%d\n",l);
	else printf("%d\n",r);
	return 0;
}