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<cstring>
#include<map>
#define maxn 200020
#define ll long long
using namespace std;
int n,a[maxn];
map<int,int>mp;
inline bool check(int x){
	mp.clear();
	for(int i=2;i<=n;++i){
		if(a[i]>a[i-1])continue;
		if(x==1)return 0;
		++mp[a[i]];
		map<int,int>::iterator it=mp.upper_bound(a[i]);
		while(it!=mp.end())mp.erase(it),it=mp.upper_bound(a[i]);
		int pos=a[i];
		while(pos&&mp[pos]==x){
			mp[pos]=0;
			++mp[--pos];
		}
		if(!pos)return 0;
	}
	return 1;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]);
	int l=1,r=n,mid=(l+r)>>1;
	while(l<r){
		if(check(mid))r=mid;
		else l=mid+1;
		mid=(l+r)>>1;
	}
	printf("%d\n",r);
	return 0;
}