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<iostream>
#include<map>
using namespace std;
const int N=2e5+10;
int n,a[N],l=1,r=N-10,mid,ans;
map<int,int>p;
inline bool judge(int x){
	p.clear();
	for(register int i=2;i<=n;i++){
		if(a[i]>a[i-1])continue;
		if(x==1)return 0;
		++p[a[i]];
		map<int,int>::iterator it=p.upper_bound(a[i]);
		while(it!=p.end())p.erase(it),it=p.upper_bound(a[i]);
		int pos=a[i];
		while(pos&&p[pos]==x)p[pos]=0,++p[--pos];
		if(!pos)return 0;
	}
	return 1;
}
int main(){
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)scanf("%d",&a[i]);
	while(l<=r){mid=(l+r+1)>>1;if(judge(mid))ans=mid,r=mid-1;else l=mid+1;}
	printf("%d\n",ans);return 0;
}