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;
const int N=2e5+11;
int a[N],n;
int chk(int m){
	int i;
	if(m==1){
		for(i=1;i<n;++i)if(a[i]>=a[i+1])return 0;
		return 1;
	}
	map<int,int> f;
	for(i=2;i<=n;++i)if(a[i]<=a[i-1]){
		f.erase(f.upper_bound(a[i]),f.end());
		int k=a[i];
		++f[k];
		while(k>0&&f[k]==m)f.erase(k),++f[--k];
		if(!k)return 0;
	}
	return 1;
}
int main(){
	cin>>n;
	int i;
	for(i=1;i<=n;++i)scanf("%d",a+i);
	int l=1,r=n,m;
	while(l<r){
		m=l+r>>1;
		if(chk(m))r=m;
		else l=m+1;
	}
	cout<<l;
}