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>
const int N=2e5+10;
int a[N],n;
using namespace std;
typedef pair<int,int> pi;
set<pi> s;
int check(int lim){
	s.clear();
	s.insert(make_pair(-1,0));
	for (int i=1;i<=n;i++){
		if (a[i]>a[i-1])continue;
		while (s.size()&&s.rbegin()->first>a[i])s.erase(*s.rbegin());
		for (int j=a[i];j>=0;j--){
			if (j==0)return 0;
			if (s.rbegin()->first!=j){
				s.insert(make_pair(j,2));
				break;
			}
			int k=s.rbegin()->second;
			s.erase(*s.rbegin());
			if (k<lim){
				s.insert(make_pair(j,k+1));
				break;
			}
		}
	}
	return 1;
}
int main(){
	cin>>n;
	int ans=0;
	for (int i=1;i<=n;i++)scanf("%d",&a[i]),ans|=a[i]<=a[i-1];
	if (!ans){
		cout<<1<<endl;
		return 0;
	}
	for (int u=1<<18;u;u>>=1){
		if (check(ans+u));
		else ans+=u;
	}
	cout<<ans+1<<endl;
}