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;
int a[200003],n;
map<int,int>built;
bool check(int num){
	built.clear();
	int l=0;
	for(int i=0;i<n;i++){
		if(a[i]>l)
			l=a[i];
		else{
			while(!built.empty()&&built.rbegin()->first>=a[i])built.erase(built.rbegin()->first);
			int c=a[i]-1; 
			built[c]++;
			while(built[c]>=num){
				built.erase(c);
				c--;
				built[c]++;
				if(c<0)return 0;
			}
			l=a[i];
		}
	}
	return 1;
}
int main(){
	cin>>n;
	for(int i=0;i<n;i++)scanf("%d",&a[i]);
	bool k=1;
	for(int i=1;i<n;i++)
		if(a[i]<=a[i-1])
			k=0;
	if(k){
		cout<<1;
		return 0;
	}
	int l=1,r=n+1;
	while(r>l+1){
		int mid=(l+r)/2;
		if(check(mid))
			r=mid;
		else
			l=mid;
	}
	cout<<r;
}