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 n,a[200005];
inline bool check(int x){
	if(x==1){
		bool flag=1;
		for(int i=1;i<n;i++)	if(a[i+1]<=a[i])	flag=0;
		return flag;
	}
	map<int,int> mp;
	int cur=0;
	for(register int i=1;i<=n;i++){
		if(a[i]<=cur){
			cur=a[i];
			while(1){
				if(mp[cur]<x-1)	break;
				mp[cur]=0;
				cur--;
			}
			mp[cur]++;
			if(cur<=0)	return 0;
		}
		else	cur=a[i];
		mp.erase(mp.upper_bound(cur),mp.end());
	}
	return 1;
}
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)	cin>>a[i];
	int l=1,r=300000,ans;
	while(l<=r){
		int mid=(l+r)>>1;
		if(check(mid))	ans=mid,r=mid-1;
		else			l=mid+1;
	}
	cout<<ans<<endl;
	return 0;
}