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;
map<int,int>mp;
int a[200100],n;

bool chk(int x){
	mp.clear();
	for(int i=1;i<=n;++i)
		if(a[i]<=a[i-1]){
			for(auto it=mp.upper_bound(a[i]);it!=mp.end();it=mp.upper_bound(a[i]))mp.erase(it);
			++mp[a[i]];
			if(x==1)return 0;
			for(int j=a[i];mp[j]>=x;--j){
				if(j==1)return 0;
				mp[j]-=x;mp[j-1]++;
			}
		}
	return 1;
}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;++i)cin>>a[i];
	int l=1,r=n;
	while(l<r){
		int mid=(l+r)/2;
		if(chk(mid))r=mid;
		else l=mid+1;
	}
	cout<<l<<'\n';
	return 0;
}
