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
//骗分不规范，爆零两行泪
#include<bits/stdc++.h>
#define ll long long
#define mp make_pair
using namespace std;
const int mxn=2e5+5;
int n,a[mxn];
inline bool ok(int md){
	if(md==1){
		for(int i=1;i<n;++i)if(a[i]>=a[i+1])return 0;
		return 1;
	}
	map<int,int>m;m.clear();
	for(int i=2;i<=n;++i)if(a[i]<=a[i-1]){
		m.erase(m.upper_bound(a[i]),m.end());
		int k=a[i];++m[k];
		for(;k and m[k]==md;)m.erase(k),++m[--k];
		if(!k)return 0;
	}
	return 1;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",a+i);
	int l=1,r=n,md;
	for(;l<r;){
		md=l+r>>1;
		if(ok(md))r=md;
		else l=md+1;
	}
	printf("%d\n",l);
}