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<cstdio>
#include<algorithm>
using namespace std;
const int N=2e5+5;
int n,a[N];pair<int,int>s[N];
bool check(int mid){
	for(int i=2,top=0;i<=n;++i)
		if(a[i]<=a[i-1]){
			if(mid==1)return false;
			while(top&&s[top].first>a[i])--top;
			if(top&&s[top].first==a[i])++s[top].second;
			else s[++top]={a[i],1};
			while(top&&s[top].second==mid){
				if(s[top].first==1)return false;
				if(top&&s[top-1].first==s[top].first-1)
					--top,++s[top].second;
				else s[top]={s[top].first-1,1};
			}
		}
	return true;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]);
	int l=1,r=n-1,res=n;
	while(l<=r){
		int mid=l+r>>1;
		if(check(mid))res=mid,r=mid-1;
		else l=mid+1;
	}
	printf("%d\n",res);
	return 0;
}
