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;
typedef long long LL;
const int N=200200;
int n;
int a[N];
map<int,int> st;
bool test(int cnt){
	st.clear();
	for(int i=1;i<=n;i++){
		if(a[i]<=a[i-1]){
			int j=a[i];
			while(++st[j]==cnt){
				j--;
				if(j==0||cnt==1){
					return false;
				}
			}
			while(!st.empty()&&(--st.end())->first>j){
				st.erase(--st.end());
			}
		}
	}
	return true;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
	}
	a[0]=0;
	int l=1,r=n;
	while(l<r){
		int mid=(l+r)>>1;
		if(test(mid)){
			r=mid;
		}
		else{
			l=mid+1;
		}
	}
	printf("%d\n",l);
}