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<iostream>
#include<algorithm>
#include<cstdio>
#include<map>
using namespace std;
const int maxn = 2e5 + 5;
int n;
int a[maxn];
map<int,int>s;
bool isok(int mid) {
	s.clear();
	for(int i=2;i<=n;i++) {
		if(a[i]<=a[i-1]) {
			while(!s.empty()&&((s.rbegin()->first) )>a[i]) {
				s.erase(--s.end());
			}
			for(int j=a[i];j>=1;j--) {
				if(s[j]+1==mid) {
					s.erase(j);
				} else {
					s[j]++; break;
				}
				if(j==1) return 0;
			}
		}
	}
	return 1;
}
int main() {
	scanf("%d",&n);
	for(int i=1;i<=n;i++) {
		scanf("%d",&a[i]);
	}
	bool fl = 1;
	for(int i=2;i<=n;i++) {
		if(a[i]<=a[i-1]) {
			fl = 0; break;
		}
	}
	if(n==1||fl) {
		puts("1"); return 0;
	}
	int L = 2; int R = n,mid,ans;
	while(L<=R){
		mid = (L+R)>>1;
		if(isok(mid)) ans = mid , R = mid - 1;
		else L = mid + 1;
	}
	printf("%d",ans);
}