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>
int a[200200],n;
inline bool check(int k){
	std::map<int,int> map;
	for(int i = 1;i <= n;++i) if(a[i] <= a[i - 1]){
		while(map.size() && map.rbegin() -> first > a[i - 1]) map.erase(--map.end());
		int now = a[i];
		for(;now > 0 && ++map[now] == k;--now) map[now] = 0;
		if(now <= 0) return 0;
	}
	return 1;
}
int main(){
	std::ios::sync_with_stdio(false),std::cin.tie(0);
	std::cin >> n; int flg = 1;
	for(int i = 1;i <= n;++i) std::cin >> a[i],flg &= a[i] > a[i - 1];
	if(flg) return std::cout << 1 << '\n',0;
	int l = 1, r = n;
	for(;l + 1 != r;){
		int mid = l + r >> 1;
		if(check(mid)) r = mid;
		else l = mid;
	}
	std::cout << r << '\n';
}
