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>

const int N = 200005;

int n, a[N];
std::map<int, int> str;

bool check(int m) {
	for (int i = 1; i <= n; ++i) {
		if (a[i] > a[i - 1]) str[a[i - 1] + 1] = 1;
		else {
			std::map<int, int>::iterator it = str.upper_bound(a[i]);
			while (it != str.end()) str.erase(it++);
			for (it = --str.end(); ; --it) {
				if (it->second < m) {
					int c = it->second + 1;
					auto nxt = it; ++nxt;
					int b = nxt == str.end() ? a[i] : nxt->first - 1;
					str[b] = c; break;
				} else {
					it->second = 1;
				}
				if (it == str.begin()) return 0;
			}
		}
	}
	return 1;
}
int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	std::cin >> n;
	for (int i = 1; i <= n; ++i) std::cin >> a[i];
	int l = 1, r = n, ans = -1;
	while (l <= r) {
		int mid = l + r >> 1;
		if (check(mid)) r = mid - 1, ans = mid;
		else l = mid + 1;
	}
	std::cout << ans << '\n';
	return 0;
}
