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;

int a[222222], s[20];
int main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
		scanf("%d", a + i);
	for (int i = 0; i < n - 1; i++)
		if (a[i] >= a[i + 1])
			goto q;
	cout << 1 << endl;
	return 0;
q:
	int l = 1, r = n;
	while (l + 1 < r) {
		int m = (l + r) / 2;
		fill(s, s + 20, 0);
		for (int i = 1; i < n; i++) {
			if (a[i - 1] < min(a[i], 20)) {
				fill(s + a[i - 1], s + 20, 0);
				continue;
			}
			if (a[i] > 20)
				continue;
			int j = a[i] - 1;
			while (j + 1 && ++s[j] == m)
				s[j--] = 0;
			if (j < 0) goto p;
		}
		r = m;
		continue;
	p:
		l = m;
	}
	cout << r << endl;
	return 0;
}
