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;

const int maxn = 2e5;
int n, a[maxn + 3];

bool check(int k) {
	map<int, int> M;
	for (int i = 1; i <= n; i++) {
		if (a[i] <= a[i - 1]) {
			if (k == 1) {
				return false;
			}
			while (!M.empty() && M.rbegin() -> first > a[i]) {
				map<int, int>::iterator it = M.end();
				M.erase(--it);
			}
			for (int j = a[i]; j >= 0; j--) {
				if (j == 0) {
					return false;
				}
				if (++M[j] == k) {
					M[j] = 0;
				} else {
					break;
				}
			}
		}
	}
	return true;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	int l = 1, r = n, mid;
	while (l < r) {
		mid = (l + r) >> 1;
		if (check(mid)) {
			r = mid;
		} else {
			l = mid + 1;
		}
	}
	printf("%d\n", l);
	return 0;
}