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 n;
int a[210000];

bool ok(int x) {
	if (x == 1) {
		for (int i = 1; i < n; i++)
			if (a[i + 1] <= a[i])
				return false;
		return true;
	}
	map <int, int> Map;
	for (int i = 1; i <= n; i++) {
		if (a[i] > a[i - 1]) {
			continue;
		}
		while (!Map.empty() && Map.rbegin()->first >= a[i])
			Map.erase(Map.rbegin()->first);
		int tmp = a[i] - 1;
		while (true) {
			int xx = 1;
			if (Map.count(tmp))
				xx = Map[tmp];
			if (xx + 1 <= x) {
				Map[tmp] = xx + 1;
				break;
			}else {
				if (Map.count(tmp))
					Map.erase(tmp);
			}
			tmp--;
			if (tmp < 0) {
				return false;
			}
		}
	}
	return true;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		scanf("%d", &a[i]);

	int l = 0, r = 1e9, mid;
	while (l < r - 1) {
		mid = (l + r) / 2;
		if (ok(mid))
			r = mid;
		else
			l = mid;
	}
	printf("%d\n", r);
}