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 <cstdio>
#include <map>
using namespace std;
int a[200010];
int n;
int can(int x) {
	map<int, int> m;
	for (int i = 1; i < n; i++) {
		if (a[i-1] >= a[i]) {
			if (x == 1) return 0;
			map<int, int>::iterator it = m.lower_bound(a[i]);
			m.erase(it, m.end());
			int c = 1;
			for (int j = a[i]-1; j >= 0; j--) {
				if (!c) break;
				if (++m[j] >= x) {
					m.erase(j);
					c = 1;
				} else {
					c = 0;
				}
			}
			if (c) return 0;
		}
	}
	return 1;
}
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d", &a[i]);
	}
	int lo = 0, hi = n;
	while (lo + 1 < hi) {
		int mid = (lo + hi) / 2;
		if (can(mid)) {
			hi = mid;
		} else {
			lo = mid;
		}
	}
	printf("%d\n", hi);
	return 0;
}
