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 N = 200005;
int n, a[N];

bool check(int mid) {
	map<int, int> b;
	for (int i = 2; i <= n; ++i) {
		while (!b.empty() && b.rbegin()->first >= a[i])
			b.erase(--b.end());
		if (a[i] <= a[i - 1]) {
			++b[a[i] - 1];
			for (int j = a[i] - 1; b.count(j) && b[j] == mid; --j) {
				b.erase(j);
				if (j == 0) return false;
				++b[j - 1];
			}
		}
	}
	return true;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i)
		scanf("%d", a + i);
	bool flag = true;
	for (int i = 2; i <= n; ++i)
		flag &= a[i] > a[i - 1];
	if (flag) return puts("1"), 0;
	int l = 2, r = n;
	while (l < r) {
		int mid = l + r >> 1;
		if (check(mid)) r = mid;
		else l = mid + 1;
	}
	printf("%d\n", r);
	return 0;
}
