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 <iostream>

const int N = 200000 + 7;

int n;
int a[N];

int check(int x) {
	static int pos[N], chr[N], top;

	auto split = [&](int p) {
		while (top && pos[top] >= p) --top;
		int c = chr[top + 1];
		if (pos[top] < p - 1) pos[++top] = p - 1, chr[top] = c;
		pos[++top] = p, chr[top] = c;
	};
	pos[top = 1] = a[1], chr[1] = 1;
	for (int i = 2; i <= n; ++i)
		if (a[i] > a[i - 1])
			pos[++top] = a[i], chr[top] = 1;
		else {
			split(a[i]);	
			while (top && chr[top] == x) --top;
			if (!top) return 0;
			split(pos[top]), ++chr[top];
			if (pos[top] < a[i]) pos[++top] = a[i], chr[top] = 1;
		}
	return 1;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) scanf("%d", a + i);
	int l = 1, r = n, m;
	while (l < r)
		check(m = l + r >> 1) ? (r = m) : (l = m + 1);
	printf("%d", r);
	return 0;
}
