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>

typedef std::map <int, int> map;
const int N = 200054;

int n, a[N];
map M;

inline bool check(int B) {
	int i, L = a[1]; bool result;
	map::iterator it; M.clear();
	for (i = 2; i <= n; ++i) if (a[i] <= L) {
		for (L = a[i]; !M.empty(); )
			if (it = --M.end(), it->first >= L) M.erase(it);
			else if (it->first == L - 1 && it->second == B - 1) M.erase(it), --L;
			else break;
		if (!L) return false;
		std::tie(it, result) = M.emplace(L - 1, 1);
		if (!result) ++it->second;
	} else L = a[i];
	return true;
}

int main() {
	int i, L, R, M; bool incr = true;
	scanf("%d", &n);
	for (i = 1; i <= n; ++i) if (scanf("%d", a + i), a[i] <= a[i - 1]) incr = false;
	if (incr) return putchar(49), putchar(10), 0;
	for (L = 2, R = n; L < R; check(M = (L + R) / 2) ? R = M : L = M + 1);
	printf("%d\n", L);
	return 0;
}