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 l[200010], n;
int act[300010];

bool incr(int poz, int base)
{
	if (poz == 0)
		return false;
	act[poz]++;
	if (act[poz] == base) {
		act[poz] = 0;
		return incr(poz - 1, base);
	}
	return true;
}

bool cbin(int nr)
{
	memset(act, 0, sizeof act);
	
	int lact = 0;
	for (int i = 1; i <= n; i++) {
		if (l[i] > lact)
			lact = l[i]; /// maresc
		else {
			for (int j = lact, c = 0; c < 20 && j > l[i]; j--, c++)
				act[j] = 0;
			lact = l[i];
			if (!incr(lact, nr))
				return false;
		}
	}
	return true;
}

int main()
{
	cin >> n;

	bool ok = 1;

	for (int i = 1; i <= n; i++) {
		cin >> l[i];
		ok &= (l[i] > l[i - 1]);
	}

	if (ok) {
		cout << 1 << '\n';
		return 0;
	}

	for (int i = 1; i <= n; i++)
		l[i] = min(l[i], 300000);

	int p = 0, q = (1 << 20);

	while (q >>= 1)
		if (!cbin(p + q))
			p += q;

	cout << p + 1 << '\n';

	return 0;
}
