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 n, is = 1, num[200007];
map<int, int>mp;
int read()
{
	int num = 0;
	char c = getchar();
	while (c < '0' || c>'9')c = getchar();
	while (c >= '0' && c <= '9')num = num * 10 + c - '0', c = getchar();
	return num;
}
int check(int mid)
{
	mp.clear();
	for (int i = 2; i <= n; i++)
		if (num[i] <= num[i - 1])
		{
			while (!mp.empty() && mp.rbegin()->first > num[i])
				mp.erase(mp.rbegin()->first);
			int pos = num[i];
			while (mp[pos] + 1 == mid)mp.erase(pos), pos--;
			if (!pos)return 0;
			mp[pos]++;
		}
	return 1;
}
int main()
{
	n = read();
	for (int i = 1; i <= n; i++)
		num[i] = read(), is &= (num[i] > num[i - 1]);
	if (is) { cout << 1 << endl; return 0; }
	int l = 2, r = n;
	while (l < r)
	{
		int mid = (l + r) / 2;
		if (check(mid))r = mid;
		else l = mid + 1;
	}
	cout << l << endl;
	return 0;
}