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 Maxn = 200005;
int n, a[Maxn];
map <int, int> Ma[Maxn];
int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		scanf("%d", &a[i]);
	for (int i = 1; i < n; i++)
		if (a[i] >= a[i + 1]) goto A;
	puts("1");
	return 0;
	A:int l = 2, r = n;
	while (l + 1 <= r)
	{
		int mid = (l + r) >> 1;
		for (int i = 1; i < n; i++)
		{
			Ma[i + 1] = Ma[i];
			if (a[i] >= a[i + 1])
			{
				while (Ma[i + 1].size() && Ma[i + 1].rbegin() -> first > a[i + 1]) Ma[i + 1].erase(--Ma[i + 1].end());
				Ma[i + 1][a[i + 1]]++;
				int pnt = a[i + 1];
				while (Ma[i + 1][pnt] == mid)
				{
					if (pnt == 1)
					{
						l = mid + 1;
						goto END;
					}
					Ma[i + 1][pnt] = 0, Ma[i + 1][pnt - 1]++;
					pnt--;
				}
			}
		}
		r = mid;
		END:;
	}
	printf("%d", l);
	return 0;
}
