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, a[200009];
vector<std::pair<int, int> > K;

bool check(int d)
{
	K.clear();
	K.push_back(std::make_pair(0, 0));
	for (int i = 1; i <= n; ++i)
		if (a[i] <= a[i - 1])
		{
			while (K.back().first > a[i]) K.pop_back();
			for (int j = a[i]; ; --j)
			{
				if (j < 1) return false;
				int t = 1;
				if (K.back().first == j) t = 1 + K.back().second, K.pop_back();
				if (t < d)
				{
					K.push_back(make_pair(j, t));
					break;
				}
			}
		}
	return true;
}

int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
	int l = 1, r = n;
	while (l < r)
	{
		int mid = (l + r) / 2;
		if (check(mid)) r = mid;
		else l = mid + 1;
	}
	printf("%d\n", l);
}