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 <cstdio>
#include <map>

std::map<int, int> mp;
int n, a[201000];

bool check(int x)
{
	mp.clear();
	int len = 0;
	for(int i = 1; i <= n; i++)
	{
		if(a[i] > len) 
		{
			len = a[i];
			std::map<int, int>::iterator it = mp.end();
			if(it != mp.begin())
			{
				--it;
				while(it -> first > a[i - 1])
				{
					std::map<int, int>::iterator tmp = it;
					if(it != mp.begin()) --it, mp.erase(tmp);
					else {mp.erase(tmp); break;} 
				}
			} 
		}
		else
		{
			if(a[i] < len) len = a[i];
			int j;
			for(j = len; j >= 1; j--)
			{
				if(x == 1) return false;
				++mp[j];
				if(mp[j] != x) break;
				else mp[j] = 0; 
			}
			if(j == 0) return false;
		}
	}
	return true;
}

int main()
{
	scanf("%d", &n);
	for(int i = 1; i <= n; i++) scanf("%d", &a[i]);
	int l = 1, r = n + 1;
	while(l < r)
	{
		int mid = l + r >> 1;
		if(check(mid)) r = mid;
		else l = mid + 1;
	}
	printf("%d\n", r);
	return 0;
}