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<pair<int,int> > A;
bool look(int d)
{
	A.clear();
	A.push_back(std::make_pair(0, 0));
	for (int i = 1; i <= n; ++i)
		if (a[i] <= a[i - 1])
		{
			while (A.back().first > a[i]) A.pop_back();
			for (int j = a[i]; ; --j)
			{
				if (j < 1) return false;
				int t = 1;
				if (A.back().first == j) t = 1 + A.back().second, A.pop_back();
				if (t < d) {A.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,ans=1;
	while(l<=r)
	{
		int mid(l+r>>1);
		if(look(mid)) ans=mid,r=mid-1;
		else l = mid+1;
	}
	return printf("%d\n",ans),0;
}