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 = 2e5 + 10;
int a[maxn], s[maxn];
int n, top;
bool check(int k)
{
	top = 0;
	for(int i = 2; i <= n; ++i)
	{
		if(a[i - 1] < a[i]) continue;
		while(top && s[top] > a[i]) --top;
		s[++top] = a[i];
		while(top >= k && s[top - k + 1] == s[top])
		{
			int val = s[top];
			top -= k;
			s[++top] = val - 1;
			if(!s[top]) return 0;
		}
	}
	return 1;
}		
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 >> 1;
		if(check(mid)) r = mid - 1;
		else l = mid + 1;
	}
	printf("%d\n", l);
	return 0;
}
/*
6
3 2 2 3 3 2
*/
	