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>
#define MAX_N 200000
#define mid ((l+r)>>1)
using namespace std;
int n, a[MAX_N+5];
bool chk(int x)
{
	map <int, int> c;
	if (x == 1) return is_sorted(a+1, a+n+1);
	for (int i = 1, v; i <= n; i++)
		if ((v = a[i]) <= a[i-1])
		{
			c[v]++, c.erase(c.upper_bound(v), c.end());
			while (v && c[v] == x) c.erase(v), c[--v]++;
			if (!v) return false;
		}
	return true;
}
int bi_search(int l, int r)
{
	int ret = n;
	while (l <= r)
		if (!chk(mid)) l = mid+1;
		else ret = mid, r = mid-1;
	return ret;
}
int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%d", a+i);
	return printf("%d\n", bi_search(1, n)), 0;
}