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 maxn 200010
using namespace std;
struct data{int l, r, x;};
int len[maxn], n;
data A[maxn];
bool check(int x)
{
	int cnt = 0;
	for (int i = 1; i <= n; i++)
	{
		if (len[i] > len[i - 1])
		{
			A[++cnt] = (data){len[i - 1] + 1, len[i], 1};
			continue;
		}
		while (A[cnt].l > len[i]) cnt--;
		A[cnt].r = len[i];
		while (cnt && A[cnt].x == x) cnt--;
		if (cnt == 0) return false;
		int pos = A[cnt].r, tp = A[cnt].x + 1;
		if (A[cnt].r == A[cnt].l) cnt--;
		else A[cnt].r--;
		A[++cnt] = (data){pos, pos, tp};
		if (pos != len[i]) A[++cnt] = (data){pos + 1, len[i], 1};
	}
	return true;
}
int main()
{
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		scanf("%d", &len[i]);
	int lef = 1, righ = n, res = 0;
	while (lef <= righ)
	{
		int mid = (lef + righ) / 2;
		if (check(mid)) {res = mid; righ = mid - 1;}
		else lef = mid + 1;
	}
	printf("%d\n", res);
	return 0;
}