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 <cmath>
#include <algorithm>
#include <queue>
#include <vector>
#include <cstring>
#include <map>
#define MAXN 200005
#define MAXM
#define LL long long
#define LD long double
using namespace std;

int n, tag, a[MAXN];

map<int, int>::iterator it;

bool check(int mid)
{
	map<int, int> num;
	for(int i=2; i<=n; i++)
	{
		if(a[i]>a[i-1]) continue;
		int temp=a[i];
		while(num[temp]>=mid)
		{
			temp--;
			if(temp==0) return false;
		}
		num[temp]++;
		num.erase(num.lower_bound(temp+1), num.end());
	}
	return true;
}

int main()
{
	scanf("%d", &n);
	for(int i=1; i<=n; i++)
	{
		scanf("%d", &a[i]);
		if(i>1 && a[i]<=a[i-1]) tag=1;
	}
	if(!tag) {printf("1\n"); return 0;}
	int l=1, r=4e5, ans=0;
	while(l<=r)
	{
		int mid=(l+r)>>1;
		if(check(mid)) ans=mid, r=mid-1;
		else l=mid+1;
	}
	printf("%d\n", ans+1);
}
