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 xx first
#define yy second
#define mp make_pair
#define pb push_back
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int MAXN=2e5+5;
int a[MAXN];
ll p[35];
int n;
bool judge(int c)
{
	memset(p,0,sizeof(p));
	int now=0;
	for(int i=1;i<=n;i++)
	{
		if(a[i]>30)
		{
			now=30;
			continue;
		}
		if(a[i]>a[i-1])
		{
			now=a[i];
			continue;
		}
		while(now>a[i])
		{
			p[now]=0;
			now--;
		}
		p[now]++;
		for(int j=30;j>=1;j--)
		{
			p[j-1]+=p[j]/c;
			p[j]%=c;
		}
	}
	return p[0]==0;
}
int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
	bool flag=false;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		if(a[i]<=a[i-1]) flag=true;
	}
	if(!flag) return 0*puts("1");
	int l=2,r=n;
	int ans=0;
	//cout<<judge(2)<<endl;
	while(l<=r)
	{
		int mid=(l+r)>>1;
		if(judge(mid))
		{
			ans=mid;
			r=mid-1;
		}
		else
		{
			l=mid+1;
		}
	}
	printf("%d\n",ans);
	return 0;
}
