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 200050
using namespace std;
 
int n;
int a[maxn];
 
void init()
{
    scanf("%d",&n);
    for (int i=1;i<=n;++i)
        scanf("%d",a+i);
}
 
int N,pos[maxn],ch[maxn];

bool judge(int ans)
{
	N=0;
	for (int i=1;i<=n;++i)
	{
	    if (a[i]<=a[i-1])
	    {
	        while (pos[N]>a[i]) --N;
 
	        int last=a[i];
	        while (last==pos[N]&&ch[N]==ans)
	            --N,--last;
	            
			if (!last)	return 0;
				 
	        if (pos[N]==last)
	            ++ch[N];
	        else
	            ++N,pos[N]=last,ch[N]=2;
	        assert(ch[N]<=ans);
//		        cout<<ans<<":"<<N<<" "<<pos[N]<<" "<<ch[N]<<endl;
	    }
	}
	return 1;
}
 
void solve()
{
	int flag=1;
	for (int i=2;i<=n;++i)
		flag&=a[i-1]<a[i];
	if (flag)
		puts("1");
	else
	{
		int l=2,r=200050;
		while (l<r)
		{
			int mid=(l+r)>>1;
			if (judge(mid))
				r=mid;
			else
				l=mid+1;
		}
		printf("%d\n",l);
	}
}
 
int main()
{
    init();
    solve();
    return 0;
}