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 MN 200005
typedef std::pair<int,int> P;
int n,a[MN],lst;
int pos[MN],val[MN],cnt;
bool check(int x)
{
    cnt=0;
    for(int i=2;i<=n;i++)
    {
        if(a[i]>a[i-1]) continue;
        for(;cnt&&pos[cnt]>a[i];cnt--);
        if(pos[cnt]<a[i]) pos[++cnt]=a[i],val[cnt]=0;
        for(;1;)
        {
            val[cnt]++;
            if(val[cnt]<x) break;
            if(pos[cnt]==1) return 0;
            val[cnt]=0;
            if(pos[cnt-1]!=pos[cnt]-1) pos[cnt]--;
            else cnt--;
        }
    }
    return 1;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    int l=1,r=n+1,ans;
    while(l<=r)
    {
        int mid=l+r+1>>1;
        if(check(mid)) ans=mid,r=mid-1;
        else l=mid+1;
    }
    printf("%d\n",ans);
}
