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>
using namespace std;
int n,a[200001],s[200001];
map<int,int> mp;
bool judge(int x)
{
    mp.clear();
    int cnt=0;
    for(int i=2;i<=n;i++)
        if(a[i]<=a[i-1])
        {
            if(x==1) return false;
            while(cnt&&s[cnt-1]>a[i])
                mp[s[cnt-1]]=0,cnt--;
            int t=a[i];
            while(mp[t]+1>=x&&t>0) mp[t]=0,t--;
            if(t<=0) return false;
            mp[t]++;
            s[cnt++]=t;
        }
    return true;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    int l=1,r=n,ans;
    while(l<=r)
    {
        int m=l+r>>1;
        if(judge(m)) ans=m,r=m-1;
        else l=m+1;
    }
    printf("%d\n",ans);
}
