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 N 200010
using namespace std;
typedef int ll;
ll p[N];
map<ll,ll>mp;
      ll a;
bool check(ll k)
{
  mp.clear();
    for(ll i=2;i<=a;i++)
        if(p[i]>p[i-1])
        continue;
    else
    {
        if(k==1)
            return false;
    
    
       while(mp.size()){
        ll u=mp.rbegin() -> first;
        if(u>p[i])
        mp.erase(u);
        else
            break;
       }


        ll j=p[i];
        while(j&&mp[j]+1==k)
        {

            mp.erase(j);
              j--;
        }
       if(j==0)
        return false;
       mp[j]++;
    }
    return true;



}
int main() {


        cin>>a;
        for(ll i=1;i<=a;i++)
            cin>>p[i];

        ll l=1,r=a,mid;


        while(l<r)
        {
            mid=(l+r)>>1;
            if(check(mid))
                r=mid;
            else
                l=mid+1;
        }

        cout<<l<<endl;
    return 0;
}
