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;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)

int main(){
    int n;cin>>n;
    int a[n];
    rep(i,n)cin>>a[i];
    bool inc=true;
    rep(i,n-1)if(a[i]>=a[i+1])inc=false;
    if(inc){
        cout<<1<<endl;
        return 0;
    }
    int ng=1,ok=n;
    while(ok-ng>1){
        int mid=(ok+ng)/2;
        vector<pair<int,int>> v;
        v.emplace_back(-1,-1);
        bool can=true;
        rep(i,n-1){
            if(a[i]<a[i+1])continue;
            int m=a[i+1];
            while(v.back().first>m)v.pop_back();
            while(v.back().first==m&&v.back().second==mid-1)v.pop_back(),--m;
            if(m==v.back().first)++v.back().second;
            else if(m)v.emplace_back(m,1);
            else {
                can=false;
                break;
            }
        }
        if(can)ok=mid;
        else ng=mid;
    }
    cout<<ok<<endl;
    return 0;
}
