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[202000], ans;

stack<int>w, c, e;

bool ok(int aim){
    w=c=e;    
    for (int i=2;i<=n;++i){
        if (a[i]>a[i-1]) continue;
        while (w.size()&&w.top()>a[i]) w.pop(), c.pop();
        int p=a[i];
        while (w.size()&&w.top()==p&&c.top()==aim) w.pop(), c.pop(), --p;
        if (p==0) return 0;
        if (w.size()&&w.top()==p) c.top()++;
        else {
            if (aim==1) return 0;
            w.push(p), c.push(2);
        }
    }
    return 1;
}

int main(){
    cin>>n;
    for (int i=1;i<=n;++i) cin>>a[i];
    int l=1, r=n;
    while (l<=r){
        int mid=l+r>>1;
        if (ok(mid)) r=mid-1, ans=mid;
        else l=mid+1;
    }
    cout<<ans<<endl;
}