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,n) for(int i = 0; i < n; i++)
const int mx = 200005;
int n, a[mx], l, r = mx;

int main(){
    scanf("%d", &n);
    rep(i,n) scanf("%d", a+i);
    while(l+1 < r){
        int mid = (l+r) / 2, hight = 0;
        bool ok = true;
        map<int, int> mp;
        rep(i,n){
            if(hight < a[i]) hight = a[i];
            else{
                if(mid == 1){
                    ok = false; break;
                }
                hight = a[i];
                while(++mp[hight] >= mid && hight > 0) hight--;
                if(hight == 0){
                    ok = false;
                    break;
                }
            }
            mp.erase(mp.upper_bound(hight), mp.end());
        }
        (ok ? r : l) = mid;
    }
    printf("%d\n", r);
}