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;
typedef long long ll;
ll n,a[200005];
map<ll,ll>p;
bool check(ll x){
    p.clear();
    for(int i=1;i<n;i++){
        ll b=a[i-1],c=a[i];
        if(b>=c){
            if(x==1)return false;
            p.erase(p.upper_bound(c),p.end());
            while(1){
                if(c==0)return false;
                if(++p[c]<x)break;
                p.erase(c);
                c--;
            }
        }
    }
    return true;
}
int main(void){
    scanf("%lld",&n);
    for(int i=0;i<n;i++)scanf("%lld",a+i);
    ll l=0,r=n;
    while(r-l>1){
        ll m=(l+r)/2;
        if(check(m))r=m;
        else l=m;
    }
    printf("%lld\n",r);
}