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>
typedef long long ll;
using namespace std;
ll n,a[200005];
bool chk(ll m){
    if(m==1){
        for(ll i=1;i<n;i++)if(a[i]<=a[i-1])return 0;
        return 1;
    }
    map<ll,ll> cur;
    for(ll i=1;i<n;i++){
        if(a[i]>a[i-1])continue;
        map<ll,ll>::iterator itr;
        while( (itr=cur.upper_bound(a[i]))!=cur.end() )cur.erase(itr);
        cur[a[i]]++;
        ll val = a[i];
        while(cur[val]>=m){
            cur.erase(val);
            val--;
            cur[val]++;
            if(val==0)return 0;
        }
    }
    return 1;
}
int main(){
    ios_base:: sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    cin>>n;
    for(ll i=0;i<n;i++)cin>>a[i];
    ll s=1,e=n;
    while(s<e){
        ll mid=(s+e)>>1;
        if(chk(mid))e=mid;
        else s=mid+1;
    }
    cout<<e;
}


