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>
#define rep(i,l,r) for (int i=l;i<=r;i++)
#define per(i,l,r) for (int i=l;i>=r;i--)
using namespace std;
typedef long long ll;
int n,x,ans;
int a[400500],st[400500];
map<int,int> c;
bool jud(int mid){
    int now=mid;
    c.clear();
    int tot=0;
    rep(i,2,n){
        if (a[i]>a[i-1]) continue;
        while (tot&&st[tot]>a[i]){
            c[st[tot]]=0;
            tot--;
        }
        st[++tot]=a[i];
        int x=a[i];
        c[x]++;
        if (mid==1) return 0;
        while (c[x]>=mid) c[x]=0,c[--x]++;
        if (x<=0) return 0;
    }
    return 1;
}
int main(){
    scanf("%d",&n);
    rep(i,1,n) scanf("%d",&a[i]);
    int l=1,r=n,ans=n;
    while (l<=r){
        int mid=(l+r)/2;
        if (jud(mid)) ans=mid,r=mid-1;
        else l=mid+1;
    }
    cout<<ans<<endl;
    return 0;
}