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<cstdio>
#include<cctype>
const int maxn=200010;
int n;
int a[maxn];
int ar[maxn],nm;
int In() {
    register char c;
    for(;c=getchar(),c!='-'&&!isdigit(c););
    register bool f=c=='-';
    register int s=f?0:c-'0';
    for(;c=getchar(),isdigit(c);)s=s*10+c-'0';
    return f?-s:s;
}
bool ck(register int ans) {
	nm=0;
	for(register int i=1;i<=n;++i) {
		if(!nm) ar[++nm]=a[i];
		else if(ar[nm]<a[i]) ar[nm]=a[i];
		else {
			if(ar[nm]>a[i]) {
				for(;nm&&ar[nm]>a[i];--nm);
				for(;nm>=ans&&ar[nm-ans+1]==ar[nm]&&ar[nm];--ar[nm-ans+1]);
				if(nm&&ar[nm]<=0) return 0;
				ar[++nm]=a[i];
			}
			for(;nm>=ans&&ar[nm-ans+1]==ar[nm]&&ar[nm];--ar[nm-=ans-1]);
			if(nm&&ar[nm]<=0) return 0;
			ar[++nm]=a[i];
		}
	}
	return 1;
}
int main() {
	n=In();
	for(register int i=1;i<=n;++i)a[i]=In();
	register int ll=1,rr=n;
	for(register int mm;mm=(ll+rr)>>1,ll<rr;ck(mm)?rr=mm:ll=mm+1);
	printf("%d\n",ll);
	return 0;
}