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
N = int(input())
A = list(map(int,input().split()))

def is_ok(k):
    length = 0
    mem = {}
    for a in A:
        if a > length:
            length = a
            continue
        dels = []
        for b in mem.keys():
            if b > a:
                dels.append(b)
        while a > 0:
            if a in mem and mem[a] >= k-1:
                dels.append(a)
            else:
                break
            a -= 1
        if a in mem:
            mem[a] += 1
        else:
            mem[a] = 1
        if a == 0 or mem[a] >= k:
            return False
        length = a
        for b in dels:
            del mem[b]
    return True

ng = 0
ok = N
while ok-ng > 1:
    m = (ok+ng+1)//2
    if is_ok(m):
        ok = m
    else:
        ng = m
print(ok)