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, = map(int, input().split())

def check(K):
    st = []
    for i, a in enumerate(A):
        #print(K, i, st, a)
        while st and a < st[-1][0]:
            st.pop()
        u = i > 0 and A[i-1] >= A[i]
        if not st:
            st.append([a, u])
            continue
        l = st[-1]
        if l[0] == a:
            l[1] += 1
            while st and l[1] == K:
                st.pop(); a -= 1
                if a == 0:
                    return 0
                if not st:
                    st.append([a, 1])
                    break
                l = st[-1]
                if l[0] == a:
                    l[1] += 1
                else:
                    st.append([a, 1])
                    break
            #print(l, st)
        else:
            st.append([a, u])
    #print(st)
    return 1

ok = 1
for i in range(N-1):
    if not A[i] < A[i+1]:
        ok = 0
if ok:
    print(1)
    exit(0)

left = 1; right = N+1
while left+1 < right:
    mid = (left + right) // 2
    if check(mid):
        right = mid
    else:
        left = mid
print(right)