Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorted in the non-decreasing order. 

Ivan wrote out integers 2a1, 2a2, ..., 2an on a piece of paper. Now he wonders, what minimum number of integers of form 2b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2v - 1 for some integer v (v ≥ 0). 

Help Ivan, find the required quantity of numbers.

Input

The first line contains integer n (1 ≤ n ≤ 105). The second input line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 2·109). It is guaranteed that a1 ≤ a2 ≤ ... ≤ an.

Output

Print a single integer — the answer to the problem.

Examples

Input

4
0 1 1 1


Output

0


Input

1
3


Output

3

Note

In the first sample you do not need to add anything, the sum of numbers already equals 23 - 1 = 7.

In the second sample you need to add numbers 20, 21, 22.
n = int(input())
I = map(int, input().split())
a = [];
for val in I:
    a.append(val);
la = len(a);
b = []; c = []; d = -1;
for i in range (0, la):
    if i == 0 or a[i] != a[i-1]:
        b.append(a[i]);
        c.append(1);
        d = d + 1;
    else:
        c[d] = c[d] + 1;
d = d + 1;
tot = 0; idx = 0;
for i in range(0, d):
    while idx < b[i]:
        if tot < 2:
            break;
        else:
            tot = int(tot / 2);
            idx = idx + 1;
    if idx < b[i]:
        idx = b[i];
        tot = c[i];
    else:
        tot = tot + c[i];
while tot >= 2:
    tot = int(tot / 2);
    idx = idx + 1;
idx = idx + 1;
res = idx;
#print (idx)
st = []; tot = 0; idx = 0;
for i in range (0, d):
    while idx < b[i]:
        if tot == 0:
            break;
        else:
            if tot == 1:
                st.append(idx);
                tot = 0; idx = idx + 1;
            else:
                if tot % 2 == 1:
                    st.append(idx);
                tot = int(tot / 2);
                idx = idx + 1;
    if idx < b[i]:
        idx = b[i]; tot = c[i];
        if tot % 2 == 1:
            st.append(idx);
        tot = int(tot / 2);
        idx = idx + 1;
    else:
        idx = b[i]; tot = tot + c[i];
        if tot % 2 == 1:
            st.append(idx);
        tot = int(tot / 2);
        idx = idx + 1;
while tot > 0:
    if tot % 2 == 1:
        st.append(idx);
    tot = int(tot / 2);
    idx = idx + 1;
lst = len(st);
print (res- lst)







