#include <bits/stdc++.h>
using ll = long long;
using ld = long double;
using namespace std;

const int MAXN = 100001;

int a[MAXN];

pair <int, bool> g(int x) {
    int j = 0;
    while ((1 << j) < x) {
        j++;
    }

    return { j,  ((1 << j) == x) };
}

int main() {
#ifdef PAUNSVOKNO
    freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false); cout.setf(ios::fixed); cout.precision(20);
    int n;
    cin >> n;
    int c = 0, ans = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        auto p = g(a[i]);
        int f = p.first;
        bool gg = p.second;
        if (c >= f) {
            c = f;
            if (!gg) c--;
        } else {
            ans += (f - c);
            c = f;
        }
    }

    cout << ans << "\n";
}
### Prompt

Create a solution in CPP for the following problem:

There are A slimes lining up in a row. Initially, the sizes of the slimes are all 1.

Snuke can repeatedly perform the following operation.

* Choose a positive even number M. Then, select M consecutive slimes and form M / 2 pairs from those slimes as follows: pair the 1-st and 2-nd of them from the left, the 3-rd and 4-th of them, ..., the (M-1)-th and M-th of them. Combine each pair of slimes into one larger slime. Here, the size of a combined slime is the sum of the individual slimes before combination. The order of the M / 2 combined slimes remain the same as the M / 2 pairs of slimes before combination.



Snuke wants to get to the situation where there are exactly N slimes, and the size of the i-th (1 ≤ i ≤ N) slime from the left is a_i. Find the minimum number of operations required to achieve his goal.

Note that A is not directly given as input. Assume A = a_1 + a_2 + ... + a_N.

Constraints

* 1 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the minimum number of operations required to achieve Snuke's goal.

Examples

Input

2
3 3


Output

2


Input

4
2 1 2 2


Output

2


Input

1
1


Output

0


Input

10
3 1 4 1 5 9 2 6 5 3


Output

10

### Response

```cpp
#include <bits/stdc++.h>
using ll = long long;
using ld = long double;
using namespace std;

const int MAXN = 100001;

int a[MAXN];

pair <int, bool> g(int x) {
    int j = 0;
    while ((1 << j) < x) {
        j++;
    }

    return { j,  ((1 << j) == x) };
}

int main() {
#ifdef PAUNSVOKNO
    freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(false); cout.setf(ios::fixed); cout.precision(20);
    int n;
    cin >> n;
    int c = 0, ans = 0;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        auto p = g(a[i]);
        int f = p.first;
        bool gg = p.second;
        if (c >= f) {
            c = f;
            if (!gg) c--;
        } else {
            ans += (f - c);
            c = f;
        }
    }

    cout << ans << "\n";
}
```