// Copyright (C) 2017 Sayutin Dmitry.
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; version 3

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; If not, see <http://www.gnu.org/licenses/>.

#include <iostream>
#include <vector>
#include <stdint.h>
#include <algorithm>
#include <set>
#include <map>
#include <array>
#include <queue>
#include <stack>
#include <functional>
#include <utility>
#include <string>
#include <assert.h>
#include <iterator>
#include <cstdint>
#include <cinttypes>
#include <string.h>
#include <random>
#include <numeric>
#include <tuple>


using std::cin;
using std::cout;
using std::cerr;

using std::vector;
using std::map;
using std::array;
using std::set;
using std::string;

using std::pair;
using std::make_pair;

using std::min;
using std::abs;
using std::max;

using std::unique;
using std::sort;
using std::generate;
using std::reverse;
using std::min_element;
using std::max_element;

#ifdef LOCAL
#define LASSERT(X) assert(X)
#else
#define LASSERT(X) {}
#endif

template <typename T>
T input() {
    T res;
    cin >> res;
    LASSERT(cin);
    return res;
}

template <typename IT>
void input_seq(IT b, IT e) {
    std::generate(b, e, input<typename std::remove_reference<decltype(*b)>::type>);
}

#define SZ(vec)         int((vec).size())
#define ALL(data)       data.begin(),data.end()
#define RALL(data)      data.rbegin(),data.rend()
#define TYPEMAX(type)   std::numeric_limits<type>::max()
#define TYPEMIN(type)   std::numeric_limits<type>::min()

#define pb push_back
#define eb emplace_back


int main() {
    std::iostream::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    
    // code here.
    int n = input<int>();
    int ans = 0;

    int prev_r = 0;
    
    for (int i = 0; i != n; ++i) {
        int a = input<int>();

        int lg = log(a) / log(2) + 1e-9;
//        while ((2 << lg) <= a)
//            ++lg;

        if ((1 << lg) == a) {
            ans += lg;
            ans -= min(prev_r, lg);
            prev_r = lg;
        } else {
            ans += lg + 1;

            if (prev_r <= lg)
                ans -= prev_r, prev_r = lg + 1;
            else
                ans -= lg + 1, prev_r = lg;
            
        }
    }

    cout << ans << "\n";
    
    return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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
// Copyright (C) 2017 Sayutin Dmitry.
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; version 3

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; If not, see <http://www.gnu.org/licenses/>.

#include <iostream>
#include <vector>
#include <stdint.h>
#include <algorithm>
#include <set>
#include <map>
#include <array>
#include <queue>
#include <stack>
#include <functional>
#include <utility>
#include <string>
#include <assert.h>
#include <iterator>
#include <cstdint>
#include <cinttypes>
#include <string.h>
#include <random>
#include <numeric>
#include <tuple>


using std::cin;
using std::cout;
using std::cerr;

using std::vector;
using std::map;
using std::array;
using std::set;
using std::string;

using std::pair;
using std::make_pair;

using std::min;
using std::abs;
using std::max;

using std::unique;
using std::sort;
using std::generate;
using std::reverse;
using std::min_element;
using std::max_element;

#ifdef LOCAL
#define LASSERT(X) assert(X)
#else
#define LASSERT(X) {}
#endif

template <typename T>
T input() {
    T res;
    cin >> res;
    LASSERT(cin);
    return res;
}

template <typename IT>
void input_seq(IT b, IT e) {
    std::generate(b, e, input<typename std::remove_reference<decltype(*b)>::type>);
}

#define SZ(vec)         int((vec).size())
#define ALL(data)       data.begin(),data.end()
#define RALL(data)      data.rbegin(),data.rend()
#define TYPEMAX(type)   std::numeric_limits<type>::max()
#define TYPEMIN(type)   std::numeric_limits<type>::min()

#define pb push_back
#define eb emplace_back


int main() {
    std::iostream::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    
    // code here.
    int n = input<int>();
    int ans = 0;

    int prev_r = 0;
    
    for (int i = 0; i != n; ++i) {
        int a = input<int>();

        int lg = log(a) / log(2) + 1e-9;
//        while ((2 << lg) <= a)
//            ++lg;

        if ((1 << lg) == a) {
            ans += lg;
            ans -= min(prev_r, lg);
            prev_r = lg;
        } else {
            ans += lg + 1;

            if (prev_r <= lg)
                ans -= prev_r, prev_r = lg + 1;
            else
                ans -= lg + 1, prev_r = lg;
            
        }
    }

    cout << ans << "\n";
    
    return 0;
}

```