CF B. Sonya and Exhibition

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索尼娅计划在其所在的直线型国家中扩展酒店业务，确保新建酒店与原有酒店间的最小距离为d。文章描述了如何确定可能的新酒店位置数量，并提供了一个示例程序。

Sonya decided that having her own hotel business is the best way of earning money because she can profit and rest wherever she wants.

The country where Sonya lives is an endless line. There is a city in each integer coordinate on this line. She has $n$ hotels, where the $i$ -th hotel is located in the city with coordinate $x_{i}$ . Sonya is a smart girl, so she does not open two or more hotels in the same city.

Sonya understands that her business needs to be expanded by opening new hotels, so she decides to build one more. She wants to make the minimum distance from this hotel to all others to be equal to $d$ . The girl understands that there are many possible locations to construct such a hotel. Thus she wants to know the number of possible coordinates of the cities where she can build a new hotel.

Because Sonya is lounging in a jacuzzi in one of her hotels, she is asking you to find the number of cities where she can build a new hotel so that the minimum distance from the original $n$ hotels to the new one is equal to $d$ .

Input

The first line contains two integers $n$ and $d$ ( $1 \leq n \leq 100$ , $1 \leq d \leq 10^{9}$ ) — the number of Sonya's hotels and the needed minimum distance from a new hotel to all others.

The second line contains $n$ different integers in strictly increasing order $x_{1}, x_{2}, \dots, x_{n}$ ( $- 10^{9} \leq x_{i} \leq 10^{9}$ ) — coordinates of Sonya's hotels.

Output

Print the number of cities where Sonya can build a new hotel so that the minimum distance from this hotel to all others is equal to $d$ .

  Examples
 
    input
    
     Copy
    
4 3
-3 2 9 16

    output
    
     Copy
    
6

    input
    
     Copy
    
5 2
4 8 11 18 19

    output
    
     Copy
    
5

Note

In the first example, there are $6$ possible cities where Sonya can build a hotel. These cities have coordinates $- 6$ , $5$ , $6$ , $12$ , $13$ , and $19$ .

In the second example, there are $5$ possible cities where Sonya can build a hotel. These cities have coordinates $2$ , $6$ , $13$ , $16$ , and $21$

有一个长为n的地方可以放rose和lily两种花，有d位游客，每位游览不同的区间，现要求每位游客游览的区间内rose数乘Lily数最大，想了好久，以为是爆搜或者是动态规划一类的难题，果断放弃。

晚上搜题解，才发现是一道考验智商的大水题，只需保证0101010这样的顺序就可以保证每位游客经历的区间不同花的个数最多了。深感遗憾和震惊！！！！

#include<bits/stdc++.h>
using namespace std;

int main()
{
    int a,b,t;
    scanf("%d%d",&a,&b);
    for(int i=0;i<b;i++)
    {
        cin>>t;
        cin>>t;
    }
    for(int i=0;i<a;i++)
    {
        if(i&1)
            cout<<'1';
        else
            cout<<'0';
    }
    cout<<endl;
    return 0;
}