Limits
2s, 512 MB

Let’s say, **min** is the minimum element of an array and **max** is the maximum element of an array. The **score** of an array is defined as the number of integers in the range from **min** to **2 * max** which can not be divided by any of the elements of the array. The **total score** of an array is defined as the sum of the score of the sub-arrays which are also the suffix of the array. You will be given an array. Show the **total score** of the array.

The first line of input consists of a single integer $n$ — the length of the array.

The next line consists of $n$ integers $a_1, a_2, a_3, ……. a_n$— the elements of the array.

$1 <= n <= 1000000$

$1 <= a_i <= 2000000$

Output a single integer that denotes the **total score** of the array.

Input | Output |
---|---|

2 2 3 | 3 |

In the sample test case, the given array is $[2, 3]$. The array has two sub-arrays which are also the suffix of the array. They are $[2, 3]$ and $[3]$.

**In sub array [2,3]:** $min = 2, max = 3 => 2 * max = 2 * 3 = 6. Range: [2, 3, 4, 5, 6]$. In the range, $5$ is not divisible by any of the elements of the sub array. So, the score is 1.

**In sub array [3]:** $min = 3, max = 3 => 2 * max = 2 * 3 = 6. Range: [3, 4, 5, 6]$. In the range, $4$ and $5$ are not divisible by any of the elements of the sub array. So, the score is 2.

So, the total score is $1 + 2 = 3.$