2748 - Number of Beautiful Pairs.

Easy

You are given a 0-indexed integer array nums. A pair of indices i, j where 0 <= i < j < nums.length is called beautiful if the first digit of nums[i] and the last digit of nums[j] are coprime.

Return the total number of beautiful pairs in nums.

Two integers x and y are coprime if there is no integer greater than 1 that divides both of them. In other words, x and y are coprime if gcd(x, y) == 1, where gcd(x, y) is the greatest common divisor of x and y.

Example 1:

Input: nums = 2,5,1,4

Output: 5

Explanation: There are 5 beautiful pairs in nums:

When i = 0 and j = 1: the first digit of nums0 is 2, and the last digit of nums1 is 5. We can confirm that 2 and 5 are coprime, since gcd(2,5) == 1.

When i = 0 and j = 2: the first digit of nums0 is 2, and the last digit of nums2 is 1. Indeed, gcd(2,1) == 1.

When i = 1 and j = 2: the first digit of nums1 is 5, and the last digit of nums2 is 1. Indeed, gcd(5,1) == 1.

When i = 1 and j = 3: the first digit of nums1 is 5, and the last digit of nums3 is 4. Indeed, gcd(5,4) == 1.

When i = 2 and j = 3: the first digit of nums2 is 1, and the last digit of nums3 is 4. Indeed, gcd(1,4) == 1.

Thus, we return 5.

Example 2:

Input: nums = 11,21,12

Output: 2

Explanation: There are 2 beautiful pairs:

When i = 0 and j = 1: the first digit of nums0 is 1, and the last digit of nums1 is 1. Indeed, gcd(1,1) == 1.

When i = 0 and j = 2: the first digit of nums0 is 1, and the last digit of nums2 is 2. Indeed, gcd(1,2) == 1.

Thus, we return 2.

Constraints:

• 2 <= nums.length <= 100

• 1 <= nums[i] <= 9999

• nums[i] % 10 != 0