A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime (2, 3, 5, or 7).
Given an integer n, return the total number of good digit strings of length n. Since the answer may be large, return it modulo 109 + 7.
A digit string is a string consisting of digits 0 through 9 that may contain leading zeros.
Examples
Example 1
Input: n = 1
Output: 5
Explanation: The good numbers of length 1 are "0", "2", "4", "6", "8".
Example 2
Input: n = 4
Output: 400
Example 3
Input: n = 50
Output: 564908303
Constraints
1 <= n <= 1015
1922. Count Good Numbers
Medium
30 Points
Math
Recursion
A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime (2, 3, 5, or 7).
Given an integer n, return the total number of good digit strings of length n. Since the answer may be large, return it modulo 109 + 7.
A digit string is a string consisting of digits 0 through 9 that may contain leading zeros.
Examples
Example 1
Input: n = 1
Output: 5
Explanation: The good numbers of length 1 are "0", "2", "4", "6", "8".