You are given an integer `n`, which indicates that there are `n` courses labeled from `1` to `n`. You are also given a 2D integer array `relations` where `relations[j] = [prevCoursej, nextCoursej]` denotes that course `prevCoursej` has to be completed **before** course `nextCoursej` (prerequisite relationship). Furthermore, you are given a **0-indexed** integer array `time` where `time[i]` denotes how many **months** it takes to complete the `(i+1)th` course.

You must find the **minimum** number of months needed to complete all the courses following these rules:

*   You may start taking a course at **any time** if the prerequisites are met.
*   **Any number of courses** can be taken at the **same time**.

Return _the **minimum** number of months needed to complete all the courses_.

**Note:** The test cases are generated such that it is possible to complete every course (i.e., the graph is a directed acyclic graph).

**Example 1:**

**Input:** n = 3, relations = \[\[1,3\],\[2,3\]\], time = \[3,2,5\]
**Output:** 8
**Explanation:** The figure above represents the given graph and the time required to complete each course. 
We start course 1 and course 2 simultaneously at month 0.
Course 1 takes 3 months and course 2 takes 2 months to complete respectively.
Thus, the earliest time we can start course 3 is at month 3, and the total time required is 3 + 5 = 8 months.

**Example 2:**

**Input:** n = 5, relations = \[\[1,5\],\[2,5\],\[3,5\],\[3,4\],\[4,5\]\], time = \[1,2,3,4,5\]
**Output:** 12
**Explanation:** The figure above represents the given graph and the time required to complete each course.
You can start courses 1, 2, and 3 at month 0.
You can complete them after 1, 2, and 3 months respectively.
Course 4 can be taken only after course 3 is completed, i.e., after 3 months. It is completed after 3 + 4 = 7 months.
Course 5 can be taken only after courses 1, 2, 3, and 4 have been completed, i.e., after max(1,2,3,7) = 7 months.
Thus, the minimum time needed to complete all the courses is 7 + 5 = 12 months.

**Constraints:**

*   `1 <= n <= 5 * 104`
*   `0 <= relations.length <= min(n * (n - 1) / 2, 5 * 104)`
*   `relations[j].length == 2`
*   `1 <= prevCoursej, nextCoursej <= n`
*   `prevCoursej != nextCoursej`
*   All the pairs `[prevCoursej, nextCoursej]` are **unique**.
*   `time.length == n`
*   `1 <= time[i] <= 104`
*   The given graph is a directed acyclic graph.


def count_good_digit_strings(n):
    mod = 10 ** 9 + 7
    even_digits, prime_digits = 5, 4
    total = 1
    for i in range(n):
        total = total * (even_digits if i % 2 == 0 else prime_digits) % mod
    return total
