Rikka with Mista

Rikka is a fervent fan of JoJo's Bizarre Adventure. As the last episode of Golden Wind has been aired, Rikka, with the help of Yuta, sets up this problem to express the love to Mista.

Mista's lucky number is $4$. Today, Mista wants to test his luck with $n$ magic cards: For each card, there is a non-negative integer on each side. The two numbers on the $i$th card are $w_i$ and $0$.

Firstly, Mista puts these $n$ cards to table one by one. For each card, the probability of the $w_i$ side to be upward is $\frac{1}{2}$, and these probabilities are independent with each other. As a result, there are $n$ integers on the table. Mista then sums up all these integers and counts the number of $4$s in the decimal representation of this sum: He uses this result to measure his luckiness.

Since it's possible for each side of each card to be upward, there are $2^n$ possible states in total. You are required to calculate the sum of the results for all these situations.

The first line of the input contains a single integer $T(4 \leq T \leq 4)$, the number of test cases.

For each test case, the first line contains a single integer $n(4 \leq n \leq 40)$, the number of the cards.

The second line contains $n$ integers $w_1, \dots, w_n(4 \leq w_i \leq 44444444)$, the positive numbers on the cards.

For each test case, output a single line with a single integer, the answer.

4
4
4 4 4 4
4
4 4 44 44
4
4 44 44 4444
4
444 44444 44444 4444444

4
10
24
38

2019 Multi-University Training Contest 9