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# [Solution] Sum of Product 1 CodeChef Solution 2022

## Problem

For an array $A$ of length $N$, let $F(A)$ denote the sum of the product of all the subarrays of $A$. Formally,

$F(A) = \sum_{L=1}^N \sum_{R=L}^N \left (\prod_{i=L}^R A_i\right )$

For example, let $A = [1, 0, 1]$, then there are $6$ possible subarrays:

• Subarray $[1, 1]$ has product $= 1$
• Subarray $[1, 2]$ has product $= 0$
• Subarray $[1, 3]$ has product $= 0$
• Subarray $[2, 2]$ has product $= 0$
• Subarray $[2, 3]$ has product $= 0$
• Subarray $[3, 3]$ has product $= 1$

So $F(A) = 1+1 = 2$.

Given a binary array $A$, determine the value of $F(A)$.

Solution Click Below:-  👉
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### Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.

• Each test case consists of multiple lines of input.
• The first line of each test case contains a single integer $N$ denoting the length of the array.
• The second line contains $N$ space-separated integers denoting the array $A$.

### Output Format

For each test case, output on a new line the value of $F(A)$.

### Explanation:

Test case $1$: Explained in the statement.

Test case $2$: There is only $1$ subarray and it has product $= 0$.

Test case $3$: All the $3$ subarrays have product $= 1$.