# Sum of Product 2 CodeChef Solution

### We Are Discuss About CODECHEF SOLUTION

Sum of Product 2 CodeChef Solution

## Sum of Product 2 CodeChef Solution

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 sum of F(A) over all the N! orderings of A modulo 998244353.

Note that orderings here are defined in terms of indices, not elements; which is why every array of length N has N! orderings. For example, the 3! = 6 orderings of A = [1, 0, 1] are:

• [1, 0, 1] corresponding to indices [1, 2, 3]
• [1, 1, 0] corresponding to indices [1, 3, 2]
• [0, 1, 1] corresponding to indices [2, 1, 3]
• [0, 1, 1] corresponding to indices [2, 3, 1]
• [1, 1, 0] corresponding to indices [3, 1, 2]
• [1, 0, 1] corresponding to indices [3, 2, 1]

## Sum of Product 2 CodeChef Solution

### 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 le
• The second line contains N space-separated integers denoting the array A.

### Output Format

For each test case, output the sum of F(A) over all the N! orderings of A, modulo 998244353.

### Constraints

• 1 \leq T \leq 1000
• 1 \leq N \leq 10^5
• 0 \leq A_i \leq 1
• The sum of N over all test cases won’t exceed 2 \cdot 10^5.

## Sum of Product 2 CodeChef Solution

### Sample 1:

Input

Output

4
3
1 0 1
1
0
2
1 1
4
1 1 0 1

16
0
6
120


## SOLUTION

Yhaa You have done it but next? if YOU Want to Get Others Please Visit Here ScishowEngineer   Then Follow US HERE and Join Telegram.

If You Want To Learn Something New Then Visit Our Official Channel YOUTUBE