Given an array of 2k integers (for some integer k), perform the following operations until the array contains only one element:

• On the 1st, 3rd, 5th, etc. iterations (1-based) replace each pair of consecutive elements with their sum;
• On the 2nd, 4th, 6th, etc. iterations replace each pair of consecutive elements with their product. After the algorithm has finished, there will be a single element left in the array. Return that element.

Example

For inputArray = [1, 2, 3, 4, 5, 6, 7, 8], the output should be arrayConversion(inputArray) = 186.

We have [1, 2, 3, 4, 5, 6, 7, 8] -> [3, 7, 11, 15] -> [21, 165] -> [186], so the answer is 186.

Hints

• push()

Input/Output

• [execution time limit] 5 seconds (ts)
• [input] array.integer inputArray

Guaranteed constraints:

1 ≤ inputArray.length ≤ 20,

-9 ≤ inputArray[i] ≤ 99.

• [output] integer