Differences of the permutations

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3.8

80 votes

Basic Programming, Basic Math, Math Basic, Math

Details

Problem

Given an integer N. Consider all the possible permutations $p[\ ]$ of all integers from $1$ to $N$ . Calculate the value of $X$ for each permutation :

$X = \sum_{i = 1}^{i = N} N - p[i]$

Determine the sum of all $X$ for all possible permutations.

Input format

First line: A single integer $T$ denoting the number of test cases
Second line: A single integer N.

Output format

For each test case, print a single line containing the answer.

Constraints

$1 \leq T \leq 5$

$1 \leq N \leq 10$

Sample Input

1
2

Sample Output

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

There are 2 possible permutations for N = 2 : p = [1, 2] and p = [2, 1].

For first permutation X = (2 - 1) + (2 - 2) = 1.

For second permutation X = (2 - 2) + (2 - 1) = 1.

So sum of X over 2 possible permutations = 2.

Contributers:

Aman Kumar

Amirreza Poorakhavan