Given n strictly positive real numbers, your task is to compute the Pythagorean means:

• The arithmetic mean « A »

• The geometric mean « G » (mean of rates of growth)

G =

• The harmonic mean « H » (mean of speeds)

Figure 1: Geometric interpretation of the Pythagorean means of two numbers a and b

Input

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. Each test case is described in two lines: the first line contains a single integer « n » (1 ≤ n ≤ 100) indicating the number of the strictly positive real numbers and the second line contains « n » space-separated strictly positive real numbers.

Output

For each test case, print a single line containing three space-separated integers: « A », « G », « H » which are respectively the arithmetic, the geometric and the harmonic means of the given strictly positive real numbers. Each mean must be given with a precision of 10^-9.

Example

Input:
3
5
4 36 45 50 75
6
1.0 2.0 4.0 7.0 14.0 28.0
8
1.0 2.0 3.0 4.0 9.0 12.0 18.0 36.0

Output:
42.000000000 30.000000000 15.000000000
9.333333333 5.291502622 3.000000000
10.625000000 6.000000000 3.388235294