B'You are given n points with integer coordinates x_1, ... x_n , which lie on a number line. For some integer s , we construct segments [ s,x_1 ], [ s,x_2 ], ... , [ s,x_n ]. Note that if x_i<s , then the segment will look like [ x_i,s ]. The segment [ a, b ] covers all integer points a, a+1, a+2, ... , b . We define the power of a point p as the number of segments that intersect the point with coordinate p , denoted as f_p . Your task is to compute sum limits_{p=1}^{10^9}f_p for each s in {x_1, ... ,x_n } , i.e., the sum of f_p for all integer points from 1 to 10^9 . For example, if the initial coordinates are [1,2,5,7,1] and we choose s=5 , then the segments will be: [1,5] , [2,5] , [5,5] , [5,7] , [1,5] . And the powers of the points will be: f_1=2, f_2=3, f_3=3, f_4=3, f_5=5, f_6=1, f_7=1, f_8=0, ... , f_{10^9}=0 . Their sum is 2+3+3+3+5+1+1=18 . The first line contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The first line of each test case contains an integer n ( 1 <= n <= 2 cdot 10^5 ) -- the number of points. The second line contains n integers x_1,x_2 ... x_n ( 1 <= x_i <= 10^9 ) -- the coordinates of the points. It is guaranteed that the sum of the values of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output n integers, where the i -th integer is equal to the sum of the powers of all points for s=x_i . In the first test case we first choose s=x_1=1 , then the following segments are formed: [1,1] , [1,4] , [1,3] . The powers of the points will be as follows: f_1=3, f_2=2, f_3=2, f_4=1, f_5=0 ... The sum of powers of the points: 3+2+2+1+0+ ... +0=8 . After that we choose s=x_2=4 . Then there will be such segments: [1,4] , [4,4] , [3,4] '...