Jaw-Dropping Set

각 n에 대해 1부터 n까지의 수 중 어떤 원소도 다른 원소를 나누지 않는 최대 크기 부분집합의 최소 합을 구한다.

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문제

A subset AA of the set 1,2,3,,n\\{1, 2, 3, \ldots, n\\} is called interesting if for any pair of different integers x,yAx, y \in A neither xx divides yy nor yy divides xx.

An interesting subset AA is called amazing if it has the maximum cardinality among all interesting subsets.

Finally, an amazing subset AA is called jaw-dropping if it has the minimum sum of elements among all amazing subsets.

Given nn, find the sum of elements in any jaw-dropping subset of 1,2,3,,n\\{1, 2, 3, \ldots, n\\}.

입력

The first line contains integer tt (1t1051 \le t \le 10^5) --- the number of test cases.

Each of the next TT lines contains an integer n_in\_i (1n_i1091 \le n\_i \le 10^9).

출력

Print TT lines with answers for each test case.