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Time Limit: 1.0 Seconds Memory Limit: 65536K

Total Runs: 403 Accepted Runs: 190

A pair of integers (*a*,*b*) is called an amicable pair if the sum of the proper divisors of *a* equals *b*, and vice versa. For example, (220, 284) is an amicable pair, since the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, and 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284, while the proper divisors of 284 are 1, 2, 4, 71 and 142 and their sum is 220. ### Input

The first line is an integer *T*, number of test cases. *T* lines follow, each contains an integer *K*. ### Output

For each case, output on a line the number of different amicable pairs satisfying the constraint above. ### Notes

Integer *a* is a proper divisor of *b* if 0 < a < b and there exists some integer *k* such that *a* * *k* = *b*.
### Constraints

1 ≤ *T* ≤ 1000
1 ≤ *K* ≤ 100000
### Sample Input

### Sample Output

### Sample Input/Output Clarification

The first three amicable pairs are (6,6), (28,28) and (220, 284).

Given *K*, output the number of different amicable pairs (*a*,*b*) where 1 ≤ *a* ≤ *K* and 1 ≤ *b* ≤ *K*. Note that (*a*,*b*) is considered the same pair as (*b*,*a*).

2 220 284

2 3

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