NOSQ - No Squares Numbers

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A square free number is defined as a number which is not divisible by any square number.

For example, 13, 15, 210 are square free numbers, where as 25 (divisible by 5*5), 108 (divisible by 6*6), 18 (divisible by 3*3) are not square free numbers. However number 1 is not considered to be a square and is a squarefree number.

Now you must find how many numbers from number a to b, are square free and also have a digit d inside it.

For example for in the range 10 to 40 te squarefree numbers having digit 3 are 13, 23, 30, 31, 33, 34, 35, 37, 38, 39

Input

The first line contains an integer T, which is the number of test-cases

Then follow T lines, each containing 3 integers a, b and d.

1 <= T <= 20,000

1 <= a <= b <= 100,000

0 <= d <= 9

Output

Print one integer which is the required number as described in the problem statement.

Example

Input:
3
10 40 3
1 100 4
1 100000 7

Output:
10
9
26318

hide comments
P_Quantum: 2014-05-31 21:29:23

nice prblm!!

innovolt: 2014-04-13 18:53:12

easy 1

Alexandre Henrique Afonso Campos: 2014-02-17 01:31:02

I'm glad that I finally got AC. I had to translate a good idea from Python to C++ to get rid of TLE. I still feel that I have to reduce just a bit to receive AC also in Python.

Jumpy: 2014-01-30 16:46:21

finally did it thanks nammo..

Mitch Schwartz: 2013-07-20 21:09:49

@Hariharan: Read the problem statement carefully; "square-free" is not the same as "not a perfect square".

Hariharan : 2013-07-20 18:34:18

How is the solution for the 2nd test case 9? We have- 14,24,34,40,41,42,43,44,45,46,47,48,54,74,84,94- there're 16 numbers not 9.

saket diwakar: 2013-01-21 14:27:02

nice one......:)

Praveen Vaka: 2012-06-06 05:11:30

@sandeep pandey I had already solved the question before posting the comment. I just wanted others to realize that there are 20,000 test cases and a trivial algorithm will not work. Kindly consider editing your comment since it gives away the approach for the problem.

sandeep pandey: 2012-04-10 17:53:20

@Praveen Vaka:You are expected to apply BinarySearch for answering each query.

M Misbachul Huda: 2011-11-02 16:32:57

he ndul, kon mbujuk ta 3 second iku??


Added by:.:: Pratik ::.
Date:2011-03-07
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64