Sangar Number

My classmate, Yasya', gave me this wonderful problem when we were high school students. The problem was about Sangar Number. The word sangar itself is the Javanese language of wonderful.

Let \(N\) is a Sangar Number if it satisfies the following conditions :

  • There are integers \(A, B, C\) such that \(\overline{AC} \times \overline{BC} = \overline{NC}\)
  • \(1 \leq N, A, B, C < 10^{9}\)
  • \(N, A, B, C\) don't have leading zero

As an example, \(309\) is a Sangar Number shown in the picture above.

Yasya' also gave me a list of \(999\) integers here. He challenged me to find out how many Sangar Numbers in there.

Can you help me to solve this problem?

This problem is taken from TOKI Open Contest January 2013 (Problemsetter : Me and Yasya')

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