Pin the tail on the factorial

You are told that the last fourteen digits of 33!33! (from the right) are 94401abc000000, \overline{94401abc000000}, where a,ba, b and cc are digits. What is the value of abc\overline{abc} ?

Details and Assumptions:

  • abc \overline{abc} means 100a+10b+1c 100a + 10b + 1c, as opposed to a×b×c a \times b \times c. As an explicit example, for a=2,b=3,c=4a=2, b=3, c=4, abc=234\overline{abc} = 234 and not 2×3×4=24 2 \times 3 \times 4 = 24.

  • The last 3 digits of the number 10231023 are 023023.

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