A mammoth counting!

Let \(f(n)\) represent the total number of straight line segments in the UPPER CASE English representation of the natural number \(n\) without adding AND and hyphen (-). For example, 12 can be written as TWELVE and if you carefully count all the straight-line segments in it, you get \(f(n) = 18\).

Call a number truthful if \(f(n) = n\). What is the sum of the all truthful numbers from 1 to 9999?

Explicit Examples:

  • The letters G, I, J, Q, R, U and X contain 1, 1, 0, 1, 2, 0 and 2 straight line segments respectively.

  • Use the word ONE for denoting a single hundred or thousand and don't use the word AND anywhere.

  • Some examples of the upper representation are:
    73: SEVENTY THREE
    105: ONE HUNDRED FIVE
    1274: ONE THOUSAND TWO HUNDREDS SEVENTY FOUR
    6001: SIX THOUSANDS ONE

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