\[ \large{\begin{array}{ccccccc} && & & & T & E&N\\ && & & & T & E&N\\ && & & N & I &N&E \\ && & E&I &G &H&T\\ + && & T&H &R & E&E \\ \hline & & &F & O&R & T&Y\\ \hline \end{array}} \]

How many solutions exists to the given addition problem, where each letter represents a distinct digit?

**Note:** The first digit of a number can be zero. For example (not necessarily true), in the number \(\overline{NINE}\), we can have it as \(\overline{0I0E}\).

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