In the addition problem:
\[
\begin{array}{cccccc}
& W & H & I & T & E \\
+ & W & A & T & E & R \\
\hline
P & I & C & N & I & C
\end{array}
\]
each distinct letter represents a different digit. Find the number represented by the answer \(\text{PICNIC}\).

Let's think step by step and output the final answer within \boxed{}.
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