If every letter corresponds a unique digit in decimal system and \[\overline{TOM}+\overline{GIVES} = \overline{MOST}+ \overline{TIME} \]
Find the value of \[\overline{EGG}+ \overline{IS} + \overline{VEG}\]

###### Image Credit: Wikimedia Genetic Algorithm by Yearofthedragon

**Details and assumptions**:

\(\bullet\) If \((A,B,C,D) =(1,2,3,4) \) , then \(\overline{BAD} = 214 \).

\(\bullet\) Everything is in decimal representation and every letter corresponds to one unique digit. That is why this has exactly one solution.

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