\[ \LARGE \square^\square \ + \ \square^\square \ + \ \square^\square \]

Six numbers \(1,2,3,4,5,\) and \(6\) are to be filled in the square boxes above (without repetition). Of all \(6!=720\) possible arrangements, find the minimum value of the resultant number.

**Details and Assumptions**

- As an explicit example, if the six numbers are \(2,2,2,3,3,\) and \(3,\) then the minimum resultant number is \(2^3+2^3+2^3=24.\)

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