Operator Square

Let the operator \square be defined for all positive integers the following way:

  • 11=11 \square 1=1.
  • For all positive integers n>1n>1, n1=(n1)1+nn \square 1=(n-1) \square 1+n.
  • For all positive integers n>1n>1, 1n=1(n1)+n1 \square {n}=1 \square (n-1)+n.
  • For all positive integers a>1a>1 and b>1b>1, ab=a(b1)+(a1)ba\square{b}=a\square(b-1)+(a-1)\square{b}.

Evaluate 555\square5.

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