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Let a,b,c,da, b, c, d be positive integers such that a+b+c+d=120,a+b+c+d=120, and define S=ab+bd+da+bc+cd.S=ab+bd+da+bc+cd. Find the number of ordered quadruples (a,b,c,d)(a,b,c,d) for which SS attains its maximum.

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