A problem by Chan Ming Xian

Level pending

Integer a, b, c, d fulfill the condition that\[(ab+cd)^{2}+(ad-bc)^{2}\]=2009 .Find out all the possible sum values of \[a^{2}+b^{2}+c^{2}+d^{2}\]Sum up all the possible values for this problem and write out the last three digits of this sum as the answer.

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