The number of ordered pairs \( (a, b) \), where \( a, b \) are inte...

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The number of ordered pairs \( (a, b) \), where \( a, b \) are integers satisfying the inequality \( \min \left(x^{2}+(a-b) x+(1-a-b)\right)\max \left(-x^{2}+(a+b) x-(1+a+b)\right) \forall x \in R \), is :
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