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In △ABC\triangle ABC△ABC, DDD and EEE are points on BCBCBC such that BD=DE=ECBD = DE = ECBD=DE=EC. FFF is a point on ACACAC such that AF=FCAF=FCAF=FC. If ADADAD and AEAEAE intersect BFBFBF respectively at PPP and QQQ. Then, the ratio BPPQ\dfrac{BP}{PQ}PQBP can be expressed as ab\dfrac{a}{b}ba, where aaa and bbb are coprime integers. Find 10a+b10a+b10a+b.
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