Alice Bob play game pile stone there number pile arrange row pile positive integer number stone pilesithe objective game end stone the total number stone pile odd tiesalice Bob turn Alice start each turn player take entire pile stone begin end row this continue pile leave point person stone winsassume Alice Bob play optimally return true Alice win game false Bob win Example 1input pile 5345output trueexplanation Alice start 5 5say take 5 row 3 4 5if Bob take 3 board 4 5 Alice take 5 win 10 pointsif Bob take 5 board 3 4 Alice take 4 win 9 pointsthis demonstrate take 5 win Alice return trueexample 2input pile 3723output true constraints2 pileslength 500pileslength even1 pilesi 500sumpilesi odd