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Problem 310

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Nim Square

Alice and Bob play the game Nim Square.
Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number of stones from a heap.
The number of stones in the three heaps is represented by the ordered triple (a,b,c).
If 0≤a≤b≤c≤29 then the number of losing positions for the next player is 1160.

Find the number of losing positions for the next player if 0≤a≤b≤c≤100 000.

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取平方数石子

爱丽丝和鲍勃正在玩取平方数石子的游戏。
取平方数石子游戏和通常玩的三堆经典取石子游戏基本一致，只是玩家每次从堆中只能取走平方数枚石子。
三堆中的石子数目用有序三元组(a,b,c)表示。
如果0≤a≤b≤c≤29，将要取石子的玩家必败的状态有1160种。

如果0≤a≤b≤c≤100 000，求将要取石子的玩家必败的状态数目。

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