World of Darkraft

Alice and Bob are playing a game set in the World of Darkraft. There are n monsters, each with attack power a[i] and defense power b[i]. Players take turns picking a monster. If a player picks a monster with attack >= the current hero attack and defense >= the current hero defense, the hero defeats it and the hero's attack becomes a[i] and defense becomes b[i]. Otherwise the player loses instantly. Alice starts with hero stats (0, 0). Both play optimally — determine if Alice has a winning strategy.

Examples
Input: [3,[1,3,2],[2,1,3]]
Output: true
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World of Darkraft

Alice and Bob are playing a game set in the World of Darkraft. There are n monsters, each with attack power a[i] and defense power b[i]. Players take turns picking a monster. If a player picks a monster with attack >= the current hero attack and defense >= the current hero defense, the hero defeats it and the hero's attack becomes a[i] and defense becomes b[i]. Otherwise the player loses instantly. Alice starts with hero stats (0, 0). Both play optimally — determine if Alice has a winning strategy.