Even Number Addicts

Alice and Bob play a game with an array arr of n positive integers. Alice goes first. On each turn, a player picks one number from the array and adds it to their total sum. After all numbers are taken, if Alice's total sum is even, Alice wins; otherwise Bob wins. Both play optimally — determine if Alice has a winning strategy.

Examples
Input: [1,2,3]
Output: false
Hints

Even Number Addicts

Alice and Bob play a game with an array arr of n positive integers. Alice goes first. On each turn, a player picks one number from the array and adds it to their total sum. After all numbers are taken, if Alice's total sum is even, Alice wins; otherwise Bob wins. Both play optimally — determine if Alice has a winning strategy.