Tonight at 7pm a professional basketball game featuring the Golden State Warriors and the Washington Wizards will be played at the Chase Center, an indoor arena in the Mission Bay neighborhood of San Francisco, California. Our teaching assistants Yang and Guangchu are making fair bets on the game. During office hours you learn that Yang thinks the Warriors will win and believes he is making a fair bet, assigning a probability of 5/6 or 83% to the Warriors winning. Guangchu is betting on the Wizards and also believes he is making a fair bet, assigning a probability of 7/12 or 58% to the Wizards winning. You seek to bet a total of $N with Yang and Guangchu and capture a guaranteed, risk-free arbitrage profit. What is the minimum value of N that ensures your arbitrage profit is greater than or equal to $100?