American Betting - Coins #7

You have a bankroll of 1400 dollars at a charity game night.

The host flips two fair coins at once.

You may bet on the event that both coins land heads. The host offers you American odds of +350 on this bet. American odds quote the payout against a 100 reference: a line of $+M$ means a stake of 100 wins a profit of $M$, and a line of $-M$ means you must stake $M$ to win a profit of 100. When you win you keep your stake plus the profit; when you lose you lose the stake.

Using the Kelly criterion (bet a fixed fraction of the bankroll, chosen to maximise the long-run growth rate of the bankroll), how many dollars of your 1400-dollar bankroll should you stake? Give the answer as an integer number of dollars.