The Toll Gate of Wyrmback Bridge

A notice, pinned by the door of the Wick & Whistle inn.

The toll-keeper at Wyrmback Bridge has lost her tally-clerk to the harvest, and the morning caravan is already queued on the far bank. She needs someone to total up a day's takings.

You are given carts, a list of carts in the order they reach the gate. Each cart is a 3-element list [kind, weight, wheels], where kind is a string, weight is a positive integer (the load in stones), and wheels is a positive integer.

The posted toll for a single cart, in coins:

• If kind is "grain": nothing at all when weight is 100 or less; otherwise 1 + (weight - 100) // 50 coins, using floor division.
• If kind is "stone": 5 coins, plus 10 more if weight is greater than 300, or else plus 4 more if weight is greater than 150.
• If kind is "cloth": 4 coins if weight is greater than 200, and 2 coins otherwise.
• Any other value of kind is not on the posted list: that cart is waved through for 0 coins, and no further charge of any sort applies to it.

Then, for every cart that is on the posted list and whose kind is not "grain", add 3 coins if wheels is greater than 4.

Write bridgeToll(carts), which returns the sum of the tolls of all the carts as an integer. An empty list of carts returns 0.