Order Book Backlog Priority Matching

An electronic crossing engine processes a continuous stream of limit orders. You are given a 2D integer array orders, where orders[i] = [price_i, amount_i, order_type_i]:

• order_type_i = 0: Represents a Buy order for amount_i shares at a maximum limit price price_i.
• order_type_i = 1: Represents a Sell order for amount_i shares at a minimum limit price price_i.

Matching Rules (Price-Time Priority):

1. An incoming Buy order matches against existing resting Sell orders in the backlog that have the lowest price $\le price_i$. Matching continues until the incoming buy order is fully filled or no eligible sell orders remain in the backlog.
2. An incoming Sell order matches against existing resting Buy orders in the backlog that have the highest price $\ge price_i$. Matching continues until the incoming sell order is fully filled or no eligible buy orders remain in the backlog.
3. Any remaining unfilled amount of the incoming order is added to the order backlog.

Your Task

Implement get_number_of_backlog_orders(orders: list[list[int]]) -> int that returns the total quantity of shares remaining in the backlog after processing all orders, modulo $10^9 + 7$.

Constraints

• $1 \le \text{len}(orders) \le 10^5$
• orders[i] = [price, amount, order_type]
• $1 \le price_i, amount_i \le 10^9$
• $order\_type_i \in \{0, 1\}$

Examples

orders = [[10, 5, 0], [15, 2, 1], [25, 1, 1], [30, 4, 0]]
# 1. Buy 5 @ 10 -> backlog buy: {10: 5}
# 2. Sell 2 @ 15 -> backlog sell: {15: 2}
# 3. Sell 1 @ 25 -> backlog sell: {15: 2, 25: 1}
# 4. Buy 4 @ 30 -> matches Sell 2 @ 15 (2 shares left), matches Sell 1 @ 25 (1 share left). Remaining 1 buy @ 30 enters backlog.
# Final backlog: Buy {10: 5, 30: 1} -> 6 shares total.
# Output: 6