Brilli the Ant decided to improve the monetary system of Brilliant by introducing a series of new Brill notes featuring Brilli doing some of her favorite problems. The current monetary unit of Brilliant is 1 Brill. After long discussions in the parliament, the following restrictions were agreed upon.

Each of the new Brill notes must be worth an integer number of Brills.

Each of the new Brill notes must be worth at least \(100\) Brills.

For all integers \(N \geq 1000\), \(N\) Brills must be expressible as a sum of several new Brill notes. Some of these notes could have the same monetary value.

What is the smallest number of new types of Brill notes that can satisfy these requirements?

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