In a game development project, you're tasked with calculating the initial health points $($HP$)$ of a character, which is determined by the factorial of the level. At each level, the character multiplies their HP by that level up to level $10.$

Use int variables level and hp$,$ and use a while loop to compute hp at level $10.$ Use no variables other than level and hp$.$ Declare and initialize level and hp with appropriate values to ensure the loop iterates correctly and calculates the factorial accurately. In the end, level should be $10,$ and hp should be $10$ factorial.