Leetcode - Climbing Stairs Solution

Input: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Input: n = 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

class Solution:
    def climbStairs(self, n: int) -> int:
        def fact(x):
            if x==1 or x==0:
                return 1
            else:
                return x*fact(x-1)
        c = {1: n , 2: 0}
        steps = 0
        while c[1]>-1:
            x,y = c.values()
            p = fact(x+y)//(fact(x)*fact(y))
            steps+= p
            c[1] -= 2
            c[2] += 1
        return steps