# Leetcode - Climbing Stairs Solution

You are climbing a staircase. It takes `n`

steps to reach the top.

Each time you can either climb `1`

or `2`

steps. In how many distinct ways can you climb to the top?

**Example 1:**

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

**Example 2:**

```
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
```

**Constraints:**

`1 <= n <= 45`

## Solution in Python

```
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
```