# Question

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

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

Example 2:

```
Input: 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
```

# Solution

To climb `n`

steps, one can climb first `n-1`

steps and climb the last 1 step, or climb the first `n-2`

step and climb the last 2 steps. Thus, the answer for `n`

is the sum of those for `n-1`

and `n-2`

.

```
class Solution:
def climbStairs(self, n):
"""
:type n: int
:rtype: int
"""
if n == 1:
return 1
if n == 2:
return 2
dp = [1, 2]
for idx in range(2, n):
dp.append(dp[idx - 1] + dp[idx - 2])
return dp[-1]
```