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# 70. Climbing Stairs

<https://leetcode.com/problems/climbing-stairs/description/>

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:**

```
class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        def choose(n, x):
            nl = 1
            for i in range(1, n+1, 1):
                nl *= i
            xl = 1
            for i in range(1, x+1, 1):
                xl *= i
            n_xl = 1
            for i in range(1, n-x+1, 1):
                n_xl *= i
            return nl/xl/n_xl
            
        num = 0
        for i in range(n/2+1):
            num += choose(n-i, i)
        return num
```