Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20×20 grid?

Look at the picture! How many lines do pass through specific box with number inside. The result would be the sum of all boxes and 1 which did not pass through box but upper sides.

Here is the code.

```
n = 20
li = []
temp = []
for i in range(n):
temp += [1]
li += [temp]
for j in range(n-1):
temp = []
for i in range(n, 0, -1):
temp += [sum(li[j][:i])]
temp.reverse()
li += [temp]
tot = 0
for i in range(n):
tot += sum(li[i])
print(tot + 1)
```

The output is: 137846528820.

This run:~ 0.017461299896240234.