blocked = {(1, 1), (2, 3)}
dp = [[0] * 5 for _ in range(5)]
for x in range(5):
    for y in range(5):
        if (x, y) in blocked:
            continue
        if (x, y) == (0, 0):
            dp[x][y] = 1
        else:
            dp[x][y] = (dp[x-1][y] if x else 0) + (dp[x][y-1] if y else 0)
assert dp[1][1] == 0 and dp[2][3] == 0
result = {"valid_paths": dp[4][4]}
import json
print(json.dumps(result, ensure_ascii=False, sort_keys=True))