Rng

Avin is studying how to synthesize data. Given an integer n, he constructs an interval using the following method: he first generates a integer r between 1 and n (both inclusive) uniform-randomly, and then generates another integer l between 1 and r (both inclusive) uniform-randomly. The interval [l, r] is then constructed. Avin has constructed two intervals using the method above. He asks you what the probability that two intervals intersect is. You should print p* ${q^{(-1)}}$(MOD 1, 000, 000, 007), while $\frac{p}{q}$ denoting the probability.

Just one line contains the number n (1 ≤ n ≤ 1, 000, 000).

Print the answer.

1
2

1
750000006

2019CCPC-江西省赛（重现赛）- 感谢南昌大学