Suresh is playing a game with **N** levels. He passes level **i** with probability **p _{i}** and the time taken for level

**i**is

**t**(regardless of whether he passes the level or not). Whenever Suresh fails any level, he has to start again from the

_{i}**first**level. Find the expected time when Suresh will be able to pass all the levels.

1 ≤ T ≤ 10

1 ≤ N ≤ 10000

1 ≤ t_{i} ≤ 10000

0 ≤ p_{i} ≤ 1