Ability

A player fights monsters in a web game and has all $N$ attack abilities equipped at once. The abilities are numbered 1 through $N$.

Ability $i$ has a trigger probability $p_i$ and a damage value $d_i$. When the player issues a trigger command to ability $i$, the ability fires with probability $p_i$ and deals $d_i$ damage to the opponent, and with probability $1 - p_i$ it does not fire and nothing happens.

One attack opportunity runs like this.

1. Choose one of the equipped abilities. Every ability is equally likely to be chosen.
2. Issue a trigger command to the chosen ability.
3. If the ability fires, the attack opportunity is spent and the process ends.
4. If it does not fire, choose one of the abilities that has not received a command yet, again with equal probability, then go back to step 2.
5. If every ability has received a command and none of them fired, the attack opportunity is spent with no damage.

Given the trigger probability and the damage of all $N$ abilities, compute the expected damage dealt in one attack opportunity.

The first line contains the number of abilities $N$ ($1 \le N \le 5000$).

Line $i$ of the next $N$ lines contains two integers $p_i$ and $d_i$ ($1 \le p_i, d_i \le 10^9$) separated by a space. Ability $i$ fires with probability $p_i / 10^9$ and deals $d_i$ damage when it fires.

Print the expected damage dealt in one attack opportunity. Write the expected value as an irreducible fraction $a/b$ and print $(a \times b^{-1}) \bmod (10^9 + 7)$ instead, where $b^{-1}$ is the multiplicative inverse of $b$ modulo $10^9 + 7$. This value exists for every input given in this problem.