When a beam of light hits a layer of glass, a certain percentage of the light passes through the glass, a certain percentage is reflected back, and the remaining light is absorbed by the glass.

Suppose that for any amount of light $x$, $x \times a_i\%$ of the light passes through the $i$-th layer, and $x \times b_i\%$ is reflected back.

Now, $n$ layers of glass are stacked together. If $1$ unit of light hits the first layer of glass, how many units of light will pass through all $n$ layers?

Input

The first line contains an integer $n$, the number of glass layers.

The next $n$ lines each contain two integers $a_i$ and $b_i$, representing the percentage of light that passes through and is reflected by the $i$-th layer, respectively.

Output

Output a single integer representing the amount of light that passes through all layers, modulo $10^9 + 7$.

It can be proven that the answer is always a rational number. If the answer is $a/b$ (where $a$ and $b$ are coprime positive integers), you should output an integer $x$ such that $a \equiv bx \pmod{10^9 + 7}$.

Examples

Input 1

2
50 20
80 5

Output 1

858585865

Note 1

As shown in the figure, light enters from the top left. $0.5$ units of light pass through the first layer, and $0.2$ units are reflected back. Of the $0.5$ units, $0.4$ units pass through the second layer, and $0.025$ units are reflected back. Of the $0.025$ units, $0.0125$ units pass through the first layer, and $0.005$ units are reflected back. Of the $0.005$ units, $0.004$ units pass through the second layer... Thus, the total amount of light passing through both layers is $0.40404... = \frac{40}{99}$. Modulo $10^9+7$, this is equal to $858585865$.

Input 2

3
1 2
3 4
5 6

Output 2

843334849

Subtasks

For $5\%$ of the data, $n=1$.

For $20\%$ of the data, $n\le 2$.

For $30\%$ of the data, $n\le 3$.

For $50\%$ of the data, $n\le 100$.

For $70\%$ of the data, $n\le 3000$.

For $100\%$ of the data:

• $1\le n\le 5\times 10^5$
• $1\le a_i \le 100$
• $0\le b_i \le 99$
• $1\le a_i+b_i \le 100$
• Each pair of $a_i$ and $b_i$ is generated randomly among integers satisfying the above constraints.