Elevator Hall Number

JAG (Japanese Alumni Group) is a mysterious organization headquartered in a high-rise building somewhere in Tokyo. The building has $N$ elevators, and the $i$-th elevator stops at every floor from $low\_i$ to $high\_i$ ($1 \le i \le N$).

X, a new JAG staff member, reached the elevator hall of the building to visit the headquarters. While waiting for an elevator after pressing the button, X noticed that the display showing the current floor of each elevator is somewhat unusual. When the $i$-th elevator is on floor $a\_i$, the display shows one number obtained by listing $a\_1, a\_2, \ldots, a\_N$ in this order and concatenating them in decimal notation, without leading zeros and without spaces. For example, when $N = 3$ and the elevators are on floors $10$, $2$, and $11$ in order, the display shows $10211$.

X became curious about how many different numbers can appear on the display. Your task is to write a program that computes this count.

The input consists of multiple datasets, each in the following format.

$N$

$low\_1$ $high\_1$

...

$low\_N$ $high\_N$

The first line of a dataset contains the integer $N$ ($2 \le N \le 6$), the number of elevators. The $i$-th of the following $N$ lines contains two integers $low\_i$ and $high\_i$ ($1 \le low\_i \le high\_i \le 99$), the range of floors served by the $i$-th elevator.

The end of the input is indicated by a line containing a single zero.

For each dataset, output on one line the number of different numbers that can appear on the display.