Megazords

Megazords are essential for defending the Earth. Assembling one megazord takes exactly three zords: one green, one red, and one blue.

The green, red, and blue rangers want to know how many different ways they can assemble a megazord. Each ranger has a set of zords. The green ranger has green zords, the red ranger has red zords, and the blue ranger has blue zords.

Three rules apply when assembling a megazord.

• The first digit of the red zord's model number must equal the last digit of the green zord's model number.
• The last digit of the red zord's model number must equal the first digit of the blue zord's model number.
• The three zords used must all have different model numbers.

Two ways are different if at least one ranger uses a different zord, even when the model number is the same. A ranger may have several zords with the same model number.

The first line contains the number of zords the green, red, and blue rangers have, $g$, $r$, and $b$ ($1 \le g, r, b \le 10^5$).

The second line contains $g$ model numbers $x_i$ of the green zords ($0 \le x_i \le 10^9$). The third line contains $r$ model numbers $y_i$ of the red zords, and the fourth line contains $b$ model numbers $z_i$ of the blue zords.

Print one integer, the number of different megazords that can be assembled.

The first sample has three megazords: $101+11+13$, $52+23+31$, and $52+23+31$. The last one is counted twice because the red ranger can use either the second or the third zord. $11+11+13$ cannot be assembled because it uses model 11 twice.