frog has $n$ integers $a_1, a_2, \dots, a_n$, and she wants to add them pairwise.

Unfortunately, frog is somehow afraid of carries (进位). She defines hardness $h(x, y)$ for adding $x$ and $y$ the number of carries involved in the calculation. For example, $h(1, 9) = 1, h(1, 99) = 2$.

Find the total hardness adding $n$ integers pairwise. In another word, find $$\sum_{1 \leq i < j \leq n} h(a_i, a_j)$$ .

Input

The input consists of multiple tests. For each test:

The first line contains $1$ integer $n$ ($2 \leq n \leq 10^5$). The second line contains $n$ integers $a_1, a_2, \dots, a_n$. ($0 \leq a_i \leq 10^9$).

Output

For each test, write $1$ integer which denotes the total hardness.

Sample Input

2
5 5
10
0 1 2 3 4 5 6 7 8 9

Sample Output

1
20