10836: ABC152 - D - Handstand 2
[Creator : ]
Description
Given is a positive integer $N$.
Find the number of pairs $(A, B)$ of positive integers not greater than $N$ that satisfy the following condition:
- When $A$ and $B$ are written in base ten without leading zeros, the last digit of $A$ is equal to the first digit of $B$, and the first digit of $A$ is equal to the last digit of $B$.
Input
Input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the answer.
Constraints
- $1 \leq N \leq 2 \times 10^5$
- All values in input are integers.
Sample 1 Input
25
Sample 1 Output
17
The following $17$ pairs satisfy the condition: $(1,1)$, $(1,11)$, $(2,2)$, $(2,22)$, $(3,3)$, $(4,4)$, $(5,5)$, $(6,6)$, $(7,7)$, $(8,8)$, $(9,9)$, $(11,1)$, $(11,11)$, $(12,21)$, $(21,12)$, $(22,2)$, and $(22,22)$.
Sample 2 Input
1
Sample 2 Output
1
Sample 3 Input
100
Sample 3 Output
108
2020
40812
Sample 4 Input
200000
Sample 4 Output
400000008