Problem:
Score : 400 points

Problem Statement

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.

Constraints

1 \leq N \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

25

Sample Output 1

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 Input 2

1

Sample Output 2

1

Sample Input 3

100

Sample Output 3

108

Sample Input 4

2020

Sample Output 4

40812

Sample Input 5

200000

Sample Output 5

400000008

Solution in Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

local n=io.read("n")
local map={}
for i=1,n do
    local itos=tostring(i)
    local first=itos:byte(1)
    local last=itos:byte(#itos)
    map[first]=map[first] or {}
    map[first][last]=(map[first][last] or 0)+1
end

local counter=0
for first,_ in pairs(map) do
    for last,_ in pairs(map[first]) do
        if map[last] and map[last][first] then
            counter=counter+map[first][last]*map[last][first]
        end
    end
end
print(counter)