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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mfl = math.floor
local n = io.read("*n")
local t = {}
for i = 1, 81 do
  t[i] = 0
end
for i = 1, n do
  local ri = i
  local btm = i % 10
  if btm ~= 0 then
    local top = btm
    if i < 10 then
    end
    while 10 <= i do
      i = mfl(i / 10)
    end
    local top = i
    local idx = (top - 1) * 9 + btm
    t[idx] = t[idx] + 1
  end
end
local ret = 0
for i = 1, 9 do
  local idx = (i - 1) * 9 + i
  -- ret = ret + t[idx] * t[idx]
  for j = 1, 9 do
    local idx1, idx2 = (i - 1) * 9 + j, (j - 1) * 9 + i
    ret = ret + t[idx1] * t[idx2]
  end
end
print(ret)