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 (Lua 5.3.5) (judge verdict: Accepted)

local read = setmetatable({}, {__index = function(t, k) local a = {} for i=1,#k do table.insert(a, '*'..string.sub(k, i, i)) end local r = io.read local u = table.unpack or unpack return function() return r(u(a)) end end})
read.N = function(N) local t={} for i=1,N do t[i]=read.n() end return t end
----

local N = read.n()

local function get(b, e)
    -- number of integer x where:
    --  - begin with b,
    --  - end with e, and
    --  - x <= N
    local c = 0
    for i=e,N,10 do
        local x = tonumber(tostring(i):sub(1,1))
        if x == b then
            c = c + 1
        end
    end
    return c
end

local cnt = 0
-- A
-- x....y
-- B
-- y....x
for x=1,9 do
    for y=1,9 do
        local cnt_a = get(x, y)
        local cnt_b = get(y, x)
        cnt = cnt + cnt_a * cnt_b
    end
end
print(cnt)