Problem:
Score : 300 points

Problem Statement

You are given N real values A_1, A_2, \ldots, A_N.
Compute the number of pairs of indices (i, j)
such that i < j and the product A_i \cdot A_j is integer.

Constraints

2 \leq N \leq 200\,000

0 < A_i < 10^4

A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.

N
A_1
A_2
\vdots
A_N

Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

7.5 \cdot 2.4 = 18

7.5 \cdot 16 = 120

17 \cdot 16 = 272

Sample Input 2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Sample Output 2

8

Solution in Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.io.*
import java.util.*
import java.lang.*
import java.lang.Math.*


fun solve() {
    val N = rd.readInt()
    val A = (0 until N).map{rd.readDouble()}
            .map{(it*1_000_000_000).toLong()}

    val fc2 = IntArray(N){0}
    val fc5 = IntArray(N){0}
    val fq = Array(50){IntArray(25){0} }

    for (i in 0 until N) {
        var num = A[i]
        var cnt = 0
        while (num%2L == 0L) {
            cnt++
            num/=2L
        }
        fc2[i] = cnt
        tAssert(fc2[i]<fq.size)

        num = A[i]
        cnt = 0
        while (num%5L == 0L) {
            cnt++
            num/=5L
        }
        fc5[i] = cnt
        tAssert(fc5[i]<fq[0].size)

        fq[fc2[i]][fc5[i]]++
    }

    var ans = 0L
    for (i2 in 0 until 50) {
        for (i5 in 0 until 25) {
            for (j2 in 0 until 50) {
                for (j5 in 0 until 25) {
                    if (i2+j2>=18 && i5+j5>=18) {
                        if (i2==j2 && i5==j5) {
                            ans += fq[i2][i5]*(fq[i2][i5]-1)
                        } else {
                            ans += fq[i2][i5] * fq[j2][j5]
                        }
                    }
                }
            }
        }
    }

    println(ans/2L)
}


//val rd = debug.Reader("agc", "047", "a", "sample-1")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        var exception: Throwable? = null
        val sth = Thread(null, SolveThread(), "solveThread", 128 * 1024 * 1024)
        sth.setUncaughtExceptionHandler { _, e -> exception = e }
        sth.start(); sth.join()
        if (exception != null) throw exception!! }
    catch (e: Exception) { throw e }
    finally { rd.close() }
}
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
data class IntPair(val first: Int, val second: Int)
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg) }
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000) }
}
class SolveThread : Runnable {
    override fun run() { solve() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readDouble: () -> Double = { br.readLine().toDouble() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
    val readListStringCol: (Int) -> List<String> = { N -> (0 until N).map { readString() } }
    val readListIntCol: (Int) -> List<Int> = { N -> (0 until N).map { readInt() } }
    val readListIntCols: (Int) -> List<List<Int>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toInt() } } }
    val readListLongCol: (Int) -> List<Long> = { N -> (0 until N).map { readLong() } }
    val readListLongCols: (Int) -> List<List<Long>> = { N -> (0 until N).map { br.readLine().split(' ').map { it.toLong() } } }
    val close: () -> Unit = { br.close() }
    protected fun finalize() { close() }
}