import kotlin.math.hypot
import kotlin.math.sqrt

fun main() {
    val n = readInt()
    val pts = List(n) { readStrings().map { it.toDouble() }}
    val totalLen2 = pts.zipWithNext { a, b ->
        (b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1])
    }.sum()
    val totalSq = pts.zipWithNext { a, b->
        (a[1] + b[1]) / 2.0 * (b[0] - a[0])
    }.sum()
    // ans = totalSq + totalLen2 * ans
    val ansDelta = if (pts.all { it[1] == 0.0 }) 0.0 else totalSq / (1 - totalLen2)
    val ans = sqrt(3.0) / 4.0 + ansDelta * 3
    println(ans)
}

private fun readInt() = readln().toInt()
private fun readLongs() = readStrings().map { it.toLong() }
private fun readStrings() = readln().split(" ")
private fun readInts() = readStrings().map { it.toInt() }