For problem statement at 1000-1999/1500-1599/1510-1519/1510/problemF.txt this is a correct solution, but verifier at 1000-1999/1500-1599/1510-1519/1510/verifierF.go ends with test 1 mismatch: expected 0.845616557381 got 3.012712585980
input:
3 4.000000
0.000000 0.000000
1.000000 0.000000
0.000000 1.000000
reference output:
0.845616557380924

participant output:
3.012712585980356

exit status 1 can you fix the verifier? package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
)

type Point struct {
	x, y float64
}

type Ray struct {
	angle float64
	orig  Point
	dir   Point
}

type Sector struct {
	F1       Point
	F2       Point
	L_hidden float64
}

func main() {
	reader := bufio.NewReader(os.Stdin)
	var n int
	var L float64
	if _, err := fmt.Fscanf(reader, "%d %f\n", &n, &L); err != nil {
		return
	}

	V := make([]Point, n)
	for i := 0; i < n; i++ {
		fmt.Fscanf(reader, "%f %f\n", &V[i].x, &V[i].y)
	}

	pref := make([]float64, n)
	cur := 0.0
	for i := 0; i < n; i++ {
		pref[i] = cur
		p1 := V[i]
		p2 := V[(i+1)%n]
		cur += math.Hypot(p1.x-p2.x, p1.y-p2.y)
	}
	P_poly := cur

	ccwDist := func(i, j int) float64 {
		d := pref[j] - pref[i]
		if d < 0 {
			d += P_poly
		}
		return d
	}

	rays := make([]Ray, 0, 2*n)
	for i := 0; i < n; i++ {
		p1 := V[i]
		p2 := V[(i+1)%n]
		E := Point{p2.x - p1.x, p2.y - p1.y}
		LE := math.Hypot(E.x, E.y)
		U := Point{E.x / LE, E.y / LE}
		
		angFwd := math.Atan2(U.y, U.x)
		if angFwd < 0 {
			angFwd += 2 * math.Pi
		}
		rays = append(rays, Ray{angle: angFwd, orig: p2, dir: U})

		Ubwd := Point{-U.x, -U.y}
		angBwd := math.Atan2(Ubwd.y, Ubwd.x)
		if angBwd < 0 {
			angBwd += 2 * math.Pi
		}
		rays = append(rays, Ray{angle: angBwd, orig: p1, dir: Ubwd})
	}

	sort.Slice(rays, func(i, j int) bool {
		return rays[i].angle < rays[j].angle
	})

	sectors := make([]Sector, 2*n)
	for k := 0; k < 2*n; k++ {
		ang1 := rays[k].angle
		ang2 := rays[(k+1)%(2*n)].angle
		if k == 2*n-1 {
			ang2 += 2 * math.Pi
		}
		mid := (ang1 + ang2) / 2.0
		ux := math.Cos(mid)
		uy := math.Sin(mid)

		maxVal := -1e18
		minVal := 1e18
		idxLeft := -1
		idxRight := -1
		for i, p := range V {
			val := -uy*p.x + ux*p.y
			if val > maxVal {
				maxVal = val
				idxLeft = i
			}
			if val < minVal {
				minVal = val
				idxRight = i
			}
		}
		sectors[k] = Sector{
			F1:       V[idxLeft],
			F2:       V[idxRight],
			L_hidden: ccwDist(idxLeft, idxRight),
		}
	}

	Pk := make([]Point, 2*n)
	for k := 0; k < 2*n; k++ {
		sec := sectors[k]
		F1 := sec.F1
		F2 := sec.F2
		D := L - sec.L_hidden

		Vorig := rays[k].orig
		U := rays[k].dir

		A := Point{Vorig.x - F1.x, Vorig.y - F1.y}
		B := Point{Vorig.x - F2.x, Vorig.y - F2.y}

		P := 2.0 * (U.x*(A.x-B.x) + U.y*(A.y-B.y))
		Q := (A.x*A.x + A.y*A.y) - (B.x*B.x + B.y*B.y) - D*D

		a_quad := P*P - 4.0*D*D
		b_quad := 2.0*P*Q - 8.0*D*D*(U.x*B.x+U.y*B.y)
		c_quad := Q*Q - 4.0*D*D*(B.x*B.x+B.y*B.y)

		disc := b_quad*b_quad - 4.0*a_quad*c_quad
		if disc < 0 {
			disc = 0
		}
		r := (-b_quad - math.Sqrt(disc)) / (2.0 * a_quad)

		Pk[k] = Point{Vorig.x + r*U.x, Vorig.y + r*U.y}
	}

	totalArea := 0.0
	for k := 0; k < 2*n; k++ {
		sec := sectors[k]
		F1 := sec.F1
		F2 := sec.F2
		D := L - sec.L_hidden

		a_el := D / 2.0
		dxF := F1.x - F2.x
		dyF := F1.y - F2.y
		distF := math.Hypot(dxF, dyF)
		c_el := distF / 2.0
		b_el := math.Sqrt(math.Max(0, a_el*a_el-c_el*c_el))

		C := Point{(F1.x + F2.x) / 2.0, (F1.y + F2.y) / 2.0}

		var Uel, Vel Point
		if distF < 1e-9 {
			Uel = Point{1.0, 0.0}
		} else {
			Uel = Point{dxF / distF, dyF / distF}
		}
		Vel = Point{-Uel.y, Uel.x}

		pStart := Pk[k]
		pEnd := Pk[(k+1)%(2*n)]

		dx0 := pStart.x - C.x
		dy0 := pStart.y - C.y
		cos0 := (dx0*Uel.x + dy0*Uel.y) / a_el
		sin0 := (dx0*Vel.x + dy0*Vel.y) / b_el
		t0 := math.Atan2(sin0, cos0)

		dx1 := pEnd.x - C.x
		dy1 := pEnd.y - C.y
		cos1 := (dx1*Uel.x + dy1*Uel.y) / a_el
		sin1 := (dx1*Vel.x + dy1*Vel.y) / b_el
		t1 := math.Atan2(sin1, cos1)

		diff := t1 - t0
		for diff < 0 {
			diff += 2.0 * math.Pi
		}
		for diff >= 2.0*math.Pi {
			diff -= 2.0 * math.Pi
		}

		term1 := a_el * b_el * diff
		term2 := a_el * (math.Cos(t1) - math.Cos(t0)) * (C.x*Uel.y - C.y*Uel.x)
		term3 := b_el * (math.Sin(t1) - math.Sin(t0)) * (C.x*Vel.y - C.y*Vel.x)

		totalArea += 0.5 * (term1 + term2 + term3)
	}

	fmt.Printf("%.15f\n", totalArea)
}