import sequtils

proc valid(a, b, c: int): bool =
    let greatThenZero = all([a, b, c], proc (x: int): bool = return x > 0)
    let equalityCheck = (a + b >= c) and (a + c >= b) and (b + c >= a)

    greatThenZero and equalityCheck

proc is_equilateral*(sides: array[3, int]): bool =
    let a = sides[0]
    let b = sides[1]
    let c = sides[2]
    valid(a, b, c) and all(sides, proc (x: int): bool = return a == x)

proc is_isosceles*(sides: array[3, int]): bool =
    let a = sides[0]
    let b = sides[1]
    let c = sides[2]
    valid(a, b, c) and (a == b or b == c or a == c)

proc is_scalene*(sides: array[3, int]): bool =
    let a = sides[0]
    let b = sides[1]
    let c = sides[2]
    valid(a, b, c) and not is_isosceles(sides)