#!/usr/bin/env python
from collections import namedtuple
from math import sqrt

def mix(a, b, amount):
    return (1-amount)*a + amount*b

def clamp(x, min, max):
    if x < min: return min
    if x > max: return max
    return x

class Vec2(namedtuple('Vec2', ('x', 'y'))):
    def __add__(self, other):
        return Vec2(self.x+other.x, self.y+other.y)
    def __sub__(self, other):
        return Vec2(self.x+other.x, self.y+other.y)
    def __neg__(self):
        return Vec2(-self.x, -self.y)
    def __mul__(self, other):
        if isinstance(other, Vec2):
            return other.x*self.x + other.y*self.y
        else:
            return Vec2(other*self.x, other*self.y)
    def __div__(self, k):
        return Vec2(self.x/k, self.y/k)
    def length(self):
        return sqrt(self.x*self.x + self.y*self.y)
    def normalized(self):
        return self/self.length()
    def dist(self, other):
        return (other - self).length()
    def cross(self, other):
        return self.x*other.y - self.y*other.x
    def mix(self, other, amount):
        return Vec2(mix(self.x, other.x, amount),
                mix(self.y, other.y, amount))
    def clamped(self, min, max):
        return Vec2(clamp(self.x, min.x, max.x),
                clamp(self.y, min.y, max.y))
Vec2.__radd__, Vec2.__rsub__, Vec2.__rmul__ = Vec2.__add__, Vec2.__sub__, Vec2.__mul__