package main

import (
	"fmt"
	"math"
	"math/rand"
	"sort"
	"time"
)

// 暴力方法
// 时间复杂度O(N^2)
// 为了测试
func inValues1(a []int, b []int) []int64 {
	n := len(a)
	ans := make([]int64, n)
	for i := 0; i < n; i++ {
		curAns := int64(math.MaxInt64)
		for j := 0; j < n; j++ {
			cur := int64((a[i]+a[j])*(a[i]+a[j]) + b[i] + b[j])
			curAns = min(curAns, cur)
		}
		ans[i] = curAns
	}
	return ans
}

func min(x, y int64) int64 {
	if x < y {
		return x
	}
	return y
}

// 正式方法
// 时间复杂度O(N*logN)
// (a[i] + a[j]) ^ 2 + b[i] + b[j]
// a[i]^2 + b[i] + 2a[i]a[j] + a[j]^2 + b[j]
// a[i] * ( a[i] + b[i]/a[i] + 2a[j] + (a[j]^2 + b[j])/a[i])
// 令S(j) = 2a[j]
// 令T(j) = a[j]^2 + b[j]
// 那么对于i来说，就是选择j，让下面得到最小值
// a[i] * ( a[i] + b[i]/a[i] + S(j) + T(j)/a[i])
// 选择最小的S(j) + T(j)/a[i]，就得到了答案
// 剩下的一切都是围绕这个
func inValues2(a []int, b []int) []int64 {
	n := len(a)
	// i a[i] b[i]
	// i s[i] t[i]
	st := make([][2]int64, n)
	for i := 0; i < n; i++ {
		st[i][0] = 2 * int64(a[i])
		st[i][1] = int64(a[i]*a[i]) + int64(b[i])
	}
	// 只需要根据S值从大到小排序即可
	// 下面的比较器定义稍复杂，因为go里没有泛型sort，只能自己写
	// 所以策略参考了S和T，其实只需要根据S值从大到小排序即可
	sort.Slice(st, func(i, j int) bool {
		if st[i][0] != st[j][0] {
			return st[i][0] > st[j][0]
		}
		return st[i][1] <= st[j][1]
	})
	stack := make([]int, n)
	r := 0
	for i := 0; i < n; i++ {
		// s 大 -> 小

		s := st[i][0]
		t := st[i][1]
		for r > 0 && tail(st, stack, r) >=
			better(st[stack[r-1]][0], st[stack[r-1]][1], s, t) {
			r--
		}
		stack[r] = i
		r++
	}
	arr := make([][3]int, n)
	for i := 0; i < n; i++ {
		arr[i][0] = i
		arr[i][1] = a[i]
		arr[i][2] = b[i]
	}
	// 只需要根据a值从大到小排序即可
	sort.Slice(arr, func(i, j int) bool {
		if arr[i][1] != arr[j][1] {
			return arr[i][1] > arr[j][1]
		}
		return arr[i][0] < arr[j][0]
	})
	ans := make([]int64, n)
	for k := 0; k < n; k++ {
		i := arr[k][0]
		ai := arr[k][1]
		bi := arr[k][2]
		for tail(st, stack, r) > int64(ai) {
			r--
		}
		sj := st[stack[r-1]][0]
		tj := st[stack[r-1]][1]
		// a[i] * ( a[i] + b[i]/a[i] + S(j) + T(j)/a[i])
		curAns := sj*int64(ai) + tj + int64(ai)*int64(ai) + int64(bi)
		ans[i] = curAns
	}
	return ans
}

func tail(st [][2]int64, deque []int, r int) int64 {
	if r == 1 {
		return 1
	}
	return better(st[deque[r-2]][0], st[deque[r-2]][1], st[deque[r-1]][0], st[deque[r-1]][1])
}

// 入参时候s1>=s2，这是一定的
// 返回当ai大到什么值的时候，(s2+t2/ai) <= (s1+t1/ai)
// 即 : ai大
func better(s1, t1, s2, t2 int64) int64 {
	if s1 == s2 {
		if t1 <= t2 {
			return math.MaxInt64
		}
		return 1
	}
	// s1 > s2
	if t1 >= t2 {
		return 1
	}
	// s1 > s2
	// t1 < t2
	td := t2 - t1
	sd := s1 - s2
	return (td + sd - 1) / sd
}

// 为了测试
func randomArray(n, v int) []int {
	ans := make([]int, n)
	for i := 0; i < n; i++ {
		ans[i] = rand.Intn(v) + 1
	}
	return ans
}

// 为了测试
func isSameArray(arr1, arr2 []int64) bool {
	for i := 0; i < len(arr1); i++ {
		if arr1[i] != arr2[i] {
			return false
		}
	}
	return true
}

// 为了测试
func main() {
	N := 100
	A := 100
	B := 50000
	testTime := 50000
	fmt.Println("功能测试开始")
	for i := 0; i < testTime; i++ {
		n := rand.Intn(N) + 1
		a := randomArray(n, A)
		b := randomArray(n, B)
		ans1 := inValues1(a, b)
		ans2 := inValues2(a, b)
		if !isSameArray(ans1, ans2) {
			fmt.Println("出错了!")
		}
	}
	fmt.Println("功能测试结束")

	fmt.Println("性能测试开始")
	n := 100000
	v := 1000000000
	a := randomArray(n, v)
	b := randomArray(n, v)
	fmt.Println("数组长度 : ", n)
	fmt.Println("数值范围 : ", v)
	start := time.Now()
	inValues2(a, b)
	end := time.Now()
	fmt.Println("运行时间 : ", end.Sub(start).Milliseconds(), " 毫秒")
	fmt.Println("性能测试结束")
}

use std::time::Instant;

// 暴力方法
// 时间复杂度O(N^2)
// 为了测试
fn in_values1(a: &Vec<i32>, b: &Vec<i32>) -> Vec<i64> {
    let n = a.len();
    let mut ans = vec![0; n];
    for i in 0..n {
        let mut cur_ans = i64::MAX;
        for j in 0..n {
            let cur = (a[i] + a[j]).pow(2) as i64 + b[i] as i64 + b[j] as i64;
            cur_ans = cur_ans.min(cur);
        }
        ans[i] = cur_ans;
    }
    ans
}

// 正式方法
// 时间复杂度O(N*logN)
// (a[i] + a[j]) ^ 2 + b[i] + b[j]
// a[i]^2 + b[i] + 2a[i]a[j] + a[j]^2 + b[j]
// a[i] * ( a[i] + b[i]/a[i] + 2a[j] + (a[j]^2 + b[j])/a[i])
// 令S(j) = 2a[j]
// 令T(j) = a[j]^2 + b[j]
// 那么对于i来说，就是选择j，让下面得到最小值
// a[i] * ( a[i] + b[i]/a[i] + S(j) + T(j)/a[i])
// 选择最小的S(j) + T(j)/a[i]，就得到了答案
// 剩下的一切都是围绕这个

fn in_values2(a: &Vec<i32>, b: &Vec<i32>) -> Vec<i64> {
    let n = a.len();
    let mut st = vec![vec![0; 2]; n];
    for i in 0..n {
        st[i][0] = (a[i] * 2) as i64;
        st[i][1] = (a[i] * a[i] + b[i]) as i64;
    }
    st.sort_by(|x, y| {
        if x[0] != y[0] {
            y[0].cmp(&x[0])
        } else {
            x[1].cmp(&y[1])
        }
    });
    let mut stack = vec![0; n];
    let mut r = 0;
    for i in 0..n {
        let s = st[i][0];
        let t = st[i][1];
        while r > 0
            && tail(&st, &stack, r)
                >= better(
                    st[stack[(r - 1) as usize] as usize][0],
                    st[stack[(r - 1) as usize] as usize][1],
                    s,
                    t,
                )
        {
            r -= 1;
        }
        stack[r as usize] = i as i32;
        r += 1;
    }
    let mut arr = vec![(0, 0, 0); n];
    for i in 0..n {
        arr[i] = (i, a[i], b[i]);
    }
    arr.sort_by(|x, y| {
        if x.1 != y.1 {
            y.1.cmp(&x.1)
        } else {
            x.0.cmp(&y.0)
        }
    });
    let mut ans = vec![0; n];
    for k in 0..n {
        let i = arr[k].0;
        let ai = arr[k].1;
        let bi = arr[k].2;
        while tail(&st, &stack, r as i32) > ai {
            r -= 1;
        }
        let sj = st[stack[(r - 1) as usize] as usize][0];
        let tj = st[stack[(r - 1) as usize] as usize][1];
        let cur_ans = sj * ai as i64 + tj + ai as i64 * ai as i64 + bi as i64;
        ans[i] = cur_ans;
    }
    ans
}

// 返回当ai大到什么值的时候，后者更好
fn tail(st: &Vec<Vec<i64>>, deque: &Vec<i32>, r: i32) -> i32 {
    if r == 1 {
        return 1;
    }

    let (s1, t1) = (
        st[deque[r as usize - 2] as usize][0],
        st[deque[r as usize - 2] as usize][1],
    );
    let (s2, t2) = (
        st[deque[r as usize - 1] as usize][0],
        st[deque[r as usize - 1] as usize][1],
    );
    better(s1, t1, s2, t2)
}

// 入参时候s1>=s2，这是一定的
// 返回当ai大到什么值的时候，(s2+t2/ai) <= (s1+t1/ai)
// 即 : ai大到什么值的时候，后者更好
fn better(s1: i64, t1: i64, s2: i64, t2: i64) -> i32 {
    if s1 == s2 {
        if t1 <= t2 {
            std::i32::MAX
        } else {
            1
        }
    } else if t1 >= t2 {
        1
    } else {
        // s1 > s2
        let td = t2 - t1;
        let sd = s1 - s2;
        ((td + sd - 1) / sd) as i32
    }
}

fn random_array(n: usize, v: i32) -> Vec<i32> {
    let mut ans = vec![0; n];
    for i in 0..n {
        ans[i] = (rand::random::<usize>() % (v as usize) + 1) as i32;
    }
    ans
}

fn is_same_array(arr1: &Vec<i64>, arr2: &Vec<i64>) -> bool {
    if arr1.len() != arr2.len() {
        return false;
    }
    for i in 0..arr1.len() {
        if arr1[i] != arr2[i] {
            return false;
        }
    }
    true
}

fn main() {
    let n = 100;
    let a = 100;
    let b = 50000;
    let test_time = 50000;

    println!("功能测试开始");
    for _ in 0..test_time {
        let n = rand::random::<usize>() % n + 1;
        let a = random_array(n, a);
        let b = random_array(n, b);

        let ans1 = in_values1(&a, &b);
        let ans2 = in_values2(&a, &b);

        assert!(is_same_array(&ans1, &ans2));
    }
    println!("功能测试结束");

    println!("性能测试开始");
    let n = 100000;
    let v = 10000;
    let a = random_array(n, v);
    let b = random_array(n, v);
    println!("数组长度 : {}", n);
    println!("数值范围 : {}", v);

    let start = Instant::now();
    let c = in_values2(&a, &b);
    let end = start.elapsed();

    println!("运行时间 : {:?}", end);
    println!("性能测试结束");
}