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Chef likes inequalities. Please help him to solve next one.
Given four integers a, b, c, d. Find number of solutions x < y, where a ≤ x ≤ b and c ≤ y ≤ d and x, y integers.

------ Input ------ 

The first line contains an integer T denoting number of tests.
First line of each test case contains four positive integer numbers a, b, c and d.

------ Output ------ 

For each test case, output a single number each in separate line denoting number of integer solutions as asked in the problem.

------ Constraints ------ 

$1 ≤ T ≤ 20 $
$1 ≤ a, b, c, d ≤ 10^{6}$

------ Subtasks ------ 

$Subtask #1: (30 points)  1 ≤ a, b, c, d ≤ 10^{3}.$
$Subtask #2: (70 points)  Original constraints.$

----- Sample Input 1 ------ 
1
2 3 3 4
----- Sample Output 1 ------ 
3
----- explanation 1 ------ 

----- Sample Input 2 ------ 
1
2 999999 1 1000000
----- Sample Output 2 ------ 
499998500001
----- explanation 2 ------

Difficulty: MEDIUM

Solutions:
for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	if d <= a:
		ans = 0
	else:
		x = max(c, a + 1)
		ans = 0
		for y in range(x, d + 1):
			ans += min(y - 1, b) - a + 1
	print(ans)


def soln(a, b, c, d):
	if d <= a:
		return 0
	c = max(c, a + 1)
	res = 0
	for y in range(c, d + 1):
		res += min(y - 1, b) - a + 1
	return res
for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	print(soln(a, b, c, d))


tests = int(input())
for i in range(tests):
	(a, b, c, d) = map(int, input().split())
	if d <= a:
		ans = 0
	else:
		c = max(c, a)
		b = min(d, b)
		ans = (b - a + 1) * (d - c + 1)
		if c <= b:
			gap = b - c + 1
			ans -= gap * (gap + 1) // 2
	print(ans)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	count = 0
	if b < a or d < c:
		print(0)
	else:
		for i in range(a, b + 1):
			if i < d:
				count += d - max(c, i + 1) + 1
			else:
				break
		print(count)


from bisect import bisect_left, bisect_right
import math
from bisect import bisect_left
from heapq import heapify, heappush, heappop
from collections import deque
import sys
from math import gcd, sqrt, log10, log2, floor, ceil, sqrt
from collections import deque, defaultdict
input = sys.stdin.readline

def il():
	return [int(a) for a in input().strip().split()]

def ip():
	return input().strip()

def ii():
	return int(input())

def ot(in_p, *args, e=' '):
	if type(in_p) == list:
		print(*in_p, end=e)
	if type(in_p) == str or type(in_p) == int:
		print(in_p, end=e)
		for l in args:
			print(l, end=e)
	print()

def a_pwr_n(a, n, mod):
	if n == 1:
		return a % mod
	if n % 2 == 0:
		val = a_pwr_n(a, n // 2, mod)
		return val % mod * val % mod
	else:
		return a % mod * a_pwr_n(a, n - 1, mod) % mod

def rg(*ag):
	if len(ag) == 3:
		return range(ag[0], ag[1], ag[2])
	elif len(ag) == 2:
		return range(ag[0], ag[1])
	elif len(ag) == 1:
		return range(ag[0])
	else:
		raise 'invalid input'

def ispal(i, j, st):
	while i <= j:
		if st[i] == st[j]:
			i = i + 1
			j = j - 1
		else:
			return False
	return True
mod = 1000000000 + 7
dx = [-1, -2, 1, 2, 2, -2, -1, 1]
dy = [2, 1, 2, 1, -1, -1, -2, -2]
for i in range(ii()):
	(a, b, c, d) = il()
	s = 0
	for i in range(a, b + 1):
		if i < c:
			s += d - c + 1
		elif i < d:
			s += d - i
	print(s)


T = int(input(''))
for i in range(T):
	l1 = [int(c) for c in input('').split()]
	if l1[0] > l1[3]:
		print('0')
	else:
		if l1[1] > l1[3]:
			l1[1] = l1[3]
		if l1[1] < l1[2]:
			x = (l1[1] - l1[0] + 1) * (l1[3] - l1[2] + 1)
			print(x)
		elif l1[1] == l1[2]:
			x = (l1[1] - l1[0] + 1) * (l1[3] - l1[2] + 1)
			print(x - 1)
		elif l1[1] > l1[2]:
			if l1[0] <= l1[2]:
				x = (l1[2] - l1[0] + 1) * (l1[3] - l1[2] + 1) - 1
				x += (l1[1] - l1[2]) * l1[3] - l1[1] * (l1[1] + 1) // 2 + l1[2] * (l1[2] + 1) // 2
				print(x)
			else:
				x = (l1[1] - l1[0] + 1) * l1[3] - l1[1] * (l1[1] + 1) // 2 + (l1[0] - 1) * l1[0] // 2
				print(x)


t = int(input())
for tc in range(t):
	(a, b, c, d) = map(int, input().split())
	ans = 0
	for x in range(a, b + 1):
		if x < c:
			ans = ans + d - c + 1
		elif x >= c and x < d:
			ans = ans + d - x
	print(ans)


T = int(input())
for i in range(T):
	(a, b, c, d) = map(int, input().split())
	res = 0
	for x in range(a, b + 1):
		if x < c:
			res = res + d - c + 1
		elif x >= c and x < d:
			res = res + d - x
	print(res)


n = int(input())
for i in range(n):
	(a, b, c, d) = map(int, input().split())
	r = 0
	for j in range(a, b + 1):
		if j < c:
			r += d - c + 1
		elif j >= c and j < d:
			r += d - j
	print(r)


t = int(input())
for _ in range(t):
	(a, b, c, d) = map(int, input().split())
	res = 0
	for x in range(a, b + 1):
		if x < c:
			res += d - c + 1
		elif x >= c and x < d:
			res += d - x
	print(res)


t = int(input())
for _ in range(t):
	(a, b, c, d) = map(int, input().split())
	(a, b) = (min(a, b), max(a, b))
	(c, d) = (min(c, d), max(c, d))
	ans = 0
	for i in range(a, b + 1):
		if i < c:
			ans = d - c + 1 + ans
		elif i < d:
			ans = d - i + ans
	print(ans)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	ans = 0
	for k in range(a, b + 1):
		k = d - max(k + 1, c) + 1
		ans = ans + max(0, k)
	print(ans)


T = int(input())
for tj in range(T):
	(a, b, c, d) = map(int, input().split())
	if max(a, b) != b or max(c, d) != d:
		print(0)
	else:
		sum_v = 0
		for i in range(a, b + 1):
			if i < c:
				sum_v += d - c + 1
			else:
				sum_v += max(0, d - i)
		print(sum_v)


from math import *
import sys

def input():
	return sys.stdin.readline().replace('\n', '').strip()
sys.setrecursionlimit(10 ** 9)
for _ in range(int(input())):
	(a, b, c, d) = list(map(int, input().split()))
	ans = 0
	if b < c:
		ans = (b - a + 1) * (d - c + 1)
	else:
		for x in range(a, b + 1):
			min_req = x + 1
			ans += max(0, d - max(min_req, c) + 1)
	if a <= b and c <= d:
		print(ans)
	else:
		print(0)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	ans = 0
	if a <= b and c <= d and (d > a):
		for i in range(a, b + 1):
			if i < d:
				ans += d - max(c, i + 1) + 1
			else:
				break
	print(ans)


t = int(input())
for i in range(t):
	count = 0
	(a, b, c, d) = map(int, input().split())
	for i in range(a, b + 1):
		if i < c:
			count += d - c + 1
		elif i < d:
			count += d - i
	print(count)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	count = 0
	for j in range(a, b + 1):
		if j < c:
			count += d - c + 1
		elif j < d:
			count += d - j
	print(count)


n = int(input())
for i in range(n):
	(a, b, c, d) = map(int, input().split())
	sum = 0
	if b < a or d < c:
		print(0)
	else:
		for i in range(a, b + 1):
			if i < d:
				sum += d - max(c, i + 1) + 1
			else:
				break
	print(sum)


import sys
sys.setrecursionlimit(10 ** 5 + 1)
inf = int(10 ** 20)
max_val = inf
min_val = -inf
RW = lambda : sys.stdin.readline().strip()
RI = lambda : int(RW())
RMI = lambda : [int(x) for x in sys.stdin.readline().strip().split()]
RWI = lambda : [x for x in sys.stdin.readline().strip().split()]
for _ in range(RI()):
	(a, b, c, d) = RMI()
	count = 0
	if b < a or d < c:
		print(0)
	else:
		for i in range(a, b + 1):
			if i < d:
				count += d - max(c, i + 1) + 1
			else:
				break
		print(count)


for _ in range(int(input())):
	(a, b, c, d) = (int(i) for i in input().strip().split())
	res_cnt = 0
	for i in range(a, b + 1):
		temp = max(i, c - 1)
		if d > temp:
			res_cnt += d - temp
	print(res_cnt)


def inequalities(a, b, c, d):
	res = [d - max(c, i + 1) + 1 for i in range(a, b + 1) if max(c, i + 1) <= d]
	return sum(res)
t = int(input())
for i in range(t):
	(a, b, c, d) = map(int, input().split())
	print(inequalities(a, b, c, d))


t = int(input())
for _ in range(t):
	(a, b, c, d) = [int(x) for x in input().split()]
	ans = 0
	for i in range(a, b + 1):
		if i < c:
			ans += d - c + 1
		elif i < d:
			ans += d - i
	print(ans)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	sum = 0
	for i in range(a, b + 1):
		if i < c:
			sum += d - c + 1
		elif i < d:
			sum += d - i
	print(sum)


for _ in range(int(input())):
	(a, b, c, d) = tuple(map(int, input().split()))
	m = range(a, b + 1)
	n = range(c, d + 1)
	count = 0
	for i in n:
		if i > a and i <= b:
			count += i - a
		elif i > a and i > b:
			count += b - a + 1
		elif i < a and i < b:
			count = count
	print(count)


def Cook(a, b, c, d):
	ans = 0
	for i in range(a, b + 1):
		left = max(c, i + 1)
		if left <= d:
			ans += d - left + 1
	return ans
for T in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	print(Cook(a, b, c, d))


t = int(input())
for i in range(t):
	arr = list(map(int, input().split()))
	a = arr[0]
	b = arr[1]
	c = arr[2]
	d = arr[3]
	count = 0
	for j in range(a, b + 1):
		if j < d:
			if j < c:
				count += d - c + 1
			else:
				count += d - j
	print(count)


t = int(input())
for i in range(t):
	l = input().split(' ')
	a = int(l[0])
	b = int(l[1])
	c = int(l[2])
	d = int(l[3])
	temp = b
	ans = 0
	count = b - a + 1
	while c <= d and a <= b:
		if b < d:
			ans = ans + count
			d -= 1
		else:
			b -= 1
			count -= 1
	print(ans)


t = int(input())
for _ in range(t):
	(a, b, c, d) = map(int, input().split())
	res = 0
	for x in range(a, b + 1):
		res += max(d - max(c, x + 1) + 1, 0)
	print(res)


for _ in range(int(input())):
	(a, b, c, d) = map(int, input().split())
	answer = 0
	for i in range(a, b + 1):
		if d >= max(c, i + 1):
			answer += d - max(c, i + 1) + 1
	print(answer)