Yet another round on DecoForces is coming! Grandpa Maks wanted to participate in it but someone has stolen his precious sofa! And how can one perform well with such a major loss?

Fortunately, the thief had left a note for Grandpa Maks. This note got Maks to the sofa storehouse. Still he had no idea which sofa belongs to him as they all looked the same!

The storehouse is represented as matrix n × m. Every sofa takes two neighbouring by some side cells. No cell is covered by more than one sofa. There can be empty cells.

Sofa A is standing to the left of sofa B if there exist two such cells a and b that x_{a} < x_{b}, a is covered by A and b is covered by B. Sofa A is standing to the top of sofa B if there exist two such cells a and b that y_{a} < y_{b}, a is covered by A and b is covered by B. Right and bottom conditions are declared the same way. 

Note that in all conditions A ≠ B. Also some sofa A can be both to the top of another sofa B and to the bottom of it. The same is for left and right conditions.

The note also stated that there are cnt_{l} sofas to the left of Grandpa Maks's sofa, cnt_{r} — to the right, cnt_{t} — to the top and cnt_{b} — to the bottom.

Grandpa Maks asks you to help him to identify his sofa. It is guaranteed that there is no more than one sofa of given conditions.

Output the number of Grandpa Maks's sofa. If there is no such sofa that all the conditions are met for it then output -1.


-----Input-----

The first line contains one integer number d (1 ≤ d ≤ 10^5) — the number of sofas in the storehouse.

The second line contains two integer numbers n, m (1 ≤ n, m ≤ 10^5) — the size of the storehouse.

Next d lines contains four integer numbers x_1, y_1, x_2, y_2 (1 ≤ x_1, x_2 ≤ n, 1 ≤ y_1, y_2 ≤ m) — coordinates of the i-th sofa. It is guaranteed that cells (x_1, y_1) and (x_2, y_2) have common side, (x_1, y_1)  ≠  (x_2, y_2) and no cell is covered by more than one sofa.

The last line contains four integer numbers cnt_{l}, cnt_{r}, cnt_{t}, cnt_{b} (0 ≤ cnt_{l}, cnt_{r}, cnt_{t}, cnt_{b} ≤ d - 1).


-----Output-----

Print the number of the sofa for which all the conditions are met. Sofas are numbered 1 through d as given in input. If there is no such sofa then print -1.


-----Examples-----
Input
2
3 2
3 1 3 2
1 2 2 2
1 0 0 1

Output
1

Input
3
10 10
1 2 1 1
5 5 6 5
6 4 5 4
2 1 2 0

Output
2

Input
2
2 2
2 1 1 1
1 2 2 2
1 0 0 0

Output
-1



-----Note-----

Let's consider the second example.   The first sofa has 0 to its left, 2 sofas to its right ((1, 1) is to the left of both (5, 5) and (5, 4)), 0 to its top and 2 to its bottom (both 2nd and 3rd sofas are below).  The second sofa has cnt_{l} = 2, cnt_{r} = 1, cnt_{t} = 2 and cnt_{b} = 0.  The third sofa has cnt_{l} = 2, cnt_{r} = 1, cnt_{t} = 1 and cnt_{b} = 1. 

So the second one corresponds to the given conditions.

In the third example   The first sofa has cnt_{l} = 1, cnt_{r} = 1, cnt_{t} = 0 and cnt_{b} = 1.  The second sofa has cnt_{l} = 1, cnt_{r} = 1, cnt_{t} = 1 and cnt_{b} = 0. 

And there is no sofa with the set (1, 0, 0, 0) so the answer is -1.

Difficulty: HARD
Tags: Implementation

Complete search
Skill types: Complete search

Starter code:

Solutions:
import sys
try:
	fin = open('in')
except:
	fin = sys.stdin
input = fin.readline
d = int(input())
(n, m) = map(int, input().split())
(x1, y1, x2, y2) = ([], [], [], [])
T = []
for _ in range(d):
	(u, v, w, x) = map(int, input().split())
	if u > w:
		(u, w) = (w, u)
	if v > x:
		(v, x) = (x, v)
	x1.append(u)
	y1.append(v)
	x2.append(-w)
	y2.append(-x)
	T.append([u, v, w, x])
x1.sort()
x2.sort()
y1.sort()
y2.sort()
req = list(map(int, input().split()))
import bisect
for i in range(len(T)):
	(u, v, w, x) = T[i]
	if req[0] == bisect.bisect_left(x1, w) - (u != w):
		if req[1] == bisect.bisect_left(x2, -u) - (u != w):
			if req[2] == bisect.bisect_left(y1, x) - (v != x):
				if req[3] == bisect.bisect_left(y2, -v) - (v != x):
					print(i + 1)
					break
else:
	print(-1)


import sys
from bisect import bisect_left, bisect_right
d = int(sys.stdin.buffer.readline().decode('utf-8'))
(n, m) = map(int, sys.stdin.buffer.readline().decode('utf-8').split())
a = [list(map(int, sys.stdin.buffer.readline().decode('utf-8').split())) for _ in range(d)]
cnt = list(map(int, sys.stdin.buffer.readline().decode('utf-8').split()))
(left, right, top, bottom) = ([], [], [], [])
for (x1, y1, x2, y2) in a:
	left.append(min(x1, x2))
	right.append(-max(x1, x2))
	top.append(min(y1, y2))
	bottom.append(-max(y1, y2))
left.sort()
right.sort()
top.sort()
bottom.sort()
for (i, (x1, y1, x2, y2)) in enumerate(a, start=1):
	c = [bisect_left(left, max(x1, x2)) - (1 if x1 != x2 else 0), bisect_left(right, -min(x1, x2)) - (1 if x1 != x2 else 0), bisect_left(top, max(y1, y2)) - (1 if y1 != y2 else 0), bisect_left(bottom, -min(y1, y2)) - (1 if y1 != y2 else 0)]
	if c == cnt:
		print(i)
		exit()
print(-1)


from sys import stdin, stdout
k = int(stdin.readline())
(n, m) = map(int, stdin.readline().split())
(left, right, down, up) = ([], [], [], [])
coordinates = []
for i in range(k):
	(x1, y1, x2, y2) = map(int, stdin.readline().split())
	if x1 == x2:
		if y1 < y2:
			coordinates.append((x1, y1, x2, y2, i))
		else:
			coordinates.append((x2, y2, x1, y1, i))
	elif x1 < x2:
		coordinates.append((x1, y1, x2, y2, i))
	else:
		coordinates.append((x2, y2, x1, y1, i))
	left.append(coordinates[-1])
	right.append(coordinates[-1])
	up.append(coordinates[-1])
	down.append(coordinates[-1])
left.sort(key=lambda x: (x[0], x[2]))
down.sort(key=lambda x: (x[1], x[3]))
challengers = [[], [], [], []]
(cntl, cntr, cntd, cntu) = map(int, stdin.readline().split())
label = 1
if cntl or not cntl:
	for i in range(cntl, -1, -1):
		if (left[i][0], left[i][2]) == (left[cntl][0], left[cntl][2]):
			challengers[0].append(left[i][-1])
		else:
			break
	for i in range(cntl + 1, k):
		if (left[i][0], left[i][2]) == (left[cntl][0], left[cntl][2]) and left[i][2] > left[i][0]:
			label = 0
		if (left[i][0], left[i][2]) == (left[cntl][0], left[cntl][2]):
			challengers[0].append(left[i][-1])
		else:
			break
if cntr or not cntr:
	for i in range(k - 1 - cntr, k):
		if (left[i][0], left[i][2]) == (left[k - 1 - cntr][0], left[k - 1 - cntr][2]):
			challengers[1].append(left[i][-1])
		else:
			break
	for i in range(k - 2 - cntr, -1, -1):
		if (left[i][0], left[i][2]) == (left[k - 1 - cntr][0], left[k - 1 - cntr][2]) and left[i][2] > left[i][0]:
			label = 0
		if (left[i][0], left[i][2]) == (left[k - 1 - cntr][0], left[k - 1 - cntr][2]):
			challengers[1].append(left[i][-1])
		else:
			break
if cntd or not cntd:
	for i in range(cntd, -1, -1):
		if (down[i][1], down[i][3]) == (down[cntd][1], down[cntd][3]):
			challengers[2].append(down[i][-1])
		else:
			break
	for i in range(cntd + 1, k):
		if (down[i][1], down[i][3]) == (down[cntd][1], down[cntd][3]) and down[i][3] > down[i][1]:
			label = 0
		if (down[i][1], down[i][3]) == (down[cntd][1], down[cntd][3]):
			challengers[2].append(down[i][-1])
		else:
			break
if cntu or not cntu:
	for i in range(k - 1 - cntu, k):
		if (down[i][1], down[i][3]) == (down[k - 1 - cntu][1], down[k - 1 - cntu][3]):
			challengers[3].append(down[i][-1])
		else:
			break
	for i in range(k - 2 - cntu, -1, -1):
		if (down[i][1], down[i][3]) == (down[k - 1 - cntu][1], down[k - 1 - cntu][3]) and down[i][3] > down[i][1]:
			label = 0
		if (down[i][1], down[i][3]) == (down[k - 1 - cntu][1], down[k - 1 - cntu][3]):
			challengers[3].append(down[i][-1])
		else:
			break
ans = set(challengers[0]) & set(challengers[1]) & set(challengers[2]) & set(challengers[3])
if not len(ans) or not label:
	stdout.write('-1')
else:
	stdout.write(str(list(ans)[0] + 1))


import sys
from collections import defaultdict as dd
from collections import deque
pl = 1
from math import *
import copy
if pl:
	input = sys.stdin.readline

def li():
	return [int(xxx) for xxx in input().split()]

def fi():
	return int(input())

def si():
	return list(input().rstrip())

def mi():
	return map(int, input().split())
d = []
from bisect import *
from itertools import permutations
from bisect import *
f = [0 for i in range(100)]
for i in range(1, 100):
	if i == 1:
		f[i] = 1
	else:
		f[i] = 2 * f[i - 1] + 1

def rec(n, k):
	s = []
	while n != 0:
		(n, r) = (n // k, n % k)
		if r < 0:
			r -= k
			n += 1
		s.append(r)
	return s
n = fi()
(p, q) = mi()
pp = []
l = []
r = []
u = []
d = []
for i in range(n):
	(x1, y1, x2, y2) = mi()
	(x1, x2) = (min(x1, x2), max(x1, x2))
	(y1, y2) = (min(y1, y2), max(y1, y2))
	l.append(x1)
	r.append(-x2)
	u.append(y1)
	d.append(-y2)
	pp.append([x1, x2, y1, y2])
l.sort()
r.sort()
u.sort()
d.sort()
f = [[0, 0, 0, 0] for i in range(n + 1)]
for i in range(n):
	f[i][0] = bisect_left(l, pp[i][1])
	if pp[i][0] < pp[i][1]:
		f[i][0] -= 1
	f[i][1] = bisect_left(r, -pp[i][0])
	if pp[i][0] < pp[i][1]:
		f[i][1] -= 1
	f[i][2] = bisect_left(u, pp[i][3])
	if pp[i][2] < pp[i][3]:
		f[i][2] -= 1
	f[i][3] = bisect_left(d, -pp[i][2])
	if pp[i][2] < pp[i][3]:
		f[i][3] -= 1
co = li()
for i in range(n):
	if co == f[i]:
		print(i + 1)
		exit(0)
print(-1)


d = int(input().strip())
[n, m] = list(map(int, input().strip().split()))
Hxds = [0 for _ in range(n)]
Hyds = [0 for _ in range(m)]
Vxds = [0 for _ in range(n)]
Vyds = [0 for _ in range(m)]
ds = []
for i in range(d):
	(x1, y1, x2, y2) = list(map(int, input().strip().split()))
	if x1 == x2:
		Hxds[x1 - 1] += 1
		Hyds[min(y1, y2) - 1] += 1
		ds.append((x1 - 1, min(y1, y2) - 1, 'h'))
	else:
		Vxds[min(x1, x2) - 1] += 1
		Vyds[y1 - 1] += 1
		ds.append((min(x1, x2) - 1, y1 - 1, 'v'))
(cl, cr, ct, cb) = list(map(int, input().strip().split()))
if (d - 1 - cl - cr) * (d - 1 - ct - cb) > 0:
	print(-1)
	return

def makeI(xs):
	I = [0 for _ in range(len(xs) + 1)]
	for i in range(len(xs)):
		I[i + 1] = I[i] + xs[i]
	return I

def find_x_Hor(IH, IV, l, cl, cr):
	if cl + cr > d - 1:
		return -1
	x = 0
	while x <= l and (IH[x] + IV[x] < cl or d - IH[x + 1] - IV[x] > cr):
		x += 1
	if x < l and IH[x] + IV[x] == cl and (d - IH[x + 1] - IV[x] == cr):
		return x
	return -1

def find_x_Vert(IH, IV, l, cl, cr):
	if cl + cr < d - 1:
		return -1
	x = 0
	while x < l and (IH[x + 1] + IV[x + 1] < cl + 1 or d - IH[x + 1] - IV[x] > cr + 1):
		x += 1
	if x < l and IH[x + 1] + IV[x + 1] == cl + 1 and (d - IH[x + 1] - IV[x] == cr + 1):
		return x
	return -1
IHx = makeI(Hxds)
IHy = makeI(Hyds)
IVx = makeI(Vxds)
IVy = makeI(Vyds)
if ct + cb >= d - 1 and cr + cl <= d - 1:
	x = find_x_Hor(IHx, IVx, n, cl, cr)
	y = find_x_Vert(IVy, IHy, m, ct, cb)
	if x >= 0 and y >= 0:
		if (x, y, 'h') in ds:
			print(ds.index((x, y, 'h')) + 1)
			return
if ct + cb <= d - 1 and cr + cl >= d - 1:
	x = find_x_Vert(IHx, IVx, n, cl, cr)
	y = find_x_Hor(IVy, IHy, m, ct, cb)
	if x >= 0 and y >= 0:
		if (x, y, 'v') in ds:
			print(ds.index((x, y, 'v')) + 1)
			return
print(-1)