Buggy python submission (verdict: Time Limit Exceeded):
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, rev_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            q = rev_dict[nx, ny]
            if q not in stacked:
                stack.append(q)
                stacked.add(q)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, rev_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            q = rev_dict[nx, ny]
            if q not in stacked:
                stack.append(q)
                stacked.add(q)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
ppp = []
rev_dict = {}
for i in range(n):
    x = xxx[i] - yyy[i]
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)
    ppp.append((x, y))
    rev_dict[x, y] = i

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax, ay = ppp[a]
bx, by = ppp[b]
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [a, b]
stacked = {a, b}
ans = 0
while stack:
    p = stack.pop()
    x, y = ppp[p]
    ans += x_check(x_dict, rev_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, rev_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, rev_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, rev_dict, y + d, x, d, stack, stacked)

print(ans // 2)


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Time Limit Exceeded):
import bisect
import sys
import random
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.indices = set()
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        while li != 0 and ri != 0:
            if random.randrange(counts[li] + counts[ri]) < counts[li]:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        if self.indices:
            ni = self.indices.pop()
            self.children[0][ni] = self.children[1][ni] = 0
            self.values[ni] = x
            self.counts[ni] = 1
        else:
            ni = len(self.values)
            self.children[0].append(0)
            self.children[1].append(0)
            self.values.append(x)
            self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.indices.add(mi)
        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, rev_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            q = rev_dict[nx, ny]
            if q not in stacked:
                stack.append(q)
                stacked.add(q)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, rev_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            q = rev_dict[nx, ny]
            if q not in stacked:
                stack.append(q)
                stacked.add(q)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
ppp = []
rev_dict = {}
for i in range(n):
    x = xxx[i] - yyy[i]
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)
    ppp.append((x, y))
    rev_dict[x, y] = i

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax, ay = ppp[a]
bx, by = ppp[b]
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [a, b]
stacked = {a, b}
ans = 0
while stack:
    p = stack.pop()
    x, y = ppp[p]
    ans += x_check(x_dict, rev_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, rev_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, rev_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, rev_dict, y + d, x, d, stack, stacked)

print(ans // 2)


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Time Limit Exceeded):
import bisect
import sys
import random
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.indices = set()
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        while li != 0 and ri != 0:
            if random.randrange(counts[li] + counts[ri]) < counts[li]:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        if self.indices:
            ni = self.indices.pop()
            self.children[0][ni] = self.children[1][ni] = 0
            self.values[ni] = x
            self.counts[ni] = 1
        else:
            ni = len(self.values)
            self.children[0].append(0)
            self.children[1].append(0)
            self.values.append(x)
            self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.indices.add(mi)
        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, rev_dict, nx, y, d):
    ret = set()
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            q = rev_dict[nx, ny]
            ret.add(q)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return ret, counter


def y_check(y_dict, rev_dict, ny, x, d):
    ret = set()
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            q = rev_dict[nx, ny]
            ret.add(q)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return ret, counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
ppp = []
rev_dict = {}
for i in range(n):
    x = xxx[i] - yyy[i]
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)
    ppp.append((x, y))
    rev_dict[x, y] = i

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax, ay = ppp[a]
bx, by = ppp[b]
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [a, b]
stacked = {a, b}
ans = 0
while stack:
    p = stack.pop()
    x, y = ppp[p]

    qqq = set()
    qs, c = x_check(x_dict, rev_dict, x - d, y, d)
    qqq.update(qs)
    ans += c

    qs, c = x_check(x_dict, rev_dict, x + d, y, d)
    qqq.update(qs)
    ans += c

    qs, c = y_check(y_dict, rev_dict, y - d, x, d)
    qqq.update(qs)
    ans += c

    qs, c = y_check(y_dict, rev_dict, y + d, x, d)
    qqq.update(qs)
    ans += c

    for q in qqq:
        if q not in stacked:
            stack.append(q)
            stacked.add(q)

print(ans // 2)


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Time Limit Exceeded):
import bisect
import sys
import random
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.indices = set()
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        while li != 0 and ri != 0:
            if random.randrange(counts[li] + counts[ri]) < counts[li]:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        if self.indices:
            ni = self.indices.pop()
            self.children[0][ni] = self.children[1][ni] = 0
            self.values[ni] = x
            self.counts[ni] = 1
        else:
            ni = len(self.values)
            self.children[0].append(0)
            self.children[1].append(0)
            self.values.append(x)
            self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.indices.add(mi)
        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, rev_dict, nx, y, d):
    ret = set()
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            q = rev_dict[nx, ny]
            ret.add(q)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return ret, counter


def y_check(y_dict, rev_dict, ny, x, d):
    ret = set()
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            q = rev_dict[nx, ny]
            ret.add(q)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return ret, counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
ppp = []
rev_dict = {}
for i in range(n):
    x = xxx[i] - yyy[i]
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)
    ppp.append((x, y))
    rev_dict[x, y] = i

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax, ay = ppp[a]
bx, by = ppp[b]
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [a, b]
stacked = {a, b}
ans = 0
while stack:
    p = stack.pop()
    x, y = ppp[p]

    qqq = set()
    qs, c = x_check(x_dict, rev_dict, x - d, y, d)
    qqq.update(qs)
    ans += c

    qs, c = x_check(x_dict, rev_dict, x + d, y, d)
    qqq.update(qs)
    ans += c

    qs, c = y_check(y_dict, rev_dict, y - d, x, d)
    qqq.update(qs)
    ans += c

    qs, c = y_check(y_dict, rev_dict, y + d, x, d)
    qqq.update(qs)
    ans += c

    for q in qqq:
        if q not in stacked:
            stack.append(q)
            stacked.add(q)

print(ans // 2)


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Runtime Error):
import numpy as np

n, a, b = map(int, input().split())

holes = np.fromiter((complex(*map(int, input().split())) for _ in range(n)), dtype=complex)
ab = holes[a - 1] - holes[b - 1]
d = abs(ab.real) + abs(ab.imag)
links = [set() for _ in range(n)]

for i in range(0, n, 10000):
    xy1, xy2 = np.meshgrid(holes, holes[i:i + 10000])
    diff = xy1 - xy2
    dists = abs(diff.real) + abs(diff.imag)

    for x, y in zip(*np.where(dists == d)):
        links[x].add(y)

visited = set()
queue = [a - 1]
while queue:
    p = queue.pop()
    if p in visited:
        continue
    visited.add(p)
    queue.extend(q for q in links[p] if q not in visited)

print(sum(p < q for p in visited for q in links[p]))


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

n, a, b = map(int, input().split())

holes = np.fromiter((complex(*map(int, input().split())) for _ in range(n)), dtype=complex)
ab = holes[a - 1] - holes[b - 1]
d = abs(ab.real) + abs(ab.imag)
links = [set() for _ in range(n)]

for i in range(0, n, 100):
    xy1, xy2 = np.meshgrid(holes, holes[i:i + 100])
    diff = xy1 - xy2
    dists = abs(diff.real) + abs(diff.imag)

    for x, y in zip(*np.where(dists == d)):
        links[x].add(y)

visited = set()
queue = [a - 1]
while queue:
    p = queue.pop()
    if p in visited:
        continue
    visited.add(p)
    queue.extend(q for q in links[p] if q not in visited)

print(sum(p < q for p in visited for q in links[p]))


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)

Buggy python submission (verdict: Runtime Error):
import numpy as np

n, a, b = map(int, input().split())

holes = np.fromiter((complex(*map(int, input().split())) for _ in range(n)), dtype=complex)
xy1, xy2 = np.meshgrid(holes, holes)
diff = xy1 - xy2
dists = abs(diff.real) + abs(diff.imag)

d = dists[a - 1][b - 1]
w = np.where(dists == d)

links = [set() for _ in range(n)]
for x, y in zip(*w):
    links[x].add(y)

visited = set()
queue = [a - 1]
while queue:
    p = queue.pop()
    if p in visited:
        continue
    visited.add(p)
    queue.extend(q for q in links[p] if q not in visited)

print(sum(p < q for p in visited for q in links[p]))


Fixed submission:
import bisect
import sys
from collections import defaultdict


class RandomizedBinarySearchTree:
    def __init__(self):
        self.children = [[-1], [-1]]
        self.values = [0]
        self.counts = [0]
        self.root = 0

    def merge(self, left_root, right_root):
        children = self.children
        counts = self.counts
        li = left_root
        ri = right_root
        stack = []
        switch = 0
        while li != 0 and ri != 0:
            if switch:
                stack.append((li, 1))
                li = children[1][li]
            else:
                stack.append((ri, 0))
                ri = children[0][ri]
            switch ^= 1

        i = li if li != 0 else ri
        while stack:
            pi, is_right = stack.pop()
            children[is_right][pi] = i
            counts[pi] = counts[children[0][pi]] + counts[children[1][pi]] + 1
            i = pi

        return i

    def split(self, root, x):
        i = root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        l_stack = []
        r_stack = []
        while i != 0:
            if x < values[i]:
                r_stack.append(i)
                i = lefts[i]
            else:
                l_stack.append(i)
                i = rights[i]

        li, ri = 0, 0
        while l_stack:
            pi = l_stack.pop()
            rights[pi] = li
            counts[pi] = counts[lefts[pi]] + counts[li] + 1
            li = pi
        while r_stack:
            pi = r_stack.pop()
            lefts[pi] = ri
            counts[pi] = counts[ri] + counts[rights[pi]] + 1
            ri = pi

        return li, ri

    def insert(self, x):
        ni = len(self.values)
        self.children[0].append(0)
        self.children[1].append(0)
        self.values.append(x)
        self.counts.append(1)

        li, ri = self.split(self.root, x)
        self.root = self.merge(self.merge(li, ni), ri)

    def delete(self, x):
        li, mri = self.split(self.root, x - 1)
        mi, ri = self.split(mri, x)

        if mi == 0:
            self.root = self.merge(li, ri)
            return

        self.root = self.merge(li, ri)
        return

    def upper_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x < values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def lower_bound(self, x, default=-1):
        i = self.root
        lefts, rights = self.children
        values = self.values
        counts = self.counts
        y = default
        c = counts[i]
        j = 0
        while i != 0:
            if x <= values[i]:
                y = values[i]
                c = j + counts[lefts[i]]
                i = lefts[i]
            else:
                j += counts[lefts[i]] + 1
                i = rights[i]
        return y, c

    def get_k_th(self, k, default=-1):
        i = self.root
        children = self.children
        values = self.values
        counts = self.counts
        if counts[i] <= k:
            return default
        j = k
        while i != 0:
            left_count = counts[children[0][i]]
            if left_count == j:
                return values[i]
            elif left_count > j:
                i = children[0][i]
            else:
                j -= left_count + 1
                i = children[1][i]
        return default

    def debug_print(self):
        print('Lefts ', self.children[0])
        print('Rights', self.children[1])
        print('Values', self.values)
        print('Counts', self.counts)
        self._debug_print(self.root, 0)

    def _debug_print(self, i, depth):
        if i != -1:
            self._debug_print(self.children[0][i], depth + 1)
            print('      ' * depth, self.values[i], self.counts[i])
            self._debug_print(self.children[1][i], depth + 1)


def x_check(x_dict, nx, y, d, stack, stacked):
    counter = 0
    if nx in x_dict:
        rbst, lst = x_dict[nx]
        ny, _ = rbst.lower_bound(y - d, y + d + 1)
        while ny <= y + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(ny)
            ny, _ = rbst.lower_bound(y - d, y + d + 1)
        i = bisect.bisect_left(lst, y - d)
        j = bisect.bisect(lst, y + d)
        counter = j - i
    return counter


def y_check(y_dict, ny, x, d, stack, stacked):
    counter = 0
    if ny in y_dict:
        rbst, lst = y_dict[ny]
        nx, _ = rbst.lower_bound(x - d, x + d + 1)
        while nx <= x + d:
            z = (nx << 32) | ny
            if z not in stacked:
                stack.append(z)
                stacked.add(z)
            rbst.delete(nx)
            nx, _ = rbst.lower_bound(x - d, x + d + 1)
        i = bisect.bisect(lst, x - d)
        j = bisect.bisect_left(lst, x + d)
        counter = j - i
    return counter


n, a, b, *xy = map(int, sys.stdin.buffer.read().split())
xxx = xy[0::2]
yyy = xy[1::2]

x_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
y_dict = defaultdict(lambda: [RandomizedBinarySearchTree(), []])
OFFSET = 10 ** 9
MASK = (1 << 32) - 1
for i in range(n):
    x = xxx[i] - yyy[i] + OFFSET
    y = xxx[i] + yyy[i]
    x_dict[x][0].insert(y)
    y_dict[y][0].insert(x)
    x_dict[x][1].append(y)
    y_dict[y][1].append(x)

for _, lst in x_dict.values():
    lst.sort()
for _, lst in y_dict.values():
    lst.sort()

a -= 1
b -= 1
ax_, ay_ = xxx[a], yyy[a]
bx_, by_ = xxx[b], yyy[b]
ax, ay = ax_ - ay_ + OFFSET, ax_ + ay_
bx, by = bx_ - by_ + OFFSET, bx_ + by_
az = (ax << 32) | ay
bz = (bx << 32) | by
d = max(abs(ax - bx), abs(ay - by))
x_dict[ax][0].delete(ay)
x_dict[bx][0].delete(by)
y_dict[ay][0].delete(ax)
y_dict[by][0].delete(bx)

stack = [az, bz]
stacked = {az, bz}
ans = 0
while stack:
    z = stack.pop()
    y = z & MASK
    x = z >> 32
    ans += x_check(x_dict, x - d, y, d, stack, stacked)
    ans += x_check(x_dict, x + d, y, d, stack, stacked)
    ans += y_check(y_dict, y - d, x, d, stack, stacked)
    ans += y_check(y_dict, y + d, x, d, stack, stacked)

print(ans // 2)