Problem:
Score : 600 points

Problem Statement

There is a grid with N rows and N columns of squares. Let (i, j) be the square at the i-th row from the top and the j-th column from the left.

Each of the central (N-2) \times (N-2) squares in the grid has a black stone on it.
Each of the 2N - 1 squares on the bottom side and the right side has a white stone on it.

Q queries are given. We ask you to process them in order.
There are two kinds of queries. Their input format and description are as follows:

1 x: Place a white stone on (1, x). After that, for each black stone between (1, x) and the first white stone you hit if you go down from (1, x), replace it with a white stone.

2 x: Place a white stone on (x, 1). After that, for each black stone between (x, 1) and the first white stone you hit if you go right from (x, 1), replace it with a white stone.

How many black stones are there on the grid after processing all Q queries?

Constraints

3 \leq N \leq 2\times 10^5

0 \leq Q \leq \min(2N-4,2\times 10^5)

2 \leq x \leq N-1

Queries are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N Q
Query_1
\vdots
Query_Q

Output

Print how many black stones there are on the grid after processing all Q queries.

Sample Input 1

5 5
1 3
2 3
1 4
2 2
1 2

Sample Output 1

1

After each query, the grid changes in the following way:

Sample Input 2

200000 0

Sample Output 2

39999200004

Sample Input 3

176527 15
1 81279
2 22308
2 133061
1 80744
2 44603
1 170938
2 139754
2 15220
1 172794
1 159290
2 156968
1 56426
2 77429
1 97459
2 71282

Sample Output 3

31159505795

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys

input = sys.stdin.buffer.readline

n, q = map(int, input().split())


class SegmentTree:
    ele = 10 ** 10
    func = min
    # SEG木は1-index
    # Aに関しては0-index

    def __init__(self, n):  # Aは0-idx
        self.n = n
        self.num = 2 ** ((self.n - 1).bit_length())
        self.SEG = [self.ele] * (2 * self.num)

    def search(self, idx):
        return self.SEG[idx + self.num]

    def initialize(self, A):
        for i in range(self.n):
            self.SEG[i + self.num] = A[i]
        for i in range(self.num - 1, 0, -1):
            self.SEG[i] = self.func(self.SEG[2 * i], self.SEG[2 * i + 1])

    def update(self, idx, val):
        idx += self.num
        self.SEG[idx] = val
        idx //= 2
        while idx:
            self.SEG[idx] = self.func(self.SEG[2 * idx], self.SEG[2 * idx + 1])
            idx //= 2

    def query(self, left, right):
        # maspy式。開区間のママ処理する
        # left, rightで値を分けているのは交換法則不成立のときのため
        # 開区間→Rが奇数→右端が偶数→1ずらしてから計算
        # 　下から上への遷移は2で割る
        # juppy氏は閉区間に直していた
        resleft = self.ele
        resright = self.ele
        left += self.num
        right += self.num
        while right - left > 0:
            if left % 2 == 1:
                resleft = self.func(resleft, self.SEG[left])
                left += 1
            if right % 2 == 1:
                right -= 1
                resright = self.func(resright, self.SEG[right])
            left //= 2
            right //= 2
        return self.func(resleft, resright)


ans = 0

tate = SegmentTree(n)
yoko = SegmentTree(n)

for i in range(q):
    s, x = map(int, input().split())
    x -= 1
    if s == 1:
        temp = tate.query(x, n)
        # print("t", i, temp)
        if temp == 10 ** 10:
            temp = n - 1
        now = yoko.search(temp)
        now = min(now, temp)
        yoko.update(now, x)
        ans += max(0, temp - 1)
    else:
        temp = yoko.query(x, n)
        # print("t", i, temp)
        if temp == 10 ** 10:
            temp = n - 1
        now = tate.search(temp)
        now = min(now, temp)
        tate.update(now, x)
        ans += max(0, temp - 1)
    # print("a", i, temp - 1)
print((n - 2) ** 2 - ans)