Problem: 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.

Examples

Input

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


Output

1


Input

200000 0


Output

39999200004


Input

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


Output

31159505795

Solution (in PYTHON3):

Solution:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


### 遅延評価セグメント木
class LazySegmentTree:
    def __init__(self, n, a=None):
        """初期化
        num : n以上の最小の2のべき乗
        """
        num = 1
        while num<=n:
            num *= 2
        self.num = num
        self.seg = [ninf] * (2*self.num-1)
        self.lazy = [f0] * (2*self.num-1)
        self.ls = [0]*(2*self.num-1)
        self.rs = [0]*(2*self.num-1)
        self.ls[0] = 0
        self.rs[0] = self.num
        for i in range(self.num-1):
            self.ls[2*i+1] = self.ls[i]
            self.rs[2*i+1] = (self.ls[i] + self.rs[i])//2
            self.ls[2*i+2] = (self.ls[i] + self.rs[i])//2
            self.rs[2*i+2] = self.rs[i]
        if a is not None:
            # O(n)で初期化
            assert len(a)==n
            for i in range(n):
                self.seg[num-1+i] = a[i]
            for k in range(num-2, -1, -1):
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def eval(self, k):
        if self.lazy[k]==f0:
            return 
        if k<self.num-1:
            self.lazy[k*2+1] = composition(self.lazy[k], self.lazy[k*2+1])
            self.lazy[k*2+2] = composition(self.lazy[k], self.lazy[k*2+2])
        self.seg[k] = mapping(self.lazy[k], self.seg[k])
        self.lazy[k] = f0
    def eval_all(self):
        for i in range(2*self.num-1):
            self.eval(i)
    def update(self,a,b,x=None,f=None):
        """A[a]...A[b-1]をxに更新する
        """
        if f is None:
            # 更新クエリ
            f = lambda y: x
        k = 0
        q = [k] # k>=0なら行きがけ順
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            if k>=0:
                self.eval(k)
                if r<=a or b<=l:
                    continue
                elif a<=l and r<=b:
                    self.lazy[k] = composition(f, self.lazy[k])
                    self.eval(k)
                else:
                    q.append(~k)
                    q.append(2*k+1)
                    q.append(2*k+2)
            else:
                k = ~k
                self.seg[k] = op(self.seg[2*k+1], self.seg[2*k+2])
    def query(self,a,b):
        k = 0
        l = 0
        r = self.num
        q = [k]
        ans = ninf
        # 重なる区間を深さ優先探索
        while q:
            k = q.pop()
            l,r = self.ls[k], self.rs[k]
            self.eval(k)
            if r<=a or b<=l:
                continue
            elif a<=l and r<=b:
                ans = op(ans, self.seg[k])
            else:
                q.append(2*k+2)
                q.append(2*k+1)
#             print(q, ans, l,r,a,b, self.seg[k])
        return ans

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

ninf = 10**15
op = lambda x,y: min(x,y)
mapping = lambda f,x: min(f,x) if f is not None else x
def composition(f1,f2):
    if f1 is not None:
        if f2 is not None:
            return min(f1,f2)
        else:
            return f1
    else:
        return f2
# composition = lambda f1, f2: min(f1,f2) if f2 is not None else f1
f0 = None
sgr = LazySegmentTree(n-2, [n]*(n-2))
sgc = LazySegmentTree(n-2, [n]*(n-2))
ans = 0
for _ in range(q):
    t,x = map(int, input().split())
    x -= 2
    if t==1:
        v = sgc.query(x,x+1)
        ans += (v-2)
        sgr.update(0,v-2,f=x+2)
    else:
        v = sgr.query(x,x+1)
        ans += (v-2)
        sgc.update(0,v-2,f=x+2)
#     print(v-2)
ans = (n-2)**2 - ans
print(ans)