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:
class lazy_segtree:
  #遅延評価セグメント木
  def __init__(s, op, e, mapping, composition, id, v):
    if type(v) is int: v = [e()] * v
    s._n = len(v)
    s.log = s.ceil_pow2(s._n)
    s.size = 1 << s.log
    s.d = [e()] * (2 * s.size)
    s.lz = [id()] * s.size
    s.e = e
    s.op = op
    s.mapping = mapping
    s.composition = composition
    s.id = id
    for i in range(s._n): s.d[s.size + i] = v[i]
    for i in range(s.size - 1, 0, -1): s.update(i)
  
  # 1点更新
  def set(s, p, x):
    p += s.size
    for i in range(s.log, 0, -1): s.push(p >> i)
    s.d[p] = x
    for i in range(1, s.log + 1): s.update(p >> i)
 
  # 1点取得
  def get(s, p):
    p += s.size
    for i in range(s.log, 0, -1): s.push(p >> i)
    return s.d[p]
 
  # 区間演算
  def prod(s, l, r):
    if l == r: return s.e()
    l += s.size
    r += s.size
    for i in range(s.log, 0, -1):
      if (((l >> i) << i) != l): s.push(l >> i)
      if (((r >> i) << i) != r): s.push(r >> i)
    sml, smr = s.e(), s.e()
    while (l < r):
      if l & 1: 
        sml = s.op(sml, s.d[l])
        l += 1
      if r & 1:
        r -= 1
        smr = s.op(s.d[r], smr)
      l >>= 1
      r >>= 1
    return s.op(sml, smr)
 
  # 全体演算
  def all_prod(s): return s.d[1]
 
  # 1点写像
  def apply(s, p, f):
    p += s.size
    for i in range(s.log, 0, -1): s.push(p >> i)
    s.d[p] = s.mapping(f, s.d[p])
    for i in range(1, s.log + 1): s.update(p >> i)
 
  # 区間写像
  def apply(s, l, r, f):
    if l == r: return
    l += s.size
    r += s.size
    for i in range(s.log, 0, -1):
      if (((l >> i) << i) != l): s.push(l >> i)
      if (((r >> i) << i) != r): s.push((r - 1) >> i)
    l2, r2 = l, r
    while l < r:
      if l & 1: 
        sml = s.all_apply(l, f)
        l += 1
      if r & 1:
        r -= 1
        smr = s.all_apply(r, f)
      l >>= 1
      r >>= 1
    l, r = l2, r2
    for i in range(1, s.log + 1):
      if (((l >> i) << i) != l): s.update(l >> i)
      if (((r >> i) << i) != r): s.update((r - 1) >> i)
 
  def update(s, k): s.d[k] = s.op(s.d[2 * k], s.d[2 * k + 1])
  def all_apply(s, k, f):
    s.d[k] = s.mapping(f, s.d[k])
    if k < s.size: s.lz[k] = s.composition(f, s.lz[k])
  def push(s, k):
    s.all_apply(2 * k, s.lz[k])
    s.all_apply(2 * k + 1, s.lz[k])
    s.lz[k] = s.id()
  def ceil_pow2(s, n):
    x = 0
    while (1 << x) < n: x += 1
    return x

import sys
    
def e():
  return N - 1

def op(s, t):
  return min(s, t)

def mapping(f, a):
  return min(f, a)

def composition(f, g):
  return min(f, g)

def id():
  return N - 1

N, Q = list(map(int, input().split()))
Query = [list(map(int, input().split())) for _ in range(Q)]

v = [N - 2] * ((N - 2) * 2)


ans = (N - 2) * (N - 2)
seg = lazy_segtree(op, e, mapping, composition, id, v)

for q, x in Query:
  x -= 2
  l = 0
  r = 0
  t = 0
  if q == 1:
    t = N - 2
  if q == 2:
    l += N - 2
    r += N - 2
  g = seg.get(x + t)
  ans -= g
  r += g
  seg.apply(l, r, x)

print(ans)