import sys from collections import namedtuple read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines INF = 10**10 Segment = namedtuple('Segment', ('x', 'y', 'dx', 'dy', 'n')) Rectangle = namedtuple('Rectangle', ('x1', 'y1', 'x2', 'y2')) Pt = namedtuple('Pt', ('x', 'y')) W, H = map(int, readline().split()) N = int(readline()) m = map(int, read().split()) XY = zip(m, m) x0, y0 = next(XY) def solve_two(x0, y0, x, y): if x0 > x: x0, x = x, x0 y0, y = y, y0 dx = x - x0 dy = y - y0 if (dx + dy) % 2 != 0: return if dx == abs(dy): if dy > 0: yield Rectangle(-INF, y, x0, INF) yield Rectangle(x, -INF, INF, y0) if dx > 1: yield Segment(x0 + 1, y - 1, 1, -1, dx - 2) else: yield Rectangle(-INF, -INF, x0, y) yield Rectangle(x, y0, INF, INF) if dx > 1: yield Segment(x0 + 1, y + 1, 1, 1, dx - 2) return d = (dx + abs(dy)) // 2 if dx == 0: y = (y + y0) // 2 yield Segment(-INF, y, 1, 0, INF * 2) elif dy == 0: x = (x + x0) // 2 yield Segment(x, -INF, 0, 1, INF * 2) elif dx < dy: yield Segment(x0,y0+d,-1,0,INF) yield Segment(x, y-d, 1, 0, INF) if dx > 1: yield Segment(x0+1,y0-1,1,-1,dx-2) elif 0 < dy < dx: yield Segment(x-d,y,0,1,INF) if dy > 1: yield Segment(x - d + 1, y - 1, 1, -1, dy - 2) yield Segment(x0 + d, y0, 0, -1, INF) elif 0 < dx < -dy: yield Segment(x0, y0-d, -1, 0, INF) if dx > 1: yield Segment(x0+1,y0-d+1,1,1,dx - 2) yield Segment(x, y + d, 1, 0, INF) elif 0 < -dy < dx: yield Segment(x0+d,y0, 0, 1, INF) if -dy > 1: yield Segment(x-d+1,y+1, 1, 1, -dy - 2) yield Segment(x-d,y,0,-1,INF) else: raise Exception def modify(seg): x,y,dx,dy,n = seg if dx == -1: return Segment(x+dx*n,y+dy*n,-dx,-dy,n) if dx == 0 and dy == -1: return Segment(x,y-n,0,1,n) return seg def ptpt(pt1, pt2): if pt1.x == pt2.x and pt1.y == pt2.y: return pt1 else: return None def segpt(seg, pt): seg = modify(seg) d = abs(seg.x - pt.x) + abs(seg.y - pt.y) k = d // (abs(seg.dx) + abs(seg.dy)) if not (0 <= k <= seg.n): return None if seg.x + seg.dx * k == pt.x and seg.y + seg.dy * k == pt.y: return pt return None def recpt(rec, pt): if (rec.x1 <= pt.x <= rec.x2) and (rec.y1 <= pt.y <= rec.y2): return pt return None def recrec(rec1, rec2): x1 = max(rec1.x1, rec2.x1) x2 = min(rec1.x2, rec2.x2) y1 = max(rec1.y1, rec2.y1) y2 = min(rec1.y2, rec2.y2) if x1 <= x2 and y1 <= y2: return Rectangle(x1, y1, x2, y2) return None def recseg(rec, seg): seg = modify(seg) if seg.dx == 0: if not (rec.x1 <= seg.x <= rec.x2): return None low_x, high_x = 0, INF * 2 elif seg.dx == 1: low_x, high_x = rec.x1 - seg.x, rec.x2 - seg.x else: low_x, high_x = seg.x - rec.x2, seg.x - rec.x1 if seg.dy == 0: if not (rec.y1 <= seg.y <= rec.y2): return None low_y, high_y = 0, INF * 2 elif seg.dy == 1: low_y, high_y = rec.y1 - seg.y, rec.y2 - seg.y else: low_y, high_y = seg.y - rec.y2, seg.y - rec.y1 low = max(low_x, low_y, 0) high = min(high_x, high_y, seg.n) if low > high: return None return Segment(seg.x + seg.dx * low, seg.y + seg.dy * low, seg.dx, seg.dy, high - low) def segseg(seg1, seg2): seg1 = modify(seg1) seg2 = modify(seg2) x1, y1, a1, b1 = seg1.x, seg1.y, seg1.dx, seg1.dy x2, y2, a2, b2 = seg2.x, seg2.y, seg2.dx, seg2.dy det = -a1 * b2 + a2 * b1 if det != 0: x, y = x2 - x1, y2 - y1 s = (-b2 * x + a2 * y) // det t = (-b1 * x + a1 * y) // det if not ((0 <= s <= seg1.n) and (0 <= t <= seg2.n)): return None x, y = x1 + a1 * s, y1 + b1 * s if (x != x2 + a2 * t) or (y != y2 + b2 * t): return None return Pt(x, y) x1, y1, a1, b1 = seg1.x, seg1.y, seg1.dx, seg1.dy x2, y2, a2, b2 = seg2.x, seg2.y, seg2.dx, seg2.dy assert a1 == a2 and b1 == b2 a, b = a1, b1 if b * x1 - a * y1 != b * x2 - a * y2: # 交わらない平行線 return None # 直線として同じ if a == 1: low_x = max(x1, x2) high_x = min(x1 + seg1.n, x2 + seg2.n) if low_x > high_x: return None return Segment(low_x, y1 + b * (low_x - x1), a, b, high_x - low_x) assert a == 0 and b == 1 low_y = max(y1, y2) high_y = min(y1 + seg1.n, y2 + seg2.n) if low_y > high_y: return None return Segment(x1, low_y, 0, 1, high_y - low_y) def intersect_two(shape1, shape2): if isinstance(shape1, Rectangle): if isinstance(shape2, Rectangle): return recrec(shape1, shape2) if isinstance(shape2, Segment): return recseg(shape1, shape2) return recpt(shape1, shape2) if isinstance(shape1, Segment): if isinstance(shape2, Rectangle): return recseg(shape2, shape1) if isinstance(shape2, Segment): return segseg(shape1, shape2) return segpt(shape1, shape2) if isinstance(shape2, Rectangle): return recpt(shape2, shape1) if isinstance(shape2, Segment): return segpt(shape2, shape1) return ptpt(shape1, shape2) def intersect(pts1, pts2): for shape1 in pts1: for shape2 in pts2: shape = intersect_two(shape1, shape2) if shape is None: continue yield shape def count_pt(shape): if isinstance(shape, Rectangle): return (shape.x2 - shape.x1 + 1) * (shape.y2 - shape.y1 + 1) if isinstance(shape, Segment): return shape.n + 1 return 1 pts = [Rectangle(1, 1, W, H)] for x, y in zip(m, m): pts1 = list(solve_two(x0, y0, x, y)) pts = list(intersect(pts, pts1)) answer = 0 for shape in pts: answer += count_pt(shape) print(answer)