output_description: Print N integers. The i-th of them should represent the number of the cities
  connected to the i-th city by both roads and railways.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N K L
      p_1 q_1
      :
      p_K q_K
      r_1 s_1
      :
      r_L s_L
attempt: H, W = map(int, input().split())
  A = [[int(i) for i in input().split()] for _ in range(H)]
  dp = [[0] * W for _ in range(H)]
  memo = [[-1] * W for _ in range(H)]
  mod = 10**9 + 7
  result = 0
  
  
  def aaa(x, y):
      move_list = [[x + 1, y], [x - 1, y], [x, y + 1], [x, y - 1]]
      val = A[x][y]
      cnt = 1
  
      for new_x, new_y in move_list:
          if 0 <= new_x < H and 0 <= new_y < W and A[new_x][new_y] > val:
              cnt += aaa(new_x, new_y) if memo[new_x][new_y] == -1 else memo[new_x][new_y]
              cnt %= mod
      memo[x][y] = cnt
      return cnt
  
  
  for i in range(H):
      for j in range(W):
          result += aaa(i, j)
  print(result)
  
problem_description: Statement
  
  There are N cities. There are also K roads and L railways, extending between
  the cities. The i-th road bidirectionally connects the p_i-th and q_i-th
  cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th
  cities. No two roads connect the same pair of cities. Similarly, no two
  railways connect the same pair of cities.
  
  We will say city A and B are _connected by roads_ if city B is reachable from
  city A by traversing some number of roads. Here, any city is considered to be
  connected to itself by roads. We will also define _connectivity by railways_
  similarly.
  
  For each city, find the number of the cities connected to that city by both
  roads and railways.
samples: [{"input": "4 3 1\n    1 2\n    2 3\n    3 4\n    2 3", "output": "1 2 2 1\n    \n\nAll the four cities are connected to each other by roads.\n\nBy railways, only the second and third cities are connected. Thus, the answers\nfor the cities are 1, 2, 2 and 1, respectively.\n\n* * *"}, {"input": "4 2 2\n    1 2\n    2 3\n    1 4\n    2 3", "output": "1 2 2 1\n    \n\n* * *"}, {"input": "7 4 4\n    1 2\n    2 3\n    2 5\n    6 7\n    3 5\n    4 5\n    3 4\n    6 7", "output": "1 1 2 1 2 2 2"}]