output_description: Print any uniforming state of the given network if T = 1, or any non-
  uniforming state if T = 2. If the required state doesn't exist, output `-1`.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M T
      x_1 y_1
      x_2 y_2
      :
      x_M y_M
attempt: N, M, T = map(int, input().split())
  xy = [list(map(int, input().split())) for _ in range(M)]
  
  state_u = list(range(N))
  state_d = list(range(N))
  for j, (xj, yj) in enumerate(xy):
      state_u[xj - 1] = yj - 1
      state_d[yj - 1] = xj - 1
  
  ans_u = [None] * N
  ans_d = [None] * N
  
  for i in range(N):
      idx = i
      while state_u[idx] != idx:
          idx = state_u[idx]
      ans_u[i] = state_u[idx]
      #
      idx = i
      while state_d[idx] != idx:
          idx = state_d[idx]
      ans_d[i] = state_d[idx]
  
  print("#", state_u, ans_u)
  print("#", state_d, ans_d)
  if ans_u.count(ans_u[0]) == N:
      print("^" * N)
  elif ans_d.count(ans_d[0]) == N:
      print("v" * N)
  else:
      print(-1)
  
problem_description: Statement
  
  A _balancing network_ is an abstract device built up of N wires, thought of as
  running from left to right, and M _balancers_ that connect pairs of wires. The
  wires are numbered from 1 to N from top to bottom, and the balancers are
  numbered from 1 to M from left to right. Balancer i connects wires x_i and y_i
  (x_i < y_i).
  
  ![pic1-small-2acea94b.png](https://img.atcoder.jp/agc041/pic1-small-2acea94b.png)
  
  Each balancer must be in one of two states: _up_ or _down_.
  
  Consider a token that starts moving to the right along some wire at a point to
  the left of all balancers. During the process, the token passes through each
  balancer exactly once. Whenever the token encounters balancer i, the following
  happens:
  
    * If the token is moving along wire x_i and balancer i is in the down state, the token moves down to wire y_i and continues moving to the right.
    * If the token is moving along wire y_i and balancer i is in the up state, the token moves up to wire x_i and continues moving to the right.
    * Otherwise, the token doesn't change the wire it's moving along.
  
  Let a state of the balancing network be a string of length M, describing the
  states of all balancers. The i-th character is `^` if balancer i is in the up
  state, and `v` if balancer i is in the down state.
  
  A state of the balancing network is called _uniforming_ if a wire w exists
  such that, regardless of the starting wire, the token will always end up at
  wire w and run to infinity along it. Any other state is called _non-
  uniforming_.
  
  You are given an integer T (1 \le T \le 2). Answer the following question:
  
    * If T = 1, find any uniforming state of the network or determine that it doesn't exist.
    * If T = 2, find any non-uniforming state of the network or determine that it doesn't exist.
  
  Note that if you answer just one kind of questions correctly, you can get
  partial score.
samples: [{"input": "4 5 1\n    1 3\n    2 4\n    1 2\n    3 4\n    2 3", "output": "^^^^^\n    \n\nThis state is uniforming: regardless of the starting wire, the token ends up\nat wire 1.\n\n![pic2-small-2acea94b.png](https://img.atcoder.jp/agc041/pic2-small-2acea94b.png)\n\n* * *"}, {"input": "4 5 2\n    1 3\n    2 4\n    1 2\n    3 4\n    2 3", "output": "v^^^^\n    \n\nThis state is non-uniforming: depending on the starting wire, the token might\nend up at wire 1 or wire 2.\n\n![pic3final-small-2acea94b.png](https://img.atcoder.jp/agc041/pic3final-\nsmall-2acea94b.png)\n\n* * *"}, {"input": "3 1 1\n    1 2", "output": "-1\n    \n\nA uniforming state doesn't exist.\n\n* * *"}, {"input": "2 1 2\n    1 2", "output": "-1\n    \n\nA non-uniforming state doesn't exist."}]