p02605 M-SOLUTIONS Programming Contest 2020 - Air Safety
M-kun is a brilliant air traffic controller.

On the display of his radar, there are N airplanes numbered 1, 2, ..., N, all flying at the same altitude.
Each of the airplanes flies at a constant speed of 0.1 per second in a constant direction. The current coordinates of the airplane numbered i are (X_i, Y_i), and the direction of the airplane is as follows:

* if U_i is `U`, it flies in the positive y direction;
* if U_i is `R`, it flies in the positive x direction;
* if U_i is `D`, it flies in the negative y direction;
* if U_i is `L`, it flies in the negative x direction.



To help M-kun in his work, determine whether there is a pair of airplanes that will collide with each other if they keep flying as they are now.
If there is such a pair, find the number of seconds after which the first collision will happen.
We assume that the airplanes are negligibly small so that two airplanes only collide when they reach the same coordinates simultaneously.

Constraints

* 1 \leq N \leq 200000
* 0 \leq X_i, Y_i \leq 200000
* U_i is `U`, `R`, `D`, or `L`.
* The current positions of the N airplanes, (X_i, Y_i), are all distinct.
* N, X_i, and Y_i are integers.

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1 U_1
X_2 Y_2 U_2
X_3 Y_3 U_3
:
X_N Y_N U_N


Output

If there is a pair of airplanes that will collide with each other if they keep flying as they are now, print an integer representing the number of seconds after which the first collision will happen.
If there is no such pair, print `SAFE`.

Examples

Input

2
11 1 U
11 47 D


Output

230


Input

4
20 30 U
30 20 R
20 10 D
10 20 L


Output

SAFE


Input

8
168 224 U
130 175 R
111 198 D
121 188 L
201 116 U
112 121 R
145 239 D
185 107 L


Output

100
```python
def main():
  import sys
  input = sys.stdin.readline
  N = int(input())
  XYU = [list(map(str,input().split())) for _ in range(N)]
  from collections import deque
  INF = float('inf')

  UD = [0] * 200001
  LR = [0] * 200001
  UR = [0] * 400001
  DL = [0] * 400001
  DR = [0] * 400001
  UL = [0] * 400001


  for X,Y,u in XYU:
    X = int(X)
    Y = int(Y)
    if u=='R':
      if type(LR[Y])==int:
        LR[Y] = deque()
      if type(UR[X+Y])==int:
        UR[X+Y] = deque()
      if type(DR[X-Y+200000])==int:
        DR[X-Y+200000] = deque()

      LR[Y].append((X,u))
      UR[X+Y].append((Y,u))
      DR[X-Y+200000].append((Y,u))
    elif u=='L':
      if type(LR[Y])==int:
        LR[Y] = deque()
      if type(DL[X+Y])==int:
        DL[X+Y] = deque()
      if type(UL[X-Y+200000])==int:
        UL[X-Y+200000] = deque()
      LR[Y].append((X,u))
      DL[X+Y].append((Y,u))
      UL[X-Y+200000].append((Y,u))
    elif u=='U':
      if type(UD[X])==int:
        UD[X] = deque()
      if type(UR[X+Y])==int:
        UR[X+Y] = deque()
      if type(UL[X-Y+200000])==int:
        UL[X-Y+200000] = deque()
      UD[X].append((Y,u))
      UR[X+Y].append((Y,u))
      UL[X-Y+200000].append((Y,u))
    else:
      if type(UD[X])==int:
        UD[X] = deque()
      if type(DL[X+Y])==int:
        DL[X+Y] = deque()
      if type(DR[X-Y+200000])==int:
        DR[X-Y+200000] = deque()
      UD[X].append((Y,u))
      DL[X+Y].append((Y,u))
      DR[X-Y+200000].append((Y,u))

  safe = True
  ans = INF
  for l in UD:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='U')and(b[1]=='D'):
            safe = False
            ans = min(ans,(b[0] - a[0])*5)

  for l in LR:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='R')and(b[1]=='L'):
            safe = False
            ans = min(ans,(b[0] - a[0])*5)


  for l in UR:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='U')and(b[1]=='R'):
            safe = False
            ans = min(ans,(b[0] - a[0]) * 10)

  for l in DL:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='L')and(b[1]=='D'):
            safe = False
            ans = min(ans,(b[0] - a[0]) * 10)

  for l in UL:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='U')and(b[1]=='L'):
            safe = False
            ans = min(ans,(b[0] - a[0]) * 10)

  for l in DR:
    if type(l)!=int:
      length = len(l)
      if length>=2:
        l = sorted(l)
        for i in range(length - 1):
          a = l[i]
          b = l[i+1]
          if (a[1]=='R')and(b[1]=='D'):
            safe = False
            ans = min(ans,(b[0] - a[0]) * 10)

  if safe:
    print('SAFE')
  else:
    print(ans)
    
main()
```