from collections import deque
def bfs(start_x, start_y, target_x, target_y):
"""Performs BFS to compute shortest path from (start_x, start_y) to (target_x, target_y)."""
queue = deque([(start_x, start_y, 0)]) # (x, y, steps)
visited = set()
visited.add((start_x, start_y))
directions = [(0, 1), (0, -1), (1, 0), (-1, 0)] # Up, Down, Right, Left
while queue:
x, y, steps = queue.popleft()
if (x, y) == (target_x, target_y):
return steps # Found shortest path
for dx, dy in directions:
new_x, new_y = x + dx, y + dy
if (new_x, new_y) not in visited:
visited.add((new_x, new_y))
queue.append((new_x, new_y, steps + 1))
return float('inf') # Should not reach here
def min_operations_to_rearrange_coins(N, coins):
"""
Given N and a list of 2N coin positions, compute the minimum operations needed
to place them in a (N × 2) grid using BFS.
"""
# Target positions: (1,1) to (N,2)
targets = [(x, y) for x in range(1, N + 1) for y in range(1, 3)]
# Sorting helps in reducing mismatches (greedy approach)
coins.sort()
targets.sort()
total_moves = 0
# Assign each coin to a target and compute BFS
for i in range(2 * N):
total_moves += bfs(coins[i][0], coins[i][1], targets[i][0], targets[i][1])
return total_moves
# Read input
N = int(input())
coins = [tuple(map(int, input().split())) for _ in range(2 * N)]
# Compute and print result
print(min_operations_to_rearrange_coins(N, coins))
