⣿⡀⡀⢸⣿⢲⢼⣽⡀⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣴⢾⣿⣿⠿⠿⠿⠾⠿⠽⠿⣿⣿⣶⣤⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡀⣿⣦⡕⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣟⣸⣭⣽⡀⡇⡀⡀⡀⡀⡀⡀⡀⡀⣠⣶⣿⠿⣛⣥⣶⣿⣿⣿⡿⣻⣿⣿⣿⣿⣶⣭⣛⢿⣿⣶⣀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡀⣿⠶⡎⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣯⡏⢵⣾⡀⡇⡀⡀⡀⡀⡀⡀⣠⡿⡿⣋⣶⡿⣿⡿⣟⣿⣟⡽⣷⡽⣾⣯⣽⣿⣿⣿⣿⣿⣶⣙⣿⣳⣄⡀⡀⡀⡀⡀⡀⢸⡀⣿⢵⣾⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣟⠷⢺⣾⡀⡇⡀⡀⡀⡀⢀⣾⣿⢠⣿⣿⣾⢿⡿⣿⡾⣿⡯⢷⢿⠽⡿⣿⣯⣯⣞⣽⣿⣿⣾⣿⣷⣕⢹⣷⡀⡀⡀⡀⡀⢸⡀⣿⣞⡚⣻⡇⡀⢸⡇
⣿⡀⡀⢸⡿⢽⣼⣿⡀⡇⡀⡀⡀⣠⣿⠙⡞⢸⣻⣿⠋⣾⢯⣿⣾⣿⣯⣽⣾⡀⣿⣿⣿⣿⣟⣿⡷⢿⡈⢿⣿⣿⢠⠛⣿⡄⡀⡀⡀⢸⡀⣿⠪⢎⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣿⣿⣽⣿⡀⡇⡀⡀⣰⣿⢋⡆⣿⣄⠉⢠⣿⣿⣽⣽⡿⢽⡿⣤⣤⡀⣤⣤⣷⣟⣿⢯⣯⣿⣿⣄⠙⢃⢸⠃⡻⣿⡄⡀⡀⢸⡀⣿⢒⢪⣾⡇⡀⢸⡇
⣿⡀⡀⢸⣯⡪⢺⢿⡀⡇⡀⢠⣿⢏⣿⣿⢌⠘⢀⡏⣿⡾⣿⣿⣷⡾⣻⣷⣿⡀⣿⣮⣿⣿⣷⣯⣽⣻⡿⠙⣆⢿⠏⣴⣿⠹⣿⡀⡀⢸⡀⣿⣚⣞⣾⡇⡀⢸⡇
⣿⡀⡀⢸⣯⣓⣻⣿⡀⡇⡀⣿⡿⣾⣿⢿⣟⡆⢸⡀⣿⠈⣷⣻⡏⣿⣿⣿⣽⡀⣿⣟⣻⣿⠏⣯⣿⡟⣿⡇⣿⠈⣿⣿⣟⣷⢿⣿⡀⢸⡀⣿⠪⢅⢾⡇⡀⢸⡇
⣿⡀⡀⢸⡯⣼⣷⣾⡀⡇⢰⣿⢱⣿⣿⣿⣿⣧⢣⡀⣿⡀⣿⣾⡇⢿⣟⣗⣽⡯⣿⣷⣯⣿⡀⣿⣽⠁⣿⡇⢠⢇⣿⣻⣿⣿⡌⣿⡆⢸⡀⣿⠻⢮⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣗⣺⣿⣿⡀⡇⣿⣿⣿⣻⣷⣿⣿⣿⣮⡀⠙⣇⠘⣿⡇⢸⡿⡿⡿⣗⣷⣟⣯⣾⡀⣿⠟⢠⡿⡀⣏⣿⣻⣿⣿⣷⣷⣿⣿⢸⡀⣿⢧⠼⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣟⢷⣲⣿⡀⡇⣷⡏⣿⣿⢿⣯⣿⣿⣟⣿⣾⣦⣙⣑⡉⢣⢿⣳⣗⣏⣟⣿⣿⠃⢂⢔⣞⣴⣧⣾⣿⣿⣿⣿⣯⣻⣿⢸⣿⢸⡀⡿⡭⠵⣿⡇⡀⢸⡇
⣿⡀⡀⢸⣯⣶⣾⣿⡀⡇⣿⡇⣿⣾⣿⣿⣿⣾⣿⣟⣿⡏⢗⡛⠿⣾⠗⣍⡍⡛⣋⠭⠐⣿⡿⠿⣛⠋⣿⣿⣿⣿⣿⣟⣿⣿⣿⢸⣿⢸⡀⣿⠰⡦⣿⡇⡀⢘⡇
⣿⡀⡀⢹⣗⣟⣵⣿⡀⡇⣷⣿⣿⣿⣻⣾⣿⣿⣷⣿⣟⣧⡈⢷⠓⣄⡗⠻⣾⣿⣯⡿⡟⣷⢞⣾⢠⣰⣷⣿⣿⣯⡿⣿⣿⣯⣿⣼⣻⠰⡀⣿⣲⡾⣻⡇⡀⠈⡇
⣿⡀⡀⣺⣟⣞⣽⣿⡀⡇⢻⣻⢹⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣈⣻⡼⣤⠐⠛⣿⡟⠛⣁⣱⠞⣋⣴⣿⣿⣿⣟⣿⣿⣯⣿⣿⡟⡷⡿⠨⡀⣿⢨⡔⣻⡇⡀⡀⡇
⣿⡀⡀⣻⡯⣻⡵⣿⡀⡇⠈⣿⡆⣿⢿⣾⣿⣿⣻⣿⣿⣽⣿⢯⣿⣷⠉⠙⡀⠻⠁⠈⠉⢿⣿⣿⣻⣿⣯⣿⣿⣾⣿⣿⣿⣿⢡⣯⠃⢐⡀⣿⢜⣩⢿⡇⡀⡀⡇
⣿⡀⡀⣻⡿⡻⢿⢿⡀⡇⡀⢻⣹⡼⣿⣿⡿⣾⣿⣿⣽⣿⡿⣿⣿⣻⣷⣧⡀⢰⡀⣶⣿⣸⣟⣿⣿⢿⣿⣿⣿⣿⣿⣻⣿⣿⢻⡿⡀⢈⡀⣿⢚⣊⣿⡇⡀⡀⡇
⣿⡀⡀⣿⣿⣟⡻⣿⡀⡇⡀⡀⢿⣿⡎⣿⣿⣿⣿⣳⣿⣿⣽⣿⣿⡏⣜⡏⠾⣥⠿⢸⡿⡀⣿⣿⣿⣿⣿⣿⣯⣿⣿⢟⣿⣿⣸⡀⡀⠐⡀⣿⣼⣲⣽⡇⡀⡀⡇
⣿⡀⡀⣿⣿⢝⣻⣻⡀⡇⡀⡀⢿⣧⣛⣷⢽⣿⣳⣿⣿⢯⣿⣿⣷⠸⢹⣿⡉⢭⣩⣿⡿⣀⢿⡿⣿⣿⡾⣿⣿⣿⣿⣹⢿⣽⠟⡀⡀⢈⡀⣿⡯⢝⣻⡇⡀⡀⡇
⣿⡀⡀⣿⡟⣯⣝⣿⡀⡇⡀⡀⡀⣭⣻⢿⣳⣽⣹⣿⣿⢿⣿⡿⡀⢃⢀⠘⣟⡿⡿⣏⣼⣹⡇⢻⣿⣿⠿⣿⠿⣿⣿⣿⣾⣿⠆⡀⡀⡀⡀⣿⢴⣲⣹⡇⡀⡀⡇
⣿⡀⡀⣿⣷⡭⣝⣿⡀⠇⡀⡀⡀⠈⠛⢻⢿⣿⢾⣼⣿⣋⣿⣷⣇⡄⠳⡐⡄⠃⡟⢳⣻⢱⠅⣧⣿⡏⣭⣟⣿⣿⣿⡿⠉⡀⡀⡀⡀⡀⡀⣿⢡⣌⢽⡇⡀⡀⡇
⣿⡀⡀⣿⣿⣫⣏⣿⡀⠂⡀⡀⡀⡀⡀⡿⣯⣯⣯⡾⣿⣽⣿⣩⣟⣼⣷⣿⣿⡀⢁⣾⢟⣾⢿⠶⡿⣻⢻⣯⣿⣯⣯⣿⡿⡀⡀⡀⡀⡀⡀⣿⢭⣬⣿⡇⡀⡀⡇
⣿⡀⡀⣿⣯⣳⣷⣿⡀⡀⡀⡀⡀⡀⠈⠙⠉⠈⣳⣽⢯⣾⢾⣛⣯⣺⣛⣭⣽⣾⣭⣽⡻⢧⣿⣰⣽⣿⣿⣯⣾⣏⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠬⠭⢻⡇⡀⡀⡇
⣿⣾⣟⣛⣛⣛⣛⣛⣛⢟⢛⢻⡛⢛⠛⠻⠻⢻⡿⠗⣷⣿⣯⡿⣻⣧⣿⣿⣿⣿⣿⡖⣯⢻⣾⣿⣿⣿⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⣆⡇
⣿⡾⣛⢲⡖⢲⡺⢳⡗⢖⡒⢲⢖⡪⠕⢣⢜⡣⢸⡢⢍⡈⣿⠿⠉⠟⠿⠿⠷⠿⠿⠿⠟⣿⣾⢨⡋⢋⢡⡑⢂⡘⢣⢜⡣⠔⢒⡒⢒⣊⡓⢕⢒⣒⣚⣊⣭⡎⡇
⣿⣪⡶⢖⠶⠧⠶⠶⠶⢲⠴⠦⠜⠣⢜⡣⡎⢸⡎⡅⡨⠜⠱⡑⢘⢂⢌⢌⢕⠸⢕⠇⢘⡇⡘⡪⢣⡅⡨⡌⠆⠰⢇⢢⠜⢪⢕⢆⢸⠮⠼⢎⠲⠖⠕⠲⣛⢊⡇
⣿⢝⠮⢅⠿⠿⢟⣿⣱⡬⠅⢟⠾⡽⢸⠅⠨⠥⠎⠱⠢⠆⡊⠨⠑⠊⠢⠊⠑⡑⠑⠢⠸⠣⠪⢣⡱⠂⠰⠪⠅⣟⢣⣴⣿⣶⣲⠆⠥⡪⠵⢬⠥⠤⠬⠵⢞⠇⡇
⣿⣟⣭⣍⡟⢥⣿⣿⡏⣡⡾⣿⣶⢬⣥⡾⣿⣷⡆⣨⣼⣷⡁⢿⣿⣼⡇⢾⣿⢢⣿⣿⢠⣿⣿⡄⣤⣿⣦⠠⣿⡿⠄⣿⢨⣾⣿⣿⣭⣼⣷⡉⣿⡟⣾⢹⠴⡅⡇
⣿⢷⣯⣛⣸⢛⣻⣿⡇⣬⡿⣻⣿⢸⣿⣿⡍⣿⡇⢸⣿⠝⡟⢺⣿⡼⣿⡐⣿⢯⢹⣿⢫⣽⣿⡇⣿⡆⣿⡵⣿⡇⡀⣿⢸⢸⣿⡇⢸⣷⡙⣿⢺⡟⠼⡇⡩⡅⡇
⣿⡯⣛⢳⡖⠳⣾⣿⡇⣿⡇⢸⣿⢸⣿⣿⡇⣿⡧⢸⡟⡟⠎⢸⣿⡕⡣⢰⣿⢸⢸⣿⠂⣿⣿⡇⣿⢣⣳⢀⣿⡇⡀⣿⢸⢸⣿⡇⢸⡿⣿⢃⢸⡧⠘⡿⣚⠎⡇
⣿⣮⡖⣰⡒⠴⣿⣿⡇⣿⡇⣸⣿⢸⣿⣿⡰⣿⣇⢸⣿⠞⠐⢸⣿⡇⠢⢰⣿⢸⢸⣿⡐⣿⣿⡇⣿⠏⡀⠐⣿⣇⡀⣿⢺⢸⣿⡇⢸⡿⠏⠪⢸⡿⠄⠴⢚⠆⡇
⣿⣟⠷⠸⣿⣌⢿⣿⡇⣿⣿⢹⣿⢇⡿⢿⠣⣿⡇⢿⢿⣿⢏⢿⣿⣿⡜⢸⣿⢇⢸⣿⢧⣿⣿⡢⣿⣿⣿⡝⣿⣿⡄⣿⢺⢸⣿⢷⢸⢿⣿⣟⣹⣿⣿⢏⠶⡅⡇
⣿⣟⣭⣭⣙⣿⠿⣻⢇⣌⣩⣅⢩⡅⡶⠿⣿⢛⠵⢰⡢⢍⡍⡢⢄⡉⠨⢄⡉⢡⡢⢍⡡⡠⢍⡅⡐⠠⣉⢔⡂⢉⡀⡿⣺⡢⢍⡡⢕⡢⡩⣃⣱⣌⣙⣋⣵⡢⡇
⣿⡷⣏⣙⣛⣙⣋⣚⣛⣋⣚⡹⣓⣑⡛⢐⣉⢡⢕⡇⠜⠪⠱⢢⡲⠪⠢⠍⡸⡕⡆⠅⠰⢢⢎⡃⡨⡜⠣⠸⢣⡑⢂⢛⢪⢕⢎⡱⢒⡒⢚⣓⣚⡓⢚⣚⣫⡊⡇
⣿⡿⣛⣒⡲⣚⢖⡗⡒⢒⡓⢣⡒⠪⢢⡂⢘⢜⡱⠣⢌⡕⢣⡰⢒⡇⢕⡑⣃⣐⡪⢕⡕⢢⡐⢃⡕⢇⡊⠱⠣⠌⢘⡊⡘⢃⢱⠇⠪⡲⡖⠲⢣⠖⠴⠖⢚⡕⡇
⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣅⡇
⡷⣿⣿⣸⣿⣻⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡿⢷⣾⢸⣿⣿⡇
⣯⣿⣿⣺⣟⣿⣿⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⢤⢤⣤⡀⢀⠤⢄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠶⢾⣿⢸⣿⣿⡇
⣿⡀⠉⣿⠿⣻⣿⣿⡀⡀⡀⡀⠠⢤⡤⡤⡤⠤⠤⠤⠤⠤⠤⠄⡀⢸⡇⠈⠈⡀⡣⡀⢹⡇⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡀⡀⡀⡀⣿⣟⣛⣿⣼⡀⡀⡇
⣿⡀⡀⣿⡟⣯⡿⣿⡀⡀⡀⡤⠄⢤⢠⡀⡤⢠⠄⠤⢤⢠⣤⠄⡀⢸⡧⠫⣳⡀⢪⣠⢦⡀⡀⡀⢠⢠⢤⡀⡃⡄⡆⣤⢰⠦⡆⡀⡀⡀⡀⣿⢷⣵⢿⣻⡀⡀⡇
⣿⡀⡀⣿⣿⣭⣽⣿⡀⡀⡀⠯⠄⠹⠸⠤⠇⠠⠇⠭⠴⠿⠿⠄⡀⡀⡀⡀⢸⡀⡪⡀⢸⣗⡀⠠⠹⠸⠱⠼⠧⠧⠃⠿⠸⠴⠇⠆⡀⡀⡀⣿⡟⣫⣿⣽⡀⡀⡇
⣿⡀⡀⣿⣷⣿⡷⣿⡀⡀⡀⡀⠠⠤⠤⠴⠢⠔⠆⠔⠲⠒⠒⠆⡀⢹⢇⣠⣸⡀⣇⣀⡼⡏⡀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⡀⡀⡀⡀⣿⢧⡻⣿⣿⡀⡀⡇
⣿⡀⡀⣿⣟⣶⣗⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠉⡀⡀⡀⠉⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡮⡺⣿⢻⡀⡀⡇
⣿⡀⡀⣿⣯⣶⣾⣿⡀⡀⡀⡀⡀⡀⢀⡀⡀⢀⣀⡀⢀⢀⡀⡀⢀⣀⢀⡀⡀⣀⢀⢀⣀⡀⢀⡀⣀⢀⡀⡀⢀⣀⡀⢀⡀⡀⡀⡀⡀⡀⡀⢿⣖⣱⣿⣺⡀⡀⡇
⣿⡀⡀⣿⣷⣷⣽⣿⡀⡀⡀⡀⡀⡀⠸⠆⠹⠸⠤⡀⠠⠎⠰⠇⠧⠭⠠⠣⠇⠯⠸⠄⠇⠯⠨⡀⠼⠠⠄⠇⠱⠼⠯⠸⠃⡀⡀⡀⡀⡀⡀⢺⣗⣚⣻⣹⡀⡀⡇
⣿⡀⡀⣿⢭⣯⣏⣿⡀⡀⡀⡀⡀⡀⡀⠠⢠⢠⡀⡤⢠⡠⠄⢠⢠⠄⠠⢠⡀⡀⠄⡤⡀⠠⢤⠠⡀⣄⡤⠄⠠�

⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡤⢒⠩⠲⠠⠥⠲⠤⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠔⢀⡀⡀⡴⠋⠉⠄⠨⠈⠤⡙⢤⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⢀⢉⢠⠁⠁⠎⡀⠨⠄⡀⠄⠨⡀⡀⠱⠳⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣾⡀⡾⠇⠸⠈⢸⠐⡎⢀⣸⡀⡰⠦⡄⡀⡀⠠⡍⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠣⠦⡇⡀⠇⡀⡇⡀⢀⡐⡇⡀⡀⡀⠈⡆⡇⠠⠸⠈⠉⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⢓⣱⢇⣌⢯⡀⡀⡇⣃⡾⠤⠈⢰⡀⢀⠤⢱⡇⡆⣄⡇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⠇⣿⢾⡀⡤⡀⡇⣧⡀⣠⠬⡀⣎⡄⠔⡤⣄⢱⠃⢸⠻⡀⡀⡀⢀⢄⣒⣒⣤⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⢸⢃⡇⢸⡆⡄⡇⣿⢸⠺⡿⠿⡀⠈⡌⠰⢟⠸⣼⣼⡜⡀⡀⢀⣪⠛⡀⡀⡀⡀⠙⢦⡑⠦⣀⡀⡀⡀⡀⡀⡀⢀⣤⠖⠛⠉⠓⠢⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⠸⢸⢢⡆⡇⡟⡆⣿⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⣵⢣⢻⣦⡂⠃⡇⡀⡀⡀⡀⡀⡀⡀⠈⠻⣦⡉⠗⢄⣠⣴⣾⣶⣶⣶⣶⣤⣀⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢾⠔⡇⠇⣿⠸⡆⠙⢄⡀⡀⡀⡀⡀⡀⢀⣿⡈⢷⣝⠃⢰⣷⣥⣴⣄⣤⣀⣀⣤⣤⣴⣶⣿⣿⣤⡀⡛⠉⡀⡀⡀⡀⠉⠻⣟⣷⣀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢸⡀⢱⢀⣿⡄⣧⢢⡀⡀⡀⡀⡀⡀⡴⠁⣟⣿⡦⠤⣡⣿⣶⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⠟⣽⠋⢿⡄⠾⡀⡀⡀⡀⡀⡀⡀⢿⣌⣦⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠰⡏⣾⣿⣿⠸⡀⢶⣭⠤⣤⣠⢫⠓⣌⠘⣄⠍⣿⠿⣿⣿⣺⣿⣻⣟⣿⣻⣿⢿⣟⡴⠋⡀⡀⡀⢻⡌⠹⡀⡀⡀⡀⡀⡀⡀⡟⣎⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⣰⣿⡿⠿⣡⢳⠰⢇⣛⠿⣤⣨⣌⡒⣧⡀⠉⢹⣿⣿⣿⣮⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣷⣤⣄⣀⣿⢱⢖⣚⣭⣭⣤⣬⣭⣇⢹⡇
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⠁⠁⡀⠙⣦⡀⠡⢦⠹⣖⠉⡀⡀⡀⡜⢸⣦⣀⢸⣿⣿⣿⣿⣯⢿⣟⣻⢽⢿⣿⣟⣻⣿⡿⢿⣿⣿⣺⢸⣿⠿⠟⠛⠛⠉⠉⠙⠻⢿
⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⡇⡀⡀⡀⡀⡀⢻⡀⠑⠣⠢⠱⣤⣀⣠⠃⠓⠚⠑⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣻⣿⣶⡻⡤⡀⡀⡀⡀⡀⠘⡀
⡀⡀⡀⡀⡀⡀⡀⡀⢠⠁⠂⡀⡀⡀⡀⡀⡀⣧⣿⢧⣙⢌⣀⠑⢤⡀⡀⡀⡀⡀⠙⢿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣻⣿⡿⠛⡀⡀⠙⢿⣿⣮⢮⢆⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡠⢁⡟⡀⠢⡀⡀⡀⡀⣾⣿⢨⡀⡀⠑⢥⠱⢄⠈⢦⡀⡀⡀⡀⡀⠙⣿⣿⣿⣿⣿⣶⣍⠙⠛⠉⠉⡀⡀⡀⡀⡀⡀⡀⠙⣿⣧⠳⡣⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡴⢀⠟⡀⡾⠁⡀⢂⡀⡀⢸⣼⠏⡀⡀⡀⡀⠈⠲⣌⠢⡙⢄⡀⡀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⡀⡀⡀⡀⡀⡀⡀⢿⣷⠘⡆⡀⡀⡀
⡀⡀⡀⡀⡀⡞⢀⠏⡀⣼⢀⠂⡀⡀⠁⡀⣰⣿⡀⡀⠄⡀⡀⡀⡀⡀⠈⠒⢌⠦⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⢿⣿⣷⣤⡀⡀⡀⡀⡀⡀⣿⡀⠸⡀⡀⡀
⡀⡀⡀⢀⡣⣠⠋⡀⢠⠇⡾⢿⡀⡀⢀⣴⣿⠃⡀⡀⡀⡀⠉⠁⡀⡀⡀⡀⡀⡀⠓⢴⠠⣉⠛⠻⠷⡙⢿⣿⣿⣿⣟⡿⡷⣦⠈⠻⣿⣄⡀⡀⡀⡀⢸⡀⡀⡀⡀⡀
⡀⡀⢠⡱⣴⠃⡀⡀⣿⢠⠁⣭⣶⣿⣿⠟⠊⡀⡀⡀⡀⢀⣀⡀⡀⡀⡀⡀⡀⡀⢀⠦⣿⣦⡀⠙⠦⣉⠲⣍⠛⣿⣻⣻⣗⢿⣮⡀⡀⠻⣆⡀⡀⡀⢸⡀⡀⡀⡀⡀
⡀⢠⢠⣼⠁⡀⡀⡀⡇⡏⢸⣼⣿⣿⣶⣿⣾⠟⠲⢤⣀⡤⠳⡄⡛⠲⠶⠤⠤⠞⠘⡀⡀⠙⢿⣿⣤⡀⠛⣄⠽⣄⠙⣿⡜⣿⣾⣿⡀⡀⢹⡀⡀⡀⠎⡀⡀⡀⡀⡀
⡀⠇⣿⠃⡀⡀⡀⢸⣰⡀⠸⣿⣮⡍⠛⠙⢉⠜⢥⡀⡀⡀⡀⡀⢷⡀⡀⡀⡀⡀⡀⢧⣿⣤⡀⠙⣿⣯⣦⠈⡄⡀⠳⠘⣷⠈⡎⣿⣏⡀⡀⡇⡀⡀⡀⡀⡀⡀⡀⡀
⢸⢠⣿⡀⡀⡀⡀⢇⠁⡀⡂⣿⣿⡇⡀⡀⡠⠊⠘⢤⡀⡀⡀⡀⠈⡄⡀⡀⡀⡀⡀⢸⠈⣿⣧⡀⡀⢻⣣⣧⢞⡀⡀⢸⣻⡀⣷⠸⣿⡀⡀⡇⢀⡠⡀⠂⠈⠁⢉⣀
⠆⣼⡏⡀⡀⡀⡰⣿⡀⡀⢱⣿⣿⣿⠈⠠⠚⢉⡀⠹⣧⠄⡀⡀⠠⢇⣀⣀⣀⡀⠒⠘⡀⢨⣿⣧⡀⠠⠋⠙⠌⢧⡀⣤⠟⠛⢧⡀⠿⡀⡡⠂⣀⡴⢲⡫⢍⡊⡑⢑
⡄⣿⡇⡀⡀⢠⡞⣿⡀⡀⠘⣿⡿⣿⣄⢀⣠⠚⡰⣮⠇⡀⡀⡀⡀⠸⡀⡀⡀⡀⡀⡀⠅⠋⡀⠁⡀⡀⣀⣤⣤⣴⠟⠒⠗⡉⡀⡀⢀⡤⢺⢝⢪⢌⢢⠕⠩⠌⢑⡣
⢰⢿⣷⡀⡀⣽⡀⢹⡇⡀⡀⡼⡟⣿⣻⣟⣿⣾⣿⣿⠁⠈⠠⣀⡀⡀⡇⣀⣀⡀⠄⡡⠙⢤⡀⡀⢰⠻⠃⡀⡀⡀⡀⡀⡀⡀⡀⡴⡱⠪⠅⢐⡊⡨⢅⢌⢅⢌⠅⠨
⠈⠘⣿⡀⢆⠃⡀⠏⣷⡀⡀⠈⣿⠙⣿⣟⢿⣿⣿⠇⡀⡀⡀⡀⡀⠁⡒⠃⠲⣾⡉⡀⡀⡀⡀⣳⣤⡀⡀⡀⡀⡀⡀⡀⡀⢀⢟⡢⢜⢪⡅⢌⡕⠱⠪⠬⠕⠪⡐⠪
⡀⢹⠹⣿⣸⡀⡀⠈⣿⡀⡀⡀⠈⢿⣈⠻⣿⣿⡿⡀⡀⡀⡀⡀⡀⡀⣷⡀⡀⡀⠈⠑⡀⡀⡀⢿⣿⣿⣦⣀⣀⣀⣀⣶⢯⣇⣙⠣⠜⡱⢆⠢⢸⠕⡘⡑⠣⠢⠪⠢
⡀⡀⠣⠙⣿⣤⣀⣀⠭⣿⡀⡀⡀⡀⠉⠳⠤⠁⡀⡀⡀⢀⣴⡀⡀⣸⣿⣆⡀⡀⡀⡀⡀⡀⡀⠐⣿⢿⣿⣿⠿⣛⢛⡏⡎⢹⠼⡪⢜⡩⢍⡒⠪⠤⡢⠔⡑⡸⡂⢑
⡀⡀⢰⠐⡀⠛⠶⠤⠤⡪⣷⡀⡀⡀⡀⠌⡀⡀⡀⡀⣠⠟⡀⣿⢀⣿⢡⠸⣜⣤⡀⡀⡀⡀⡀⢸⣿⣯⣶⢋⣽⣿⡏⢃⡸⢗⢎⡱⢜⡑⡂⠔⢘⢑⡂⡈⠆⡂⡑⠡
⡀⡀⣸⡆⡇⡀⠉⠉⡀⡀⠈⢷⡀⡀⡀⡀⡀⡀⡀⢀⡏⡀⣼⣿⣿⡱⣼⣺⣲⣿⣮⣛⡛⣿⣿⠛⢇⣻⡴⣿⣿⣿⡇⡪⢕⢪⢧⡎⠕⡑⢂⡕⢪⡪⠕⠑⡀⡐⠢⡢
⡀⡀⢻⢳⣿⡀⡀⡀⡀⡀⡀⡀⠈⠒⠁⡀⡀⡀⡀⢸⡀⣼⣿⣿⣥⡎⡿⣿⣗⣿⣗⣺⣽⠹⣿⣷⣘⢾⢇⡢⡩⢎⡱⢎⡣⢎⡱⢪⢔⡆⠸⢃⢰⢜⠜⢂⠐⠂⠌⠐
⡀⡀⠘⡀⠪⣧⡀⡀⡀⡀⡀⣴⡀⡀⡀⡀⡀⡀⡀⠈⣿⣿⡿⢴⣗⢡⢣⢿⣞⣿⠿⠿⣛⢓⣙⣿⣿⡿⡮⡇⢸⡇⡸⣓⢣⡎⠸⢇⡊⢔⠢⢢⡐⢠⠢⢑⡐⠂⢐⡂
⡀⡀⡀⡀⡀⡀⠙⡀⡀⡀⡀⣿⡀⡀⡀⡀⢠⣇⡀⣼⣿⡿⣞⣟⢽⣼⣼⣻⣯⢸⣿⣿⠈⠸⠿⣿⡿⣀⡷⡇⢱⡎⢚⢕⡪⢅⡨⢜⢎⡸⡪⡢⠢⡢⠔⢊⡐⠂⠨⠅
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⡀⡀⡀⢀⣟⣿⡟⣿⣿⣼⣿⣻⢺⣯⣶⡏⢉⢦⣿⡿⢰⠉⠙⠋⡀⡀⣿⡇⢪⣎⡹⢇⡸⠢⠌⠡⢰⡘⢡⡅⡂⢅⠠⠨⢁⡁⢌⣈
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠜⠈⡆⡀⢀⡿⡀⠉⢠⠃⠓⠭⣛⣛⠕⡛⠟⡣⠚⢬⢄⡞⡀⡀⡀⡀⡀⢀⡇⢸⡮⡪⢕⡊⢑⡸⡕⡱⡕⢅⢨⢌⠱⠱⠪⠢⡢⠄⢅⠪
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡌⡀⡴⠿⠟⠉⡀⡀⡀⢸⣳⡏⠛⠗⠋⠁⠉⠁⡀⡀⡀⢻⡇⡀⡀⡀⡀⡀⣸⡪⢕⡃⢘⡣⢕⡱⢕⡊⢕⡘⢡⢌⣅⡌⢌⡐⡐⢂⡐⡈⠌
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠘⡀⡀⡀⡀⡀⡀⡀⠘⡕⢙⠦⣤⣀⣀⡀⡀⡀⡀⡀⠈⡇⡀⡀⡀⢀⠾⣵⡪⠬⢕⡪⢕⡎⣩⡽⠛⠁⠛⠷⣧⡥⠪⡡⠄⢐⢆⡢⡃⡐
⡀⡀⡀⡀⡀⡀⡀⡀⡰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠹⡩⡄⡀⡀⡀⡀⠙⣄⡀⡀⡀⡇⡀⡀⣼⠁⡀⡟⢣⡕⢕⣪⡵⠋⡀⡀⡀⡀⡀⡀⡀⠈⠳⣌⡈⡑⡩⠕⡐⠢
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠻⣚⣀⣀⡀⡀⢀⡴⠁⡀⡀⡇⡀⡀⠧⣠⢺⡼⠋⠈⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠛⣬⠇⢰⡊⠨
⡀⡀⡀⡀⡀⡀⡐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠙⠾⡀⡀⠉⠙⠲⠤⣀⡀⢸⡀⡴⠉⡀⠛⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠙⠶⡂⢐