Paizuri Emoji Combos

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

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

new iatneh iruziap bojboob bojtit stit no muc muc mreps lrigtac stit gib sboob gib tra tod tra txet tra iicsa

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

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

new lrigtac iruziap muc stit gib stit no muc iruzap tra tod tra txet tra iicsa

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

new iatneh iruziap bojboob bojtit stit no muc muc mreps lrigtac stit gib sboob gib stsaerb gib noitalucaje iruzap tra tod tra txet tra iicsa

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

new iatneh iruziap bojboob bojtit stit no muc muc mreps lrigtac stit gib sboob gib stsaerb gib etalucaje tra tod tra txet tra iicsa

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⣿⣿⣿⣿⢿⠙⠋⠛⠞⠶⠶⠶⠷⣿⢿⣿⣿⣿⣿⣿⣿⣿⠻⠻⠛⠛⠾⡶⣶⣶⢒⠒⠷⡿⣿⣿⣿⣿⣻⣛⣿⣿⣿⣿⢿⠛⠉⡀⡀⡀⡀⡀⡀⠓
⣿⣿⣿⣶⣤⣀⡀⡀⡀⡀⡀⡀⡇⣸⡏⣸⡀⡟⣰⣀⣀⣀⣀⣀⡀⠉⠉⠛⠛⠞⠶⡶⣶⣶⢠⡀⡀⡇⣿⣿⣿⣿⣷⣿⣿⣯⣿⢿⠙⠈⡀⡀⡀⡀
⣠⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢸⣿⢀⠇⣼⡀⡀⡀⠋⠿⣾⣴⣤⣀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⣿⣿⣿⡌⣿⣄⣭⣤⣿⣿⣿⣿⠿⠻⠛
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠃⣿⣇⣿⡀⣿⢡⠋⠟⡾⣠⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣆⣴⣇⢠⣛⠸⣈⣌⣿⣿⣿⣿⣿⣿⣿
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣿⡘⣿⠞⣿⣿⣾⣠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣡⠃⣿⣹⠝⢚⣄⣿⣿⣾⣫⢉⡀
⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⡟⡆⢸⣿⢸⣿⣼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⣾⣄⣶⢀⡄⣠⣾⢻⡀⢀⡀
⣇⡀⡀⡀⠄⠠⠄⠦⠦⣷⣿⣿⢸⢱⡇⢸⣼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⣶⢀⡀⡀⠉⡀⡇⢸⡇⠻⡀⡀
⡀⢸⡀⡀⡀⡀⡀⡀⡀⡀⣆⣿⣿⡜⡌⢹⢸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡠⢀⡀⡀⠇⣼⢦⡷⢸⣿⣿⠻⠈
⡀⠃⡀⡀⡀⡀⡀⡀⡀⡀⡀⣆⣿⣿⡜⢹⢱⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡁⠠⡀⡀⡀⡀⣆⠙⡀⢢⣿⣷⣿⣿
⡀⡀⠨⡀⡀⡀⡀⡀⡀⡀⡀⡀⣇⣿⣿⣟⡈⠱⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠒⠠⡀⡀⡀⡀⡀⡀⡀⡀⠹⡀⣿⡿⣿⣿
⡀⡀⠃⡀⡀⡀⡀⡀⡀⡀⡀⣤⣤⣤⣀⣄⢻⡀⢁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⠿⣿⣿⣿⣿
⡀⡀⡀⢡⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣇⠘⡀⡣⠣⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠉⠋⠟⡰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠋⡾⣴⣯⣿⣿⣿
⡀⡀⡀⡀⠸⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡇⢻⡀⡀⠰⢡⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⡠⢁⠛⡿⣾⣿⣿⣿
⠁⠉⠋⠟⢻⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡃⣿⡀⡀⡄⡇⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⠁⠞⣠⠋⡠⠁⣿⣿⣿
⣿⣿⣿⣿⣿⠹⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⣿⡀⡀⡀⡇⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⡀⡀⡀⠁⠔⢀⡀⡾⢥⠭⢀⣿⣿⣾
⣿⣿⣿⣿⣿⣿⠻⡀⡀⡀⡀⡀⡀⡀⡀⡀⠓⣿⡀⡀⡀⠟⠶⠶⠱⠚⠒⡀⠤⡀⡀⡀⡀⡀⡀⡀⡀⠁⠜⢀⡀⠁⠞⢠⠁⠋⡴⢀⡀⡀⡇⣿⣵⠟
⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⡀⡀⡀⡀⡀⠎⡇⢸⡀⡀⠇⣿⡿⣿⣛⠙⡀⠄⡀⡀⡀⠈⡀⡀⡀⡀⠋⣠⠈⡀⠎⣠⡀⠏⣴⢳⠈⡀⡀⠃⣾⢫⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⠏⠻⠛⠟⢰⣾⡀⡀⠍⣿⣾⣶⣶⣷⣸⡀⠁⡀⠄⠁⠆⠘⡀⠃⡽⢋⡼⠁⡴⢀⠁⠗⢸⡀⡀⣀⡀⠟⣡⠟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣸⠏⢀⡀⠏⣻⠾⠶⠶⠶⠷⠻⠟⠊⠿⣿⣿⠋⣿⠛⣿⣿⣼⠎⣠⡀⡀⠠⡄⢳⠈⡀⡀⠃⢫⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣹⡀⠟⣹⠛⠿⣿⣿⣶⣶⣶⣶⣿⡽⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⠊⡀⡀⡀⡀⢷⠙⠁⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣀⢀⡀⡀⡀⡀⡀⡀⣧⣿⣿⣿⣿⣿⣿⣾⢠⡀⠞⢀⡀⡀⡀⡀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣄⣿⣿⣿⣿⣿⣿⠛⡾⢀⡀⡀⡀⡀⡀⡀⠇⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡀⡀⡀⡀⡀⡀⡀⠢⠐⡀⡀⡀⡀⣷⣿⣿⣿⣿⣿⢀⡀⡀⡀⡀⡀⡀⠋⣿⣿⣿⣾⣄⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡄⣿⣿⣿⣿⢿⠛⠉⠉⠉⠉⠛⡿⣿⣿⣿⣾⢀⡀⡀⡀⣦⣿
⣿⣿⣿⣿⣼⣿⣾⣱⣿⣿⣽⣿⣿⣿⣰⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣿⣴⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⡀⡀⡀⡟⣠
⣿⣿⣿⣿⢻⣿⡀⡟⣿⣣⣾⣿⣿⣿⠹⠇⠛⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⡀⡀⡀⡟⢠⡀
⣿⣿⣿⣿⣿⣇⠆⣾⢀⡀⡄⣄⣏⢘⣄⣶⣶⣿⣻⢚⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⡀⡀⡀⡟⢠⡀⡀
⣿⣿⣿⣿⣿⡆⢿⢠⡀⡀⡀⠁⣿⡑⠐⡀⡀⡀⡀⡀⡶⣶⠶⠠⡀⡀⣧⣿⡹⢩⡟⣿⣿⣿⢸⣿⣇⣿⣾⣥⣛⣿⣿⣾⢀⡀⡀⡀⡀⡟⢠⡀⡀⡀
⣿⣿⣿⣹⣯⠾⣿⠠⡀⡀⡀⡇⡄⡀⣄⠈⠇⡀⡀⡀⡀⡀⡀⡀⡀⡀⡆⡇⣠⣁⣿⣿⣴⣇⢸⣰⣾⣫⠿⣿⣿⣿⣾⢀⡀⡀⡀⡀⡟⢠⡀⡀⡀⡀
⣿⣿⣿⣀⢀⠃⣸⡀⡀⡀⡀⡆⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⠁⢳⠹⠁⡿⣿⣺⡀⡇⢸⠃⣟⣿⣿⣿⣿⣾⢀⡀⡀⡀⡀⡟⢠⡀⡀⡀⡀⡀
⣿⣿⣿⠘⠛⡈⢰⡀⡀⡀⡀⡀⡀⡀⡀⡀⢰⡼⡀⡀⡀⡀⡀⡀⣿⡜⣼⡇⠰⡁⣧⡀⡀⡆⠁⡿⣿⣿⣿⣿⣾⢀⠂⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⠁
⣿⣿⣿⢹⠇⡧⢿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⡀⠁⣿⢇⢃⣰⡀⡀⠰⡀⡀⠰⡟⣿⣿⣿⣿⣿⢀⡀⠐⡀⡀⠏⢠⡀⡀⡀⡀⡀⠁⡿
⣿⣿⣿⣿⡟⡀⣬⠁⡀⡀⡀⡀⡀⡀⡀⡀⡇⡀⡀⡀⡀⡀⡀⠃⢠⠠⡀⡀⡀⡀⡀⡀⠄⡟⣿⣿⣿⣿⣿⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⠁⡿⣿
⣿⣿⣿⣿⣿⡀⢀⡇⠱⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡐⡀⡀⡀⡀⡀⡀⡀⠏⣿⣿⣿⣿⣿⣿⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⠁⡿⣿⣿
⣿⣿⣿⣿⣿⡀⡀⡀⠈⡀⡀⡀⡀⠁⡀⡀⡀⡀⡀⡀⡀⡀⡌⡀⡀⡀⡀⡀⡀⠁⠔⡟⣿⣿⣿⣿⣿⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⡀⡿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⡀⠁⡀⡀⠄⠑⡀⡀⠡⠃⠁⡀⡀⡀⠁⡐⡀⡀⡀⡀⡀⡀⡀⢢⡀⣿⣿⣿⣿⣶⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⡀⡇⢻⠈⡀⡀⢀⠣⠛⢯⣿⠙⠁⠟⢿⠊⠐⠁⠊⠔⡀⠨⡀⡀⣆⣿⣿⣻⢿⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢸⠸⡇⣿⢿⠈⡀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢦⡀⡀⡀⡑⡀⠁⠯⣿⣿⣿⢠⡀⡀⡀⡀⠏⢠⡀⡀⡀⡀⡀⡀⡟⣿⣿⣿⣿⣿⣿

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

new bojtit iatneh emina enrobhsayaj agnam lrigtac

Warning: This item may contain sensitive themes such as nudity.

🍆✨🍈🍈➡️💦🍈🍈

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⚫️🚀⚫️

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💦

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💦🍈🍈

new cum on tits titfuck finish paizuri finish pearl necklace

(‿ˠ‿)🍆

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⣀⣄⠷⣛⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣀
⠀⠀⠀⡀⣄⢦⠳⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠖⡤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⣇⣦⢶⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠶⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⣀⣀⣤⢤⠶⠶⠓⠛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠋⠛⠛⠛⠛⠛⠚⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠒⠶⠴⡤⣤⣀⢀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣈⣀⣀⣌⣤⣤⣶⣽⣤⣴⣤⣤⣴⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣥⣤⣤⣤⣴⣤⣶⣤⣮⣤⣠⣤⣠⣀⣀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⡠⢀⠀⠀⠇⢀⠀⠀⠀⡀⢳⠈⠀⠀⠚⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠀⠀⠁⡔⢀⠀⠀⠀⡄⠘⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⡠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⢀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⢄⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⡀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠋⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⣒⠭⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡬⢒⠒⠒⠒⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⠀⠀⠁⠉⠒⠔⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠒⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠒⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠢⠒⠉⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢦⠈⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢤⠤⠒⠒⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠚⠒⠔⠤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠓⠈⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⠀⠃⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢄⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣧⣿⣼⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠊⣠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠑⠈⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠁⠋⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠛⠛⠙⠈⠀⠀⠀⡀⢶⠙⠀⠀⠀⠀⠀⠀⠀⠉⠚⣤⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠒⠛⠁⠉⡞⢀⠀⠀⠀⠋⡾⣠⣀⠀⠀⠀⣀⣄⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣴⣠⣀⠀⠀⠀⣀⣤⢶⠛⠈⠀⠀⡄⢳⠉⠁⠚⠒⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠋⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠁⣸⠀⠀⠀⠀⠁⠂⠒⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠈⠀⣀⡀⠄⠤⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠠⠂⠀⠉⠀⠀⠀⠀⣇⠘⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡇⢀⠁⠚⠀⠀⠁⠛⠶⠶⠶⠛⠈⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⠶⠶⠛⡈⠀⠀⠑⠈⡀⢹⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢀⠀⠀⠃⣴⢈⠔⠂⠒⠉⣄⠸⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠋⣰⠁⠐⠀⠒⠉⣇⠸⠀⠀⠀⠀⣇⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠌⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡀⢦⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣧⠀⠀⠀⠀⢹⠀⠀⠀⠈⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⡇⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡞⠀⠀⢀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⡇⠘⠀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⡇⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⡞⠀⠀⠀⡜⠀⠀⠀⠁⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢳⠀⠀⠀⡀⠸⠀⠀⡆⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡟⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠇⢰⠀⠀⠃⢰⠀⠀⠀⡏⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⡆⠸⠀⠀⠀⣧⠈⠀⠀⣀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠃⢰⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⣧⠘⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠐⠀⠀⠀⡟⢠⠀⠀⠃⣼⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⣆⠘⠀⠀⡀⢦⠙⢈⠀⠀⠁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⠀⠀⠝⠟⣾⢀⠀⠀⠃⣴⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠀⠀⠀⠀⣄⠱⠀⠀⠀⡀⣤⣶⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣴⣠⠀⠀⠀⠋⣰⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⡄⠷⠙⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡜⢀⠀⠉⠞⣠⠀⠀⠀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⣀⢤⠓⠈⠀⠂⡀⠢⠀⠀⠀⠀⠀⠉⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣢⠀⣔⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠙⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠚⡴⢀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⡀⣄⠦⠒⠛⠛⠛⠛⠟⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠻⠛⠛⠛⠛⠒⠶⣠⢀⠀⠀⠀⠀⠀⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠑⠈⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠉⠖⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡤⣠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⡀⣄⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠦⠪⠒⠑⠉⠉⠉⠉⠉⠉⠒⠓⠴⠷⣀⢀⠀⠀⠀⠀⠀⠉⠊⠔⠤⠏⣠⠀⣄⢼⠤⠒⠑⠉⠀⠀⠀⠀⠀⡀⣁⠼⠻⠚⠒⠉⠉⠉⠉⠉⠉⠒⠒⠗⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⢫⢧⠈⠀⠉⠞⠤⣀⠀⠁⡜⠏⢠⠀⠠⠀⡄⠹⠳⠈⠀⣀⠤⠓⠈⠀⠁⡼⡵⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠑⠈⠀⠀⠀⠀⠀⠀⠀⢢⣏⢿⠞⣤⠤⠢⠙⠀⡴⠏⢠⠀⠀⠀⠀⠀⡄⠹⢧⠀⠋⠔⠤⣤⠳⡾⡑⣼⠀⠀⠀⠀⠀⠀⠀⠁⠖⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠤⠒⠒⠂⠒⠤⡠⣀⢀⠀⠀⠀⠀⣿⠀⠏⢠⠀⠉⠉⠉⠉⠉⠀⡀⠱⠀⢸⠀⠀⠀⠀⡀⣀⢤⠤⠒⠐⠒⠒⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣶⠶⣴⣤⣤⣠⣀⣄⣀⣄⣤⣤⣦⠶⢲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠤⣠⢀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⡀⢀⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣠⠀⠀⠀⠀⠀⠀⠀⠉⠜⡠⢀⠁⠊⠶⠑⠉⡈⢄⠲⠙⠀⠀⠀⠀⠀⠀⡀⣄⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠋⠷⡾⢒⠽⠮⣴⢀⠀⠀⠀⣄⣗⠪⢕⠉⣟⠿⠛⠀⠀⠀⠀⠀⠀⡀⢳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢤⠠⡇⢈⠒⠤⠤⠀⠀⡄⠟⡤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠥⠿⡿⣿⣸⠀⠀⠤⠤⠒⡑⢹⠆⣦⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠏⣤⣀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣠⠀⠀⠀⠀⠀⠀⠀⣀⢦⠹⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢶⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠀⡄⢦⠑⠈⠀⠀⠀⠁⠉⠉⠁⠉⠉⠚⣅⠲⠉⠀⠀⠀⠂⠁⠋⡖⢪⠓⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢄⠑⠀⣄⠢⠽⣈⢀⡀⠦⠓⡛⢺⠴⣀⠁⡈⣀⠤⠥⡼⣀⠀⠀⡀⠢⣓⠛⠚⡤⠀⣀⢄⠦⠑⣪⠠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⢤⡶⣙⣈⢀⠀⠀⠀⡜⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠤⠦⠦⠶⣶⠻⠈⠀⠇⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠀⠈⠀⣀⢤⠶⠓⠛⢸⡀⢧⢈⠀⠀⠁⠀⠋⠚⠒⠒⠒⠒⠒⠒⠒⠐⠒⠄⠠⠀⠀⠋⡰⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠀⠆⡂⣄⠶⡄⢀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡼⢨⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠤⣀⡀⢿⠄⠅⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠉⠋⠒⠤⡠⣀⠀⠀⠀⠀⠀⣸⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣫⣴⠤⠤⠤⠤⠤⣀⣀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢋⡴⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⡡⠋⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠒⣠⢑⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⡢⣻⠉⠀⣀⢄⠤⡦⠒⠒⠑⠉⠉⠉⠉⠉⠉⠉⠊⠒⠖⢤⠤⡠⣀⠀⠀⠀⠁⠕⢞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡇⠀⠀⠀⠀⠉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⠒⠒⢲⠈⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠄⠠⠤⠄⠀⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠐⠐⠒⠂⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠀⠀⠀⠀
⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣑⣏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⠀⠀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣽⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀
⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠙⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⠀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠉⠉⠉⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐

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