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