Paizuri Emoji Combos

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(.)(.)👉👌

🍈🍆🍈

🍉🍆🍉

🍊🍌🍊

🍈💦🍈

🍈👉👌🍈

(oYo)🍆

🍒🍆🍒

🍈↔️🍆

🍈🍆🍈💦

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

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

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

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

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

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