Wafer Emojis & Symbols

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠈⢻⡿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⣷⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢛⣷⣶⣾⣻⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋


⣿⠿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢉⣴⠾⠛⠛⠻⢶⣤⣀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣴⠟⠁⠀⣠⡶⠟⠷⣮⡙⠿⣦⣄⠀⠉⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢁⣴⠟⠁⠀⢠⡾⢋⣴⠗⠀⠘⢻⡆⠀⠙⠻⣦⣄⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣴⠟⠁⠀⢀⠀⠻⣧⣘⠁⠀⢀⣴⠟⢁⣴⠶⣦⣄⠙⠻⣦⣄⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⠟⠁⠀⢀⣼⠛⠷⣦⡈⠙⢷⣴⠟⢃⣴⠟⣡⡆⠀⠙⢻⡆⠀⠙⠻⣦⣄⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢁⣴⠟⠁⠀⠀⣴⠟⣵⠟⠀⠈⠻⣦⠀⠀⠀⢺⣇⠘⠋⠀⠀⣠⡿⠁⢀⣴⣦⡀⠙⠷⣦⡀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣴⡟⠁⠀⠀⠀⠀⠻⣦⡀⠀⠀⣠⡾⠃⠀⣠⣤⡀⠙⠳⣦⣤⡾⠋⣠⡴⢟⣥⠈⠻⣦⡀⠈⠛⢷⣄⠀⠉⠻⣦⣄
⠀⠀⠀⠀⠀⠀⣴⠟⣠⡾⠋⠀⢀⣴⠟⢷⣤⡀⠈⢿⣤⡾⠋⢀⣴⠟⣋⠈⠛⢷⣄⠀⠁⠀⣴⠏⠰⠟⠁⠀⢀⣾⠃⠀⠀⠀⠙⢿⣦⡠⣬⡙⢷⣤⡀
⠀⠀⠀⠀⢀⣾⠃⣴⠟⠁⠀⣠⡾⣿⠆⠀⠈⠻⣦⠀⠀⠀⢠⡟⢡⡾⠋⠀⠀⣠⡿⠁⠀⡀⠘⢷⣄⠀⢀⣴⠟⠁⢀⣴⠟⠻⣶⣄⠙⢿⣌⢡⣄⠙⢿⣄
⠀⠀⠀⢠⡿⢁⣼⠋⠀⠀⢸⣏⠺⠋⠀⠀⠀⣠⡟⠁⣠⡀⠈⠻⣦⣄⠀⣠⡼⠏⠀⣠⡾⠛⢷⣄⡙⠻⠟⠁⠀⣰⢟⣵⠗⠀⠀⠙⣷⠄⠹⣇⢹⡇⣾⣿⡀
⠀⠀⢠⡿⢁⣾⠃⠀⢀⣤⣀⠙⢷⣄⠀⣠⡾⠋⣠⡾⠋⠙⢷⣄⠀⠙⠻⠋⠀⣠⡾⣫⡶⠀⠀⠉⣿⠂⠀⠀⢸⣏⠚⠃⠀⠀⠀⣴⠏⠀⣰⡏⠉⢰⡟⢸⡇
⠀⠀⣾⠃⣼⡏⠀⣠⡾⣋⠙⠳⣦⡉⠛⠉⢀⣼⢏⣼⠏⠀⠀⢙⣷⠀⠀⠀⠀⢿⣄⠋⠀⠀⣠⡾⠃⠀⣰⠶⣦⡙⠿⣦⣀⣠⡾⠋⠀⢠⡿⠁⢀⡿⠁⣾⠃
⠀⢰⣿⠀⣿⡇⢰⡟⣴⠟⠀⠀⣸⠟⠀⠀⠻⣧⣈⠁⠀⠀⣠⡾⠃⠀⣴⠷⣦⡀⠙⠷⣤⡶⠏⠀⣠⡾⣋⠀⠈⠛⢶⣄⠉⠉⠀⠀⣰⡿⠁⢀⣾⠁⣸⡟
⠀⠀⣿⡀⠸⣧⠘⢷⣄⠀⢀⣾⠋⠀⣰⡿⢷⣦⡙⠷⣦⡾⠋⠀⣠⡾⣣⡄⠈⠛⢶⣄⠀⠀⠀⣴⠟⣾⠋⠀⠀⠀⢠⡿⠃⠀⠀⣰⡟⠀⢀⡾⠃⣠⡟
⠀⠀⠘⣷⡀⠹⣧⡀⠙⠛⠛⠁⢀⣾⢋⣴⠀⠈⠻⣶⡀⠀⠀⣴⠟⡾⠋⠀⠀⠀⣠⡿⠁⢀⣀⡙⠳⣦⡀⠀⠀⣴⠟⠁⠀⢀⣼⠏⠀⣠⡿⠁⣰⡟
⠀⠀⠀⠈⠻⣦⡈⠻⣦⡀⠀⠀⣿⡁⠛⠁⠀⠀⣴⠟⠀⢀⣤⡙⠷⣤⡀⠀⢀⣼⠏⠀⣠⡾⠋⠻⣦⣌⠛⠷⠾⠋⠀⠀⢠⣾⠃⠀⣴⠟⢀⣼⠏
⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦⣄⠈⠛⢷⣄⣀⣾⠋⠀⢠⡿⣉⠛⠷⣮⣛⠷⠟⠁⢀⣼⢫⡾⠃⠀⠀⢙⣷⠀⠀⠀⠀⣰⡟⠁⢠⣾⠋⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠙⢷⣤⡀⠉⠛⠁⠀⣰⡟⠶⠟⠀⠀⠈⣹⡇⠀⠀⣿⣅⠉⠀⠀⠀⣴⡿⠋⠀⠀⢀⣾⠋⠀⣴⠟⠁⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡈⠛⢷⣄⡀⠀⠙⠻⣦⣀⠀⢀⣼⠏⢀⣼⠿⢮⣝⠷⣦⣠⡾⠋⠀⠀⠀⣰⡟⠁⣠⡾⠋⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠉⠻⢶⣄⡀⠈⠙⠷⠟⠁⢠⡾⣣⡶⠀⠙⢷⣌⠉⠀⠀⠀⢠⡾⠋⢠⣾⠋⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠉⠻⢶⣤⡀⠀⠀⢻⣇⡛⠀⠀⢀⣾⠃⠀⠀⢀⣴⠟⢁⣴⠟⠁⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠈⠛⠷⣤⣀⠙⠻⢦⡶⠟⠁⠀⢀⣴⠟⢁⣴⠟⠁⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⡈⠙⠷⣦⣤⣄⣀⣤⡶⠟⢁⣴⡿⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣤⣀⣉⣉⣁⣤⣶⣟⣉⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⢀⡠⠐⠁⠀⠀⢸⠀⠀⠀⣠⣄⡒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⢀⠀⠀⢀⠀⠈⡀⠀⠀⡀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠆⠀⠠⠄⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢈⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠤⠊⠁⢀⠀⠀⢂⠀⠀⠂⠀⠐⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⣤⠀⠈
⠀⠀⠄⠊⠀⠀⠠⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠁⢀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠸⠀⠀⠀⠒⠂⠀⠠⠤⠄⠀⣀⣀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠀⠀⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⢀⠀⠒⠀⠀⠀⠤⠀⠀⠀⠀⢀⡠⠊⠀⠠
⠀⠀⠃⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠄⠀⠀⣀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢊⣁⣀⣙⠛⠉⠉⠱⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠊⣀⣀⡀⠀⠀⠀⠉⠉⠉⠵⠊⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡠⠄⠒⢉⠀⠀⠀⠠⠀⠂⠀⠀⠀⠉⠐⡆⠀⠀⡂⠀⠠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⠈⠢⠤⠤⠄⠒⠒⠄⣀⢀⣀⠔⠉
⠀⠀⠈⣁⠀⠀⠂⠈⠁⠀⠁⡀⠁⠀⢁⡠⠐⠈⠀⠀⠀⢀⠀⠘⢀⠀⠒⠀⠀⠠⠀⠀⠻⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠤⠈⠁⠤⠀⠀⠰⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠉⢀⡀⠈⠀⡀⠀⠀⢘⠀⡇⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡠⠎⠀⠀⢸⠀⠀⠂⠀⠀⠠⠀⠁⠀⢐⢸⠀⡇⢸⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠉⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⢸⠀⠀⠄⠈⠁⠄⠀⠁⠀⢸⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⣀⠠⡤⢤⠤⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠉⢀⡀⠐⠂⠀⢸⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠒⠀⠀⠀⠄⠀⠘⢨⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠉⠀⠀⠀⠈⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⠀⠠⠄⠈⠀⠀⠀⢸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠒⠀⠁⠀⡀⠐⠀⠀⠀⢸⠁⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠠⠄⠁⢀⡀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⢀⠀⠠⠀⠀⡇⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠒⠀⠠⠄⠀⠋

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣄⢤⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡙⠟⠿⠿⡻⣿⠟⠁⠀⢺⢙⡘⡎⡅⠀⠀⠀⠀⣌⣡⣾⡟⣳⠏⣴⢂⡄⠀⠀⢨⢥⡴⣃
⠀⠀⠀⠀⠀⠈⠀⠀⠊⠉⠀⠀⠀⠈⣧⢧⢲⢸⡅⠀⠀⠀⢿⣿⣿⣼⣿⣺⠟⣌⡜⠀⠀⠈⢧⡸⣩⡄
⠀⠀⠀⠀⣠⡺⢦⢠⡰⡜⡅⠀⠀⠀⣽⠽⠮⠷⠛⠀⠀⠀⠀⠾⠿⡛⣵⡟⡯⠟⠁⠀⠀⠀⠀⡈⠉⠁
⠀⠀⠰⢮⣳⣶⡈⢦⢳⡩⡜⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⣠⡟⡴⢏⡗⡀
⠀⠀⠀⠀⠙⢾⣵⡈⣧⣳⣭⠾⠃⠀⠀⡄⣦⣄⣀⣰⣶⣶⢀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠏⣼⢁⡞⢡⡧
⠀⠀⠀⠀⠀⠀⠞⠁⠋⠁⠀⠀⠀⠀⠀⠓⠛⠛⠛⢿⠿⠓⠛⠚⠃⠀⠀⠠⣄⢤⣇⡄⠈⠁⠞⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣢⡵⢿⣿⣿⣷⣓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢽⣶⣿⣻⣿⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠘⢿⢯⣽⣦⣿⣿⣿⣴⠄⠀⠀⠀⣀⡔⣶⢰⡆⣄⠀⠀⠀⠉⠉⠙⠛⠁
⠀⠀⠀⠀⠀⣀⡱⡶⢤⣄⠉⣢⣿⡿⢅⠐⠀⠀⠀⠰⣆⡺⠆⢳⣲⠆⠀⢀⡄⠄⣦⢝⡪⡖⣀
⠀⠀⠀⠀⠀⠙⠿⣿⣦⣯⣭⣿⢿⣿⠿⠚⠁⠀⠀⠀⠻⣛⣯⠻⡫⠃⠀⠐⣂⢚⡒⣮⡉⢾⢡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠜⠲⠏⠈⠁⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⣿⡛⠛⠛⠛⣿⣿⡛⠛⠛⢛⣿⣟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠈⠻⣦⣴⠟⠁⠈⠳⣦⣴⠟⠁⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⠞⠻⣦⡀⢀⣴⠟⠳⣄⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⠀⢈⣿⣿⡁⠀⠀⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣴⠟⠁⠈⠻⣦⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣦⡀⢀⣴⠟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⢈⣿⣿⡁⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠁⠈⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠆⠂⠈⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠁⠏⠀⠸⠇⠀⣿⡀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠳⠒⠒⠶⣦⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠈⠉⡸
⡠⠖⠋⠁⡟⠉⣶⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢀⡇⠀⢐⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅
⠉⠟⠒⣾⠦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉
⠐⠀⠀⣏⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠀⠀⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣄⢈⠆⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⢁⠀⠀⠊⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢰⠉⢇⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⢘⢃⣀⣀⣀⡈⠀⢀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡀⠀⠣⣀⡼⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⢉⡹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⢙⣦⠞⠉⢦⠀⠛⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠀⠱⠄⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠠⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣠⠤
⡠⠠⡄⠀⠀⠈⠙⢷⣄⠠⡄⠀⠀⠀⠀⠀⠀⢠⣀⠴⠞⠉⢸⠉⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⣄
⠃⠠⠈⠙⣦⠀⡠⠀⠙⣶⠇⠀⠀⠀⠀⠀⠀⣇⠀⣸⠀⢀⡎⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠈⢳⡄
⠀⠀⠠⠈⢀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⠉⠉⠹⠓⢺⡧⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠽
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂⠀⢸⠁⣠⣿⠀⠀⠀⠀⠀⠀⢀⠔⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⣉⠀⠀⠀⠀⠀⢀⠊⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣄⠀⢻⠀⠰⡀⠐⡈⠀⠀⠐⣄⡀
⠀⣀⣄⣀⣙⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢇⠀⠈⠀⠈⣧⠀⠀⠈⢧⠀⣄
⠈⠉⠉⠉⠈⠉⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢸⡗⠏
⣀⣤⡀⠱⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣄⣠⡢⠂⠀⠀⠀⠀⠀⠀⡀⠂⠀⡐
⠀⠐⠁⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢆⢉
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⣀⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⠛⠛⠳⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⡗⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⢈⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⢰⠇⠀⠀⠀⠀⠀⣠⠴⢻⠀⠀⠇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠂⠉⠙⠃⠁⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠷⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣻⣳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⣉⣳⣤⣿⡽⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣉⣿⣤⣿⣿⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣟⢙⣯⣠⣷⡤⠿⣞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣛⣿⣭⣿⣶⢿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠚⠻⣏⣉⣧⣤⠿⡶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢻⣯⣙⣿⣤⣿⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠾⢿⠋⠹⣅⣈⣷⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠾⣿⡛⢻⣏⣙⣷⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣽⡤⠾⣷⠛⠻⡍⢈⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⠾⣿⡛⢻⣏⣉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣇⣀⣿⡤⠼⣷⠚⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣅⣀⣿⣶⠾⣿⠛⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠙⣇⣀⣷⡤⠾⣷⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⣙⣧⣬⣿⣴⠾⣿⣻⠋
⠀⠀⠀⠀⠀⠀⢀⣿⠚⣿⠉⠙⣇⣀⣷⡴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿⠛⢹⣧⣬⣷⡶⣾⠃
⠀⠀⠀⠀⠀⢀⣾⡽⡶⠞⣟⠋⢹⣄⣤⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣷⠿⣿⢛⣻⣯⣼⣿⠃
⠀⠀⠀⠀⠀⢾⣽⣤⣽⡶⠻⣟⠉⢹⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣦⣿⣶⠿⣟⠋⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⣶⣛⡏⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣿⡟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠈⠕⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢷⡄⠀⠙⠛⢷⣦⣤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠄⢉⠉⢀⠀⠀⢰⣶⠚⣯⣷⠾⠋⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⡥⠀⠁⠀⠀⢲⣶⣭⡛⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠰⠠⡊⠀⡀⠀⠙⢉⠁⠀⠀⠀⠹⣿⣹⣏⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣎⣩⠀⠀⠀⢀⠀⠀⠀⣾⠿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆⠀⠀⡀⠁⠀⢀⡀⢸⠠⠤⠄⠀⡀⠉⠹⢿⣿⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠠⠐⠂⡘⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡦⠀⠈⢒⣨⠀⠀⡴⠋⠀⠀⠀⠀⠀⠐⢄⠑⠄⠀⠙⢯⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠐⠁⠀⠀⠈⠁⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢸⣿⣿⣇⣼⠁⠀⣁⡂⠀⢐⣀⡏⢨⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣀⡀⠀⠀⠀⢀⣤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⢨⢭⣍⣉⠉⠳⡤⢊⣾⣿⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠍⡇⠀⠀⠻⣿⣿⣿⣆⠀⠀⡈⠉⢉⠁⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠠⠞⡤⠠⠋⠀⡜⣳⡙⠃⣀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⡀⠀⠉⣀⠀⠊
⠀⠀⠀⠀⠀⠀⡄⢰⠄⡀⣦⣾⣿⣿⡏⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⢊⠇⠀⠀⣀⣠⣹⣿⣿⡿⢀⣶⢨⣿⣷⣶⣾⣲⡄
⠀⠀⠀⠀⢀⠔⢁⣀⡀⠈⢻⣿⣿⣿⡇⠀⣄⣀⣹⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠠⠒⠉⠀⠀⠀⠈⠻⠁⠀⠘⢿⣽⣿⣷⣿⣿⣷⣄
⠀⠀⠀⢠⠏⠀⠻⡿⣧⠀⠀⡰⡼⠋⢀⠀⠈⠚⠛⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⣿⣿⣿⡍⢿⣿⣿⣷
⠀⠀⠀⢻⡀⠀⠈⠋⠋⠀⢀⡾⠁⠀⣼⣿⣗⡂⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠔⠋⣹⠀⢀⡠⠚⠉⠉⠉⠣⠘⢿⣿⡇⠀⠻⠋⡄⠠
⠀⠀⠀⠈⠻⢦⡤⠊⠀⠀⠸⣇⠀⠀⠰⢷⠷⠃⠀⠀⡘⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⡇⠀⠐⠀⢂⡀⡀
⠀⢀⠀⠀⡴⠊⠀⠀⠀⠀⣀⡽⢮⡀⠀⠀⠀⢀⣠⡚⠁⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠷⠀⠀⣀⠴⠁⠀⠀⠀⢀⠀⢀⣡⢞⣙⡷⠆⠀⠁
⠀⠈⠣⡺⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⠉⠉⠉⠀⠈⠙⠶⣤⡀⠀⣰⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠙⣄⣀⣀⣠⠴⠁⢶⣫⣭⣾⣿⡄
⠀⠀⠀⠼⠄⠃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡴⠀⠀⠀⠀⠀⠀⠲⠜⠃⠀⠀⠀⢮⡀⠀⠀⠉⠉⠀⠀⠺⣧⣬⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣤⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦
⠀⠀⠀⠀⢰⢀⠀⠀⠒⠀⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠻⡖⠶⠶⠷⡈⠱⠊⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠆
⠀⠀⠀⠀⠀⠈⠻⠞⢈⣀⣁⡄⢱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢰⢁⢂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⡆⢀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠃⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⢀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠵⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠐⠿⠿⠗⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠨⠀⠄
⠀⠀⠀⠀⣄⠀⢰⡒⠊⢎⡀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⣲⣴⣤⠄⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠃⠀⠘⠓⠂⠀⠂
⠀⠀⠀⡸⠀⣙⣦⠈⠛⠂⢑⠀⠀⠀⠀⠀⠀⠀⢠⡿⢉⠀⠀⠀⠸⠿⢷⢷⣖⣦⠀⠀⠀⠀⢿⢆⠀⠀⠀⢀⠀⠀⣴⡆⠀⠱⠀⠀⠂⢀
⠀⠀⢰⠇⠠⣿⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣀⠀⠀⠀⠒⠾⣟⢻⠁⠀⠀⠀⠀⠀⣸⠀⠀⠄⢢⠀⡀⠺⠁⠀⠸⣄⠐⠀⠰⠂
⠀⠀⠀⠓⠶⠄⠀⢠⣴⣮⣙⣄⢑⣦⡀⠀⠀⠀⠈⠻⣿⣭⣓⠄⠀⠀⠀⠀⣀⣠⠂⠀⣀⣠⡴⠃⠀⠀⠀⠈⠂⠀⠒⠤⢤⡀⠀⠙⠇⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠞⠛⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠐⠮⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣔⢒⣙⡛⠿⢿⣶⣦⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠇⠀⠀⠉⣭⣽⣛⡻⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠞⠀⠀⠀⠀⠀⣒⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⣁⠀⠀⠀⠶⣄⠀⠀⠈⠛⠉⢙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣀⠤⠖⢩⠏⠀⠀⢀⣀⣊⠼⣫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠴⠁⠀⠀⠈⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣴⡶⠶⠶⣄⡀⣠⢞⣽⣷⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⡦⣤⠀⠀⣿⡁⢾⡟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⣴⠤⡎⠀⢰⣏⣶⡤⠄⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠨⣇⣆⣴⣤⣿⣿⣿⣇⠅⠀⠈⡟⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠶⠋⠙⢾⣿⣿⣿⣿⣿⠭⠴⣄⣴⣽⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢠⡴⡶⠄⠀⠙⢯⢙⡿⠃⠀⠀⠁⠈⠙⠻⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠙⣳⣻⣷⠀⣠⢞⡽⠁⠀⣰⣼⡶⠄⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠏⣡⠞⠁⣾⡇⠀⠀⠳⣟⢻⣳⠄⠀⠀⣟⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣠⠞⠁⠀⠀⢻⡇⠀⠀⠈⠻⠙⠅⠀⠀⣰⠇⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⢀⣿⣦⣁⡀⠀⢀⣠⡴⠾⣥⣀⠀⠀⠀⠀⢨⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣰⠋⠀⠀⠀⠀⣠⡾⠋⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⠙⠛⠶⣤⣄⢿⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡓⢤⡀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠛⠲⠋


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⡏⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢀⡠⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡡⠐⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡠⠒⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠂⢁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⡧⢂⠡⢺⠁⠀⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠳⠥⠄⠐⠀⠀⠀⠀⠀⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠈⠏⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠠⠔⠂⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⠀⡏⠁⠒⠆⠀⠀⢤⠀⠄⣤⠠⠀⠖⠒⠈⢹⠀⠀⢠⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠰⠀⠀⢰⠀⠀⢰⠀⠀⢸⠀⠀⡇⠀⠀⡆⠀⠀⡆⠀⠀⠆⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠇⠀⠀⡄⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⢠⠀⠀⠸⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⡀⠀⢠⠀⠀⡆⠀⢠⠀⠀⠀⠀⠰⠀⠀⡄⠀⢀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠅⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⡀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠂⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠧⠄⢠⡀⢰⠀⢠⠀⠀⠆⠀⡆⢀⣄⠀⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠻⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⡾⠃⠀⠀⠀⣰⡟⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠘⣷⡀⠀⠀⠀⠻⣦⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣿⠁⠠⣿⣉⣻⡇⠀⠀⣿⣋⣹⡧⠀⢹⡇⠀⠀⠀⠀⠈⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣦⠀⠀⣿⡄⠀⠙⠻⠛⠁⠀⠀⠙⠻⠛⠁⠀⣼⡇⠀⢀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠸⣷⡀⠀⠀⣤⡀⠀⠀⣠⡄⠀⠀⣰⡿⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠈⠛⠛⠛⠋⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⣿⠓⠀⠉⠛⠿⠶⠶⠶⠾⠟⠋⠀⠐⢻⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠿⠀⠀⠀⣤⣀⠀⠀⠀⢀⣤⡄⠀⠀⠸⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣤⣤⣤⣤⣤⣬⣽⣷⣦⣶⣿⣭⣤⣤⣤⣤⣤⣄⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⣦⣼⠿⣧⣤⡿⢿⣤⣼⠿⣧⣤⡿⢿⣤⣾⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⡿⠷⠶⠾⠿⠶⠶⠿⠷⠶⠾⠿⠶⠶⠿⣿⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⡾⢻⣷⠟⠻⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⣠⡾⠟⠁⠀⢘⣿⣀⠀⠀⠙⠿⣦⡀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣿⠿⠋⠀⠀⣀⣴⠟⠋⠛⢷⣄⡀⠀⠈⠻⢿⣇⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⠛⠁⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠙⠻⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣶⣶⣶⠆





⣿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣟⣿⣟⣛⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⠔⠊⢹⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⢀⣀⢀⡜⠁⡰⠃⠀⠀⢸⠀⣠⠀⡰⠊⠉⠲⣄
⣴⡖⠤⠋⠈⠋⠀⠰⡁⠀⠀⠀⣸⡤⠄⠠⢇⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠓⠊⠉⡆⢀⡠⠤⣈⢧⠀⢼⡡⠤⠄⠒⢶⣸⢶⡖⣒⡇⠀⣀⣀⠤⠤⠤⠔⠲⠤⢄⡀⠀⠀⠀⠀⢾⡵⠒⣷⣄⣤⣄⣀⡀
⠀⠀⠀⠀⠉⠁⠀⣀⣈⣯⣷⠀⠉⠓⠒⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠸⡅
⠀⠀⠀⠀⠀⢀⣸⡁⠠⠶⠮⠁⠀⠀⢀⡀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡔⠛⢤⠀⠀⡟⠲⡁
⠀⠀⠀⠀⠀⠈⢧⢈⣲⠶⠒⢢⠀⠈⠙⡧⣄⠀⠀⠀⠀⠉⠂⠄⢀⡀⠀⠄⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢱⠸⠊⠀⠀⠈⡯⣉⣱
⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⢀⡜⢣⠀⠀⠹⡜⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⠤⢤⣤⣀⠠⠄⣶⠤⠒⠁⣀⠷⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠑⢤⣣⣀⡀⠈⠃⠀⠙⠂⠀⠀⣀⣀⣀⣀⡤⢄⣈⢻⠉⠓⠤⢀⠀⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡝⠀⠙⠢⠤⣄⣈⣉⠉⠉⠉⠁⠀⠀⡆⠀⠀⠉⠳⠝⠂⠀⠃⠉⠛⣢⣄⡀⠀⢀⣀⢠⣤⠤⠒⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠂⠃⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⠀⠤⠋⠁⠀⡠⠊⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⠌⡒⢄⠄⠀⢀⡞⠁⠀⣀⠄⣠⣞⠾⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡛⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⠞⠛⠂⠤⢾⣴⠊⢉⣼⡶⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢦⣕⡢⢄⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠑⠻⣁⠀⣀⡠⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠉⠓⠮⣕⣢⢄⣠⢎⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⠀⠀⢀⣀⠜⣹⠙⠓⠦⠭⣕⣢⣤⣄⣀⣀⣠⡯⠛⠉⡷⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠤⠖⣊⠭⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⢹⠀⠀⠀⡰⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠦⠒⣹⠁⠀⠀⣘⠤⠢⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠻⠔⣒⡺⠅⢴⣉⠦⢶⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠉⠀⠐⢁⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⠿⠿⠿⢿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠐⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣍⣁⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣔
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠋⠀⠁⠀⠂⠀⠀⠁⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⠟⠁⠀⣜⠐⢶⣶⡄⠀⠀⠰⠿⠛⠀⠇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⡀⠀⠰⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠄⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈⣷⣉⠛⣛⣿⣿⠿⠱⠿⣿⣍⣉⣤⣴⣶⣶⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠠⠄⢻⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⠏⢻⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠈⢿⠿⠷⠀⠀⠀⠀⠐⠛⠛⠿⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⣩⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢄⠛⠃⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠤⠰⠲⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠉⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡷⡦⣄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⡐⠶⠓⠄⢁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⢀⣉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢙⡆⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡑⢀⡈⣳⠒⠓⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⢁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠃⣡⠀⠡⡁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠐⡒⠜⠂⠁
⠀⠀⠀⠤⢤⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡀⡀⠂⠀⠀⠀⠄⠉⠰⠢⠀⠀⠀⠀⠀⠐⠒⠂⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⢳⡄⡄⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠢⠄⣀⡀⠀⠀⢀⣀⡤⠐⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠠⢠⠊⠉⠁⢀⣀⡀
⠀⠀⠀⠤⢴⣠⣆⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢋⡀⠁⠀⠀⠀⠀⠀⠀⠁⠀⣄⠏⠁⠈⠑
⠀⠀⠀⠐⠤⠜⣹⣗⣐⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣶⣶⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡠⠄⡀⠁
⠀⠀⢠⠌⣀⢀⢘⢣⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⢿⡤⠄⡀⢀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠡⠤⠤⠄⠀⠈⠀⠀⡄⠀⠠⠀⠀⢚
⠀⠀⠀⠀⠀⢀⠈⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⢈⢡⠀⠀⠄⢀⠀⠀⡒⠣⡐⢢⠂⠀⠀⠀⠀⠐⠂⠄⠄
⠀⠀⠀⠀⠀⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢶⡀⠀⠈⠁⠈⠀⠀⠒⠗⢀⣀⠀⠀⠰⠂⠀⠀⠀⡄
⠀⠀⠀⠀⠰⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢙⠄⡀⠀⢐⣤⠀⣤⠀⡈⠀⠀⠑⣶⠀⠀⠈⢉⡔⠋⠄⢈⣙⡣⠊⠠⢤⣮⡀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡞⠁⠀⠀⢠⠖⠉⠁⢀⣅⠀⠊⠁⠀⢶⣾⡤⠀⠠⡀⠸⠀⠀⠀⠈⣺⠃⠀⡀⢠⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠸⠁⠧⠀⠛⢀⡀⠀⠈⠃⢦⡀⠀⢰⠞⠳⣄⠀⠀⠼⠚⠒⠢⢀⠁⢻⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠐⣧⠀⣁⡀⠀⠚⣀⣀⣀⠈⠚⢽⠞⠁⠀⠀⠉⡰⠟⠀⠀⠀⢈⠸⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⡩⠃⠀⠀⠀⠈⠉⠡⠀⠀⠈⠚⠒⠀⡀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠐⠒⠤⡀
⠀⠀⠀⢀⠐⠉⠀⠀⠉⠰⠁⠀⠀⠀⠀⠀⠀⠈⠳⡊⠉⠈⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⡖⠁⠀⠀⠀⠀⠀⠀⠈⢖⠈⠉⠈⠁⠢⣄
⠀⠀⡐⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂
⠀⢠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠐⡄⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡱⢒⠤⠤⠐⢎⡁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⠕⠢⠤⠤⠐⣌⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠈⠁⠐⠖⠀⡩⠀⠈⠀⠉⠈⠩⠉⣀⣐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⢰⠂⢈⠡⠀⠀⠀⠁⠈⠏⠡⣀⡒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⣇⠘⠉⠣⠀⠀⠀⠀⠀⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡱⠦⠀⠀⠀⠀⠀⡂⠘⠃⢀⠀⠀⠐⠋⠧⡀⠹⠍⠛⠀⠀⠠⡀⠚⠃⡄⠀⠀⠀⠀⢀⠴⢎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠗⠂⢀⠀⠀⠀⠀⢃⠠⢲⣤⠄⠰⠁⢰⠄⢸⠀⢴⠄⠰⠀⢤⡇⠄⠶⠀⠀⠀⠀⠀⡀⠐⠢⠂⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠛⠶⣤⠖⡏⠀⠸⠀⠀⣷⣄⡀⠀⠈⠀⠀⣀⣠⡇⠀⡅⠀⢸⠓⢦⣤⠶⠛⠁⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣄⡀⠈⢻⡇⠀⠙⠉⠈⣿⠏⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠎⠀⠀⢱⠀⠀⠈⠀⡖⠐⢮⠀⠀⠀⡸⠀⠹⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⢠⡆⠀⠀⢀⡇⠀⠘⡆⠀⢠⠇⠀⠀⠙⠒⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠃⠀⠀⠀⠀⠳⣄⣠⠼⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢲⡶⠒⠲⣶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⢸⡇⠀⠀⣿⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⠿⠿⠿⠇⠀⠀⠿⢿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢷⠀⠀⠀⠀⠀⠀⡟⠈⣷⠀⠀⠀⠀⠀⠀⢰⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠀⠀⠀⠀⠀⠘⣇⣀⡿⠀⠀⠀⠀⠀⠀⢸⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⡀⠀⠀⠈⣿⠀⠀⠀⠀⣀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⡄⠀⠀⣿⠀⠀⠀⣼⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠿⠶⠶⠾⠿⠿⠷⠶⠶⠿⠶⠶⠶⠿⠿⠿⠶⠶⠾⠷⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⣴⠶⢦⡀⠀⣴⠶⣦⠀⠀⢠⡟⠉⠻⣆⠀⣼⠏⢿⡀⠀⡿⠙⣧⠀⢰⡿⣆⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠃⠀⢸⡇⢀⡿⠀⢸⡇⠀⣼⠁⠀⠀⠙⠶⠏⠀⢸⡇⢸⡇⠀⠘⠷⠾⠃⠙⢧⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⠞⠁⠀⠀⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡀⣀⢀⣀⢀⣀⣀⢀⡀⢠⣀⢰⢀⣀⣄⣠⣀⢀⣠⢀⣀⢀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠓⠟⢹⠾⢻⠿⠋⡿⠁⠘⠞⠛⠛⠁⠳⠛⠘⠙⠾⠒⠟⢸⠏⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⣀⢠⡀⢀⢀⠀⡀⡀⢀⡀⡄⢀⢠⡄⣀⡀⡤⣀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠘⠁⠀⠁⠁⠈⠁⠁⠀⠈⠀⠉⠀⠁⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡢⡄⢀⣴⡆⣶⣄⠀⡤⣲⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣌⢳⡡⢼⣟⡓⢻⣿⠤⣱⢋⡜⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⣷⣦⡀⠈⢿⢿⡛⡧⠹⣼⢦⣙⡮⢨⡾⠡⡟⣻⢿⠏⢀⣴⠿⠋⣀⣤⡤
⠀⠀⠀⠀⠀⠀⣤⣙⣿⣷⡤⠜⠛⣲⢼⣶⣽⢰⢂⣶⡝⢨⠐⣴⣆⠲⢸⣵⣾⠻⣍⣁⠒⢾⠿⣷⣶⠆
⠀⠀⠀⠀⠀⣴⣾⠋⣱⣞⣀⣼⣻⣷⣬⣿⡮⢨⣟⢞⡓⠄⠔⣻⢞⣯⠨⣼⣯⣵⣌⡱⠦⣌⢿⣆⠙⢿⣆
⠀⢀⡄⢲⣜⠋⢀⣼⠋⠉⠅⠀⠉⠉⠉⠁⠈⠁⠁⠉⠁⠀⠀⠉⠁⠁⠉⠈⠉⠙⠋⠡⠠⢀⠈⠻⢄⠀⢉⣶⠂⣄
⣠⣬⣌⣿⣿⠊⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⢺⣿⣏⣬⣤
⠈⠙⢿⠿⣻⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢸⡿⢾⠟⠉
⠀⠐⠈⢶⢟⣀⡌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⣄⡘⢷⠎
⠀⠀⠀⠀⣉⣿⡁⠀⠀⠀⠀⠃⠈⠀⢣⠢⢂⠔⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠈⠐⠂⢀⠀⠀⠀⠀⠀⣹⣏⡁
⠀⠀⢐⠾⣦⠉⢓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡋⢥⡾⢖⠂
⢀⣤⣾⢖⣿⠒⠟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠗⢺⣗⢾⣢⣄
⠉⢛⢉⢿⣿⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢼⣿⢏⢙⠋
⠈⠈⠃⠘⢏⡀⠈⢲⣄⠈⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠀⠂⡀⢰⠈⠀⠀⡙⠄⠋
⠀⠀⠀⠀⠈⢿⣶⡈⢻⣎⠛⢶⣻⣿⠾⣷⠮⠱⣗⣽⣃⠤⢄⣻⣕⡷⠩⢿⣿⣾⣗⣢⡴⠎⣴⡟⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠾⢛⣷⣾⠦⠌⢉⡳⢿⣿⢾⢨⡙⣾⢇⠰⢀⢿⡞⣩⢸⢾⣿⣋⠟⠛⣀⣼⣭⡶⢛⡍
⠀⠀⠀⠀⠀⠀⠐⠛⠉⢡⣶⡾⠋⠀⣽⣴⣋⣦⢠⢶⡽⢞⡦⠴⢦⠠⣎⣳⣼⡅⠙⢶⣤⡌⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠉⢉⠟⣱⠫⢼⣗⣋⣸⣾⠬⢳⡙⢏⠉⠙⠀⠀⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡣⠇⠘⢿⡇⣿⠟⠀⠧⣻⣼
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠠⢤⡜⠉⠁⠀⠀⠀⠀⠀⠀⠤⡠⠊⠁⠀⢀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⣀⣀⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢥⣈⠖⣄⠀⢀
⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⡈⠑⢶⠉
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡼⠁⠀⠀⠀⠀⢀⠠⠐⡺⠹⣆⠀⠳⡀
⢰⡇⢀⣠⡴⣶⣶⣶⣶⣶⣶⣤⣄⡀⢸⣠⢏⣤⠶⠶⠒⠶⠛⠛⠒⠂⠐⣦⣜⣼⠁⠀⡀⢤⠒⠈⠀⠀⠀⠀⠀⠙⠆⠀⢧
⡜⣴⣿⠿⣵⣦⠙⠃⠉⠁⣽⣿⢿⣿⣮⣿⢿⡇⠀⣶⡆⠀⠀⠀⢠⣶⡄⠸⡿⣿⠀⢨⠁⢰⣶⠀⠀⠀⠀⣰⣦⠀⠀⠀⣸
⡟⢿⡿⠀⠙⠋⠀⠀⠀⠀⠙⠋⠈⢿⠿⣻⢆⡇⠀⠛⠃⠀⠀⡀⠈⠛⠁⢀⣠⢿⡀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠋⠀⢠⢀⡏
⢻⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⢀⡏⠀⠹⣦⣀⣀⡀⠀⠀⣀⣀⡤⠞⠀⠈⠃⠿⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢏⠘⡀
⠀⠳⡀⣸⠭⠽⣟⣛⣛⠋⠩⠩⣇⢀⠞⠀⠀⠀⡸⠑⢨⠉⠉⠉⠉⠐⠙⡄⠐⡴⠀⢀⠀⣾⡉⠉⠉⠉⠉⢉⣹⠀⠠⣠⠇
⠀⠀⢙⡟⢠⠀⠀⠀⠀⠀⠀⡄⠙⡏⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⡀⢱⠀⠁⢀⢾⡞⠀⡈⠉⢰⡖⠈⢁⠈⢆⠘⡹
⠀⠀⡼⢠⡾⠀⠀⠀⠀⠀⠔⡿⡤⢻⡀⠀⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⢃⢨⡇⠀⠀⣜⠁⣾⡅⠀⢨⡇⠀⢸⣆⠘⣾⠃⠰
⠀⠀⠙⠚⡇⠀⠀⠀⢠⢋⡉⠉⢉⢺⢁⠁⠀⠘⢾⠁⠀⠀⠀⠀⠀⠀⠸⠾⠃⠀⠐⣽⠛⢹⠣⢤⠥⠥⠠⢿⣭⣿⣿⣦⡀
⠀⠀⠀⢠⠇⡀⠀⠀⢼⢨⣁⢆⣉⣸⠈⢀⡂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠉⠢⣼⠀⠀⡿⡇⠀⢸⠁⡆⠀⢰⠸
⠀⠀⠀⠸⢅⣀⣀⣀⣈⣓⣿⡿⠟⠋⠀⠈⠉⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠉⠀⠀⠀⢸⡀⢀⡇⣇⠀⣸⣔⠦⠭⠴⣺
⠀⠀⠀⠀⢰⣃⣉⡿⢹⣉⣘⡇⠀⠀⠀⠀⠀⠀⠉⣟⣛⣑⠖⢶⣘⣛⡯⠁⠀⠀⠀⠀⠀⣞⣈⣀⠇⢟⣈⣘⡏⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⢠⠐⠈⡁⠁⠉⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⠀⠀⢫⠀⠀⠀⠠⠌⠀⠈⠀⠀⠀⠀⢂⠐⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢏⠀⠀⠀⠀⡀⠀⠓⠳⠢⡀⠀⠀⠀⠐⠆⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⠄⠀⠀⠀⢀⠀⡐⠃⠉⠂⠀⠽⡃⠀⠀⠀⠀⠀⡀⠠⢆⠰⠀⠈⠀⠀⠐⠁⡘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠦⣁⡇⠘⣠⣀⠀⡌⣅⠀⡀⠘⠀⠇⢀⠀⢠⠂⠘⠀⠀⠈⠀⡇⠈⠐⡎⠀⠀⠀⢊⠀⡀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⢀⣁⠉⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠁⠀⠀⠀⠉⣐⠴⠂⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠊⠁⠤⠨⠀⠀⠀⠀⠀⠂⠀⠀⠀⠅⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠊⠉⠁⣲⢄⡀
⠀⠀⠠⠀⠃⠑⠂⢠⡠⠚⠗⠂⢐⢲⠀⠀⠐⠒⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⡤⢠⠀⠤⣶⣶⠄⠀⠰⠁⢁⡨⠂⠀⡁⢡
⠀⢀⡀⠄⠀⠀⠚⠆⡐⠁⠀⠀⠈⣚⠄⠀⠀⠀⠀⢀⡆⠙⢲⠀⠀⠀⠀⡎⠀⠎⠐⢠⡀⠀⠀⠀⠀⠈⠀⠀⡤⠈⢱⡈
⠀⠀⠀⠠⣠⠌⠼⡀⠳⡄⠄⠀⡜⠁⠀⠀⠤⢠⡚⢁⠛⢆⡀⠑⠊⠑⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠂⠃⠀⠀⠀⠀⠰⡊⠀⡰⠆⢚⡙⠁⠐⠀⠈⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢕⣠⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣚⣊⡤⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⠭⠉⠀⠀⠐⡷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⣀⡠⠄⠀⠀⠀⢀⡗⢆
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠐⠒⠒⣊⠩⠀⠼⠓⡄⠀⠀⠀⠀⠀⠤⠐⠒⠂⠐⠒⠂⠀⣉⠥⠄⠤⠋⡆
⠀⠀⠀⠀⠀⠀⠤⠒⠒⠀⠀⠤⠔⠊⢁⠤⠄⠀⢠⣁⠀⠀⠀⠀⠀⠔⠒⠒⠂⠤⠤⠒⠉⢀⠤⠄⠀⢀⠇
⠀⠀⠀⠀⠀⠾⢦⡄⣀⣀⣤⣴⣂⣀⣀⡤⠤⡤⡸⠻⠀⠀⠀⠀⠀⠚⠒⠒⠀⠔⠒⠒⠊⠓⠉⢊⠉⡇
⠀⠀⠀⠀⠀⢘⢤⢨⠀⠙⠉⠉⢉⠁⢀⠉⡈⢀⠀⡆⠀⠀⠀⠀⠀⠈⠄⢆⢰⠀⡄⣄⢰⠀⡇⡘⡘
⠀⠀⠀⠀⠀⠈⡘⠘⠀⠰⠀⠀⢸⠀⠈⢀⠃⠘⢰⠀⠀⠀⠀⠀⠀⠀⠘⠘⠘⠀⠇⠻⠈⠠⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠤⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠈⠢⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⡡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢓⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⣈⠂⠀⠀⠊⣢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠲⠀⠀⠁⠉⠉⠀⠥⡀
⠀⠀⠀⠀⠀⠀⡇⠸⡉⠒⡒⠤⢤⣉⠒⠒⢉⣀⣰⠀⠀⠀⠀⠀⠀⡄⢘⠦⣀⡀⠀⠐⠤⢀⠠⠔⠁⢄
⠀⠀⠀⠀⠀⢠⡯⣁⣈⣓⢌⣓⣦⣠⢕⡢⢤⡠⠠⡅⠀⠀⠀⠀⢀⠣⣈⠢⡀⠤⡉⠑⠢⢄⠀⠐⠐⠂⣀
⠀⠀⠀⠀⠀⠈⡄⢠⠀⡄⢁⠀⠀⠀⡄⢀⠀⡰⢀⠃⠀⠀⠀⠀⠟⠶⣤⣤⣬⣀⣈⢭⣤⣤⡬⣤⠶⠞⡙
⠀⠀⠀⠀⠀⠀⠘⡌⠇⢳⠈⡇⢸⠀⡇⣸⠀⠇⠎⠀⠀⠀⠀⠀⢨⢀⢨⠀⡉⢈⠀⢩⠀⠀⠀⡄⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠈⠘⠀⠇⠘⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡘⠘⠀⠡⠈⠀⠘⠀⠇⢰⠁⠎⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠠⠤⠤⠤⠤⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠔⠁

⠀⢠⠄⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⠠⡂⠀⢠⠄⠀⠀⡀⠤⡄⠠⠄⡀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⢠⠀⣀⣀⢀⡀⣀⡀
⠀⡔⠃⢀⠌⡑⠄⠀⡈⠆⡀⢠⢲⠐⠃⠀⢘⣃⡄⠰⠈⠁⣾⠈⣰⠃⢄⠀⣿⢁⡽⣈⠇⢨⡇⣯⡋⣿⡇⡠⠂⠐⢄⡀⠤⢌⡀⠥⠄⣀⠄⠀⠠
⠀⢐⠀⠀⢈⢌⡄⠈⡥⠔⢀⠸⠐⠚⠀⠘⠌⢤⠠⢀⠬⡲⠍⠹⣤⡀⠤⠁⠻⠿⠿⣿⣿⡿⠿⠿⠿⠛⠀⠃⠰⢤⠸⢁⣰⡀⠑⣠⣀⠙⠀⣦⡄
⠀⠢⠸⢀⠂⠈⢥⠢⣒⢐⠈⠀⢘⠌⠊⠐⠤⠄⠊⠀⢨⡄⠃⢀⠘⠁⠀⡰⢄⢀⠀⠀⠛⠁⡘⡂⠀⢠⠄⠡⢈⣁⠠⠈⠒⢁⡌⠓⠉⡰⢀⣉⡁
⠀⠀⢀⠶⠀⡀⠤⢀⠀⠠⡢⠠⢊⢍⠢⠀⠀⢐⡄⠀⠉⡀⢀⠃⢀⠔⠈⠁⠁⠀⢰⠀⠀⢠⢜⠦⠀⢠⣜⠀⠀⠁⠀⠈⠒⠁⠈⠑⠋⠀⠈⠁
⠀⠔⠱⢆⠈⠁⠆⡐⡠⢒⣓⢔⠀⢡⠄⡇⡠⢚⠢⡀⠀⠀⠀⠀⣻⡈⠀⠤⠈⠀⢈⠓⢠⢸⠀⢸⠀⡧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢄⠃⠂⠄⠐⡰⠀⠅⣉⣈⢈⠘⠀⠊⠀⠰⠀⡰⠀⠰⠒⡂⠪⣈⠒⠒⢐⣀⠩⠄⠐⠁⢸⠀⢸⠀⢃⢈⡇⠠⠰⢆⠀⠸⠝⠀⠀⢉⠟⢄
⠀⠀⠈⠁⠀⠀⠀⢀⡂⠥⠥⠮⠀⠉⡝⠀⠂⠤⠄⠁⠀⠱⠁⠀⠀⠀⠀⣀⢸⡆⠄⠀⠀⠘⠂⠊⠀⣆⠠⠅⠀⠀⠁⠠⠀⠠⠀⠀⡖⡀⠈⠄
⢀⠄⠀⠠⡄⡀⠊⠀⣈⡢⠐⢙⠗⢖⠒⢒⠶⠒⠒⠒⠶⠒⠐⡲⠫⡀⠀⡄⠈⠁⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡄⠀⢠⠀⠀⠸⠁⢁⠂⡈⠄
⢘⣠⣤⣤⢸⠙⡀⣾⣿⣿⠁⠀⠀⠈⢧⠎⡀⠐⢄⠌⠀⠙⠴⠃⠀⠀⠲⠀⠀⡂⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡐⠈⠑⠈⢱⠀⡇⣀⢀⠁⠀⠸
⠈⣿⣿⣿⠏⠀⠈⠚⠛⠫⣇⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢀⠠⠤⢐⠶⠒⠶⠤⢤⣀⠐⡀⠀⠀⠀⡸⠉⠀⠂⠱⣑⠀⡀⡄⠀⠀⠀⠀⢀
⠀⠈⢩⠉⠀⠀⠀⢀⠄⠀⢈⠷⡠⢀⣀⣸⢄⣀⠀⠀⠀⢠⡇⠀⠀⠀⠐⢠⠀⡄⢈⠀⢗⡈⠲⠒⠊⠀⠀⠀⠀⠀⠳⡀⠐⠁⠀⠄⠀⠘⠋
⠀⡀⢼⠤⡀⠀⠠⠃⠀⠁⡌⠈⠀⡁⠀⠈⠀⠀⢘⠀⠀⡖⠀⠰⠒⠐⠔⠠⠂⡇⢨⠀⠁⠂⠀⠀⡄⠀⠀⢀⠜⠀⠀⠑⠀⠀⠀⢄⠸⠄⠀⡠
⠀⠀⠈⠀⡀⡀⢨⠀⠀⠀⣨⠀⡎⠐⡠⡀⠀⠀⠔⢱⠀⠳⠀⢂⠀⢁⢀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠋⠈⢀⠒⠐⢂⠀⠀⠀⠂⠐⢄⠈⢄⡀
⠠⠤⠀⢰⠻⡀⠐⡄⠀⠀⡖⢀⣃⠋⠀⠂⠐⠂⢈⢘⠀⠈⠖⡔⠀⠀⠉⠈⠁⠀⠉⣄⠖⠀⢀⠀⠀⣀⣀⣘⠁⠀⠉⣄⣀⣀⠂⠀⢀⣀⡀⠁⡀
⠀⠆⢀⠋⠀⠱⠀⠡⢀⢀⠃⢎⠣⢌⡀⠀⠀⣀⠠⢜⡁⠀⠀⠈⠀⠓⠐⠒⠒⣉⣀⠀⠀⠀⠟⠂⠘⢿⡟⠁⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠐
⠀⠀⡞⠀⠀⠀⢣⠀⠉⠀⣀⣠⣁⠀⡔⠀⠀⠒⠐⢉⡀⢤⡔⢀⠀⠀⢀⠐⠨⠂⢀⠄⣉⢀⣠⡀⠀⡊⡅⠐⠀⠀⠐⠀⢸⠢⠀⠔⠒⠉⠉⣉⠢
⠀⢸⡀⡀⢀⡀⡀⡇⠀⣸⠀⠈⠁⠈⠋⢁⠀⠀⣠⠊⠄⠐⢀⢀⡀⡀⠐⡮⠥⣐⡥⠊⠀⠈⠚⠡⠀⠀⠁⣀⠀⠀⢀⣠⠁⠀⢠⡀⠙⠁⡂⠡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡄⠂⡂⡂⢨⠀⡰⠃⠀⠀⠂⣈⠜⠃⠀⠀⠡⠀⠀⢃⠀⢀⠄⠀⢖⠦⠀⣨⣀⣽⣼⣧⣠⡇⠀⠀⠁⠂⠀⠐⠀⠁
⠀⠀⠀⠘⠻⢃⡀⠀⠐⠦⠘⠐⡀⠂⠀⡈⠸⣥⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠑⠂⠬⠔⠁⠰⡷⢀⣀⣀⣈⣉⢙⣛⡋⠉⠁⢀⣀⡀⠀⣀⠠⢿⠂
⠀⣴⠋⢲⡶⣃⡱⢀⠀⠀⢀⢀⠀⠀⠀⢀⡀⠀⠀⠀⡸⠖⠉⠉⣣⡴⠒⠒⠀⠀⠀⠠⠀⠀⠁⢀⠇⠀⠞⠈⠀⠀⡅⡏⢉⠉⠈
⠀⡖⠝⠋⠉⣑⢡⠨⠁⢂⠀⡀⠀⠀⠰⡈⠈⠐⠀⢨⣑⠢⠤⢀⣀⠇⡀⠀⢠⠀⠀⠀⠘⠄⠀⠘⠋⠑⠇⠰⠐⠠⠃⠷⠛⠦⠀⠖⠀⠒
⠀⣀⠀⠨⠁⠀⠠⢨⠀⣠⣀⠀⠀⢀⠀⢓⢵⠃⠀⠀⢀⡀⠐⠀⠞⡰⠙⡄⠈⢱⠀⠀⡀⠀⢤⠀⢤⠀⡤⠀⠀⢀⢀⠀⢀⢀⢠⢀⡤⠀⢀
⠀⠈⠢⢴⠀⠤⠒⠊⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢣⡈⠁⡜⠀⠘⡐⠓⠒⡺⠀⠀⡀⠀⢈⠃⢸⠐⠐⠂⠀⢨⠅⠀⣨⠌⠀⠂⠀⠀⡀
⠀⠔⠒⠂⠀⠀⠐⠂⠠⢠⠣⠀⠀⠀⠀⠀⠃⠇⠀⠣⠀⠀⠐⠀⠀⠀⢙⠀⠀⡄⠀⠀⠀⢀⠈⠀⠀⠀⡀⠈⡀⣉⢀⡀⢁⠀⠈⠁⣀⡀⢀⡀⣀
⠀⠀⠀⠸⠉⠇⠀⡠⢀⠀⠀⠁⠀⠀⡄⠀⢀⣀⢀⣀⣀⣀⣀⣀⢬⠼⢆⢢⡰⠀⠀⢨⠀⡀⠀⢀⡃⡇⠀⠘⠁⢘⠂⢰⠀⠈⠂⠠⠡⠄⠀⡂⠁
⠀⠓⠀⠀⠀⠀⠀⠋⠀⠈⠒⠀⠈⠉⠀⠀⠘⠀⠈⠒⠒⠒⠒⠒⠒⠐⠀⠀⠀⠀⠉⠀⠁⠘⠁⠙⠀⠃⠀⠃⠀⠈⠀⠈⠈⠈⠁⠀⠀⠈⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣆⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣄⠹⣿⣿⣿⣿⣆⠹⣷⡄
⠀⠀⠀⠀⠀⢰⣿⣿⣷⡈⠻⣿⣿⣿⣦⠙⣿⣄
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⠈⠛⠉⠀⣀⡀⠈⠣⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢋⡤⠒⠉⠁⠀⠀⠉⢐⣛⠲⠖⢊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⠴⠒⠈⡽⠦⠄⠏⠑⢏⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢰⣿⠀⠀⠀⠁⣀⡄⠀⢚⠞⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠹⠷⠀⠀⠀⠀⠀⢀⡤⠤⣄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣶⣧⠀⡀⠀⠐⠯⠀⠀⢘⣼⣅⣀⡀
⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣌⠓⠆⣤⣤⡖⠙⢿⣿⣿⣿⣶⣤⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⢻⣿⣿⣃⣀⡿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⢹⣿⣿⣿⣿⣿⣿⣟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡧⠷⢾⣿⣿⢻⣷⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠈⣿⣿⣿⣿⣿⠿⠿⣁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠘⠚⡛⢿⣿⠟⠬⢽⣿⡏⠀⠀⠉⠉⢿⣿⣿⣿⣿
⠀⢹⣿⣿⡫⠀⠀⠀⠈⢹⡞⣱⢠⣿⣿⣿⣿⣿⣿⠋⠉⣥⢩⡄⣽⡀⣒⣀⣿⡁⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠉⠉⣇⠀⠀⠀⠀⣀⡏⠁⣼⣿⣿⣿⣿⠟⠉⠉⢉⣁⣨⡭⣿⠄⠀⠤⣽⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠲⠖⠐⠚⠉⠁⣼⣿⣿⣿⠟⣃⢈⠓⠒⠒⠀⢈⡁⣿⣈⣉⠋⣿⣀⢔⠉⠀⠈⠀⢙⢮⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠈⠣⣤⠄⠀⠉⠃⣙⢶⡗⠀⠐⣺⠧⣴⠋⠀⠀⠀⠀⠀⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠈⠛⠦⣭⣉⣻⣾⣂⣠⠞⠁⠀⠘⠢⣀⠄⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣇⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⢚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⡀⠀⠀⠀⠀⢱⡀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠔⠘⡇⠀⠀⠀⠀⠀⠳⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠦⠤⣤⣀⣀⣳⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠠⣤⣤⢴⣧⡤⡤⠤⠴⠤⠤⠤⢷⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠿⢷⣶⣦⣄⡀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⣿⣿⣶⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠓⠲⠶⠶⠶⡏⣀⣀⣠⣴⣇⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣔⠿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠷⠬⠝⠖⠃⠀⢀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠉⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⢀⣀⡀⡀⠀⠀⠀⠀⢰⡆⢰⡆⢲⡆⢺⡇⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⢹⡿⣷⣶⡿⢻⣿⡟⣿⠁⠀⠀⠀⠀⠀⠸⣷⢸⡇⢸⡇⣾⠁⣿⠀⠀⠀⠀⠘⠛⠿⠛⠻⡿⠟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⢸⡇⣿⢠⡿⠀⠀⠀⠀⢰⣦⣀⣠⣤⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⣄⣇⣸⡇⣿⣸⠇⠀⠀⠀⠀⠀⠛⠻⠛⠻⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠁⣠⣬⣍⠀⠃⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⣹⡿⠿⣿⣯⣀⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⣿⣷⡿⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⣿⠉⣿⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠥⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⡧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠙⢆⠀⠀⠀⠀⠀⡄⠀⠀⠰⠀⠈⢀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈⠀⠀⠀⡐⠀⠀⠠⠄⠀⠀⠀⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⣀⠁⠀⠀⠀⠀⢀⡀⠄⢀⣀⠤⢀⣀⠤⣀⠀⠀⠀⠐⢄⠄⠐⠄⠠⡀⠲⠄⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡏⣹⣿⢻⣿⠀⠀⠀⠀⠀⠛⠃⠀⠘⠋⠀⠙⠛⠀⠛⡃⠀⠀⠀⠀⠐⣿⠀⢸⣿⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣷⣿⣧⣬⡟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⠀⠸⠿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⠌⠙⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠆⠞⢤⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠙⢂⢀⡖⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠡⠀⠁⠀⠀⠀⢀⣀⡀⢄⠠⠤⡠⣤⠒⠲⡖⠂⣼⡃⢠⢤⠆⠤⣤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡁⢮⡽⣽⠵⣈⡓⢡⢶⢑⢇⡈⠊⠱⢎⢒⣃⠮⢜⣛⡍⠌⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠀⠀⢡⠀⣴⣡⠇⣈⡗⢡⠲⠑⠮⢟⡃⡰⡗⢿⡺⢈⡛⠧⠊⢰⢢⠓⡧⡀⢎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠆⠀⠀⠀⠡⣇⡤⡘⠒⡡⡑⠃⡐⡲⢧⡫⡈⡗⢄⠤⠘⣬⢲⢢⠈⣚⠀⣉⠚⡠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⡌⢱⠉⡉⡚⢠⢻⢡⢴⢭⠋⢫⡁⣚⠦⢝⡡⡯⠮⠼⢦⢠⣄⡭⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⢀⠂⠀⠀⠄⠙⢹⠀⣶⢥⡇⢸⡼⡁⢸⠀⠈⠑⠁⠀⠘⣬⠃⡶⢫⣸⢸⢸⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡠⠁⠀⠀⡐⠀⠀⢸⡄⠈⠉⠀⢸⠋⢯⣿⠀⠀⠀⠀⠀⠀⠉⠒⠁⢸⡐⢸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡠⠈⠀⠀⠀⡐⠀⠀⠀⠀⢣⡀⠀⠀⢸⠸⣵⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⡀⠈⢣⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡠⠀⠁⠀⠀⡀⠔⠈⠀⠀⠈⠶⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠠⠄⠂⢁⡀⠀⠐⠀⠁⠀⠀⠀⠀⢀⠠⠘⢷⠐⠲⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣖⡐⠂⠀⠉⠀⠀⠀⠀⢀⡀⠠⠀⠂⠈⠀⢀⠠⠘⠀⢈⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠠⠀⠀⠀⡀⠀⠀⢀⠄⠦⠴⠊⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠀⠀⣠⣿⣿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⡀⠀⠀⠀⢀⡀⠄⡁⠛⠉⠀⠉⠢⡀
⠀⠀⠀⠀⠀⣰⠃⡠⠄⣉⠉⠀⠐⠀⢀⠀⠈⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⢠⠄⠀⠀⠀⢨⡁⠈⡁⠀⠘⢿⠂⢠⡇
⠀⠀⠀⠀⠀⠑⠀⠒⡾⠁⠀⠀⣀⠄⠘⠓⠂⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠸⠋⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠸⡀⢦⣴⡾⠁⠀⢀⠌
⠀⠀⠀⠀⠀⢠⠏⠀⠠⠂⠀⠀⠀⢟⠀⠠⠀⠄⣠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠄⡀⠉⣢⡄⡀⠀⣼⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣠⠛⠀⠀⢀⠠⠀⢀⠄⢚⠤⠀⠂⡀⠀⠀⠀⠄⠲⠀⠀⠃⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠂⣄⢸⣶⣿⣿⣷⣤⣾⣿⣿⡿⠻⣿⣿⣿
⠀⠀⠀⣰⠃⠀⢠⡼⠋⠘⠀⠄⠀⠈⠃⠀⠌⠄⠈⠀⢀⡤⠴⠒⠀⠈⠃⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣿⣿⣿⣿⣿⣿⠏⢉⠒⢾⣿⡿⠃
⠀⠀⢠⠏⠀⢀⡝⠀⡀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠁⢁⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠀⠚⠉⠉⠙⠿⣇⣩⣮⣴⡄
⠀⠀⡎⡀⢠⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⢉⠵⠷⠶⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⠉⡑
⠀⣴⠟⠁⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠛⠛⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠃⠀⠀⡀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡀⢀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠋⣁⣵⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣶⠿⢛⠉⠐⣨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡴⠃⢠⣤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡬⢔⣮⣵⡄⠀⠁⢠⠈⢆⠀⢀⡀⠀⠀⠀⠀⠀⢈⠇⠀⠨⠣⣀
⠀⠀⠀⠀⠀⠘⢷⣀⠀⠛⠁⠀⠀⠂⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠛⠻⠃⠀⠀⠀⠀⠀⠎⢠⠷⠀⠀⠀⠀⡀⠉⠀⠉⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠈⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢳⡙⠤⠁⠀⠀⠀⠐⠂⠀⡂⠈⠑⢌⠀⡰⠂⠄⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⣀⠀⠀⡀⠐⣁⡀⠀⠀⢨⡇⣶⣤⣤⡆⠀⠀⠔⠀⣀⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡷⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣼⣦⡀⠘⠀⠁⠀⠀⣼⠀⠈⠀⢠⢀⣨⠄⢀⣾⣭⣭⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠩⣭⠅⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢻⡀⢨⣤⠈⠁⠀⠀⠀⢤⠴⠞⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢄⠀⠠⠤⠀⣽⠁⣾⣏⡏⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠛⠉⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⢰⡙⠛⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠁⢊⠀⠀⠀⠁⠀⠀⢀⣿⢹⡏⣹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠇⠘⣦⠀⡀⠶⠷⣥⣾⠖⠛⠁⠀⠀⠀⠀⠀⠀⢀⣸⣥⡤⠂⠹⣤⠴⠤⠀⠀⠀⠀⠀⠀⠀⢠⡴⡴⠂⠀⠀⠱⠴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠈⠁

⣿⣿⠿⡟⠛⠛⠻⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⡟⠛⠛⢻⠿⣿
⣿⣧⠖⡆⠀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠰⠤⠀⢰⠲⣼
⣿⣿⣤⠖⠲⣄⠀⢠⣴⣶⣦⣤⣤⣤⣤⣤⣴⣦⣤⣴⠶⠛⠛⠶⠬⠥⢄⣀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣥⣿
⣿⠉⣂⠐⠶⠃⠀⡸⠛⠛⠻⣿⣿⡟⠋⠅⠀⠀⠀⠀⠀⠀⠰⠙⢲⣦⡴⠀⠀⠀⠀⠀⠀⠀⠘⠶⠂⣐⠉
⣿⣼⡥⣤⡀⠀⠀⠀⠀⠀⠀⡏⡿⠀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢬⣧
⣿⠋⠠⠜⠃⠀⠀⠀⠀⠀⢠⡏⣿⠈⠀⠀⠀⠸⠿⠂⣠⣼⠿⣷⠘⡇⡇⢀⣿⣦⢄⠀⠀⠀⠀⠈⠣⠄⠙
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⠀⣤⣀⣄⡑⣶⡞⣿⡇⠀⠋⠸⡇⣷⠟⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⣿⠙⣿⡏⡇⢻⣧⣀⣠⢾⣷⡿⣷⣦⣀⠀⠀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣷⣿⠀⠁⣧⡇⠀⠙⠛⠋⡸⣿⡃⠈⠙⠿⢷⣤⡼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⣼⣿⣀⡴⠻⠛⠚⢁⡀⠉⠀⠈⣩⣷⣶⣦⡄
⣿⠀⠀⠀⠀⠀⠀⢠⣄⣀⣈⣀⣀⣊⣠⡄⢡⣀⣀⣴⠞⡵⡎⣑⡲⢟⣿⣿⣿⣿⠃
⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⠿⡇⠀⣿⣿⣴⣀⣳⣣⢷⣁⢆⡽⣿⣿⡏
⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⡇⢀⡀⠁⠐⠛⠛⠛⠉⢀⣈⣐⠒⠉⠀⣌⠉⢀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠈⣿⣾⣧⢀⣴⡾⣷⡆⢀⣤⣭⡛⠺⡿⠟⠛⠉⠑
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⡇⡄⠛⢸⢻⡴⠟⠁⠀⣀⣏⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⢻⡗⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣷⡇⠀⢨⢸⠀⠀⡇⣼⡁⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟
⣿⣀⠧⡀⠀⠀⠀⠀⠀⢀⣾⣿⣄⠚⠉⠛⠂⠈⠛⠛⠋⠀⠈⠛⠉⠉⠴⠻⢧⡤⠀⠀⠀⠀⠀⠀⢀⠼⣀
⣿⠙⢳⡄⠀⠀⠀⠀⠈⠉⠉⠁⢉⢁⢀⢀⢀⠀⡀⢀⠀⠀⠀⢀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⣿⢏⠻⣇⡠⢤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡤⢄⣸⠟⡹
⣿⣶⣽⣮⣭⣍⣵⣶⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣮⣭⣭⣥⣯⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠲⡦⠀⠀⠂⠤⠠⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠄⠀⠀⠀⠀⢦⣤⡶⠆
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠁⠀⡀⢢⡢⠀⠈⠀⢠⡀⠀⠾⠓⠆⠀⢰⠸⠁⠀⠀⡀⠀⠀⠀⢀⠰⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣅⠀⠀⠀⠀⢁⡼⠀⠁⣼⠁⠀⠀⠀⠄⢷⣄⠀⠀⣀⣴⡟⠀⠀⢠⠜⠁⠀⠀⠀⠀⠊⠀⠀⠀⡄⡘⠀⠀⠀⢀⠠⠘
⠀⢀⠠⠆⠀⠀⠀⢀⡷⡤⢠⣈⡀⠒⠖⠒⠛⠀⠀⢠⠇⢠⠀⠀⠆⠘⠢⡉⠙⠛⠛⠉⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣧⡇⠀⢀⢀
⠀⡁⠀⠀⠈⠄⢀⣤⣠⣴⣾⣿⡿⠒⠀⠀⠀⠀⠀⡾⠀⠈⠀⠀⠀⠀⠦⠀⠱⡖⡲⠲⣶⠂⡀⠀⠀⠀⠀⠀⡙⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠣⠄
⠀⠁⠤⠤⠞⠀⠸⣿⠿⠿⠛⢉⠑⠁⠀⠠⠆⢠⡄⢠⡄⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⢀⠉⠀⠲⡀⢠⡀⠀⠀⣓⡀⠀⠁⠀⠀⠀⠀⠀⠸⠀⠘⣧⠀⢻
⠀⢀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠦⡀⠀⢐⠎⠁⠀⡈⠀⠀⠀⠀⠠⠬⠐⠀⠀⢠⡀⣤⡀⠀⠀⠀⣄⡁
⠢⠈⠥⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣄⣀⠀⠃⠀⠀⠀⡀⠀⠰⠞⠒⣆⠳⡄⠀⠀⠀⡠⠄⣤⡀⠀⠀⠀⡛⠀⠀⣞⠸⡃⠕⢸
⠀⠃⠀⡼⠻⣦⠀⠀⠀⠀⢂⠲⠙⠶⠠⠁⠉⠀⡀⠀⠠⠀⠀⢂⠀⠀⠀⠈⢧⠙⠆⢠⠊⠀⠀⣿⠇⠀⣤⣤⠀⠀⠀⢰⠀⠁⠈⢨⠀⢀⠄⠀⠀⠃
⠀⠀⠰⠛⡁⠘⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠠⠄⠀⠀⠈⠓⠒⠃⠀⠀⢠⡿⠀⠀⣉⣉⡇⠀⠀⠐⠄⡣⣠⠞⠀⠘⠀⠠
⠀⠀⠀⠀⠤⠄⢧⠀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠂⠀⠀⠀⢤⢨⠄⢲⢚⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⣤⠄⠀⠄⠀⠀⠀⠀⠄⢁⣲⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠂⡀⠀⢸⢐⠀⡠⠴⡕⢾⡄⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋
⠀⠀⠐⠀⠀⠀⠀⠙⠓⠛⠀⠀⢂⠀⠀⠀⠀⠀⠘⠧⠀⠘⢨⠈⠳⠊⢀⣸⠃⢀⠆⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠐
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⣟⠋⠁⠀⠂⠀⢀⡿⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠰⣶⣶⣴⣶⡦
⠀⢠⡄⠘⠃⠀⠀⠰⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣽⠀⢠⡃⠀⣠⡾⠁⠀⠀⠀⢀⡀⠁⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⡆⠀⢀⡀
⠀⠈⣗⣄⠀⠀⠀⠀⢫⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠀⣠⣄⠓⠒⠋⠀⠀⠁⠚⠛⠁⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠘⠒⠒⠒⠚⠀⠟⢻⣿⣿⣦
⠀⠀⢋⡈⣳⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⡎⠙⠏⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠤⠄⠀⠀⠋⠈⠉⡀
⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⢰⣲⠆⢠⠀⠐⢶⣯⠈⠛⠁⢀⣀⠄⠀⠤⠚⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢃⠀⠀⠀⠠⠂⠁⠢⠀⠀⠀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠈⠙⠀⠘⠉⡀⠈⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⣫⡇⠀⠃⠀⠀⣠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣀⢀⣀⡀⠀⣶⣖⠄⠐⠒⠂⠈⣁⠠⠼⠀⠀⠄⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠂⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠠⠂⡀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⣠⡀⠀⠀⢀⠄⠒⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠂⠄⠀⠐⠚⠙⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠘⣀⡀⠀⠀⠈⢀
⠀⠉⢁⠰⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠠⠂⠀⣸⣷⠟⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣷⣿⠀⠀⠸⣭⣡⠴⣼⠁
⠀⠉⠀⠊⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠠⠤⣤⠄⣄⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡏
⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠆⢰⠀⠀⢠⣋⡴⠃⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⣠⢲⢓⢀⡀⠀⠀⠴
⠈⢠⣴⣦⡀⠀⠀⠀⠀⠂⢀⡀⠒⠂⠉⢁⡀⠀⠀⠀⠈⠀⠀⢢⡄⠀⠀⠄⢀⠀⠘⡄⠀⠀⢠⠃⢰⠆⢀⠔⠲⠀⠀⠀⢹⢀⢂⠀⠃⠀⠀⠀⠀⠡
⠀⠘⣏⣼⠇⠀⠐⠠⠄⠂⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠘⢢⠀⠉⠀⠄⠁⠈⠀⠘⠇⠀⠀⠁⠀⣤⡶⢾⡿⠿⢿⠀⠀⠰⠒⠣⠼⠃⠠⠶⠤⣤⣤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠤⠤⠚⠁⢴⡒⢪⣹⡇⠀⠀⠀⠀⠀⠠⠜⠀⠲⢿⡟⠀⠀⠀⠘⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⢘⠖⠲⠘⠳⠚
⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠠⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⢁⠀⠂⠐⠁⣠⠦⠀⠐⠀⠀⠀⠀⣧⠀⠀⠇⢀⣟⢟⠣⠀⠀⠀⠁⢀⠀⠐⡂
⠀⠈⠈⠁⠀⠠⠂⠚⠉⠀⠀⠀⠀⠀⠀⠬⠱⠤⢀⠀⠀⡠⣦⠀⠀⠘⠀⠈⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⢀⣨⡤⡄⠒⠀⢀⡀
⠀⠀⠀⠀⢀⣤⠤⠀⠐⢠⠀⠀⠀⡄⠀⠀⠏⠊⣹⢇⢼⠉⢉⡇⠀⠀⠉⠁⢠⣶⣶⠀⠀⠩⣤⡤⣧⠀⠀⠠⠀⠀⠈⠑⠠⠆⡰⠔⠃⠀⠻⣿⣾⣿
⠀⠀⠀⠀⠈⢿⡀⠀⡠⠋⠀⠀⠀⠀⠈⠀⠀⠀⠍⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢄⣁⠤⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣁⣴⣁⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢛⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡢⢔⡪⠋⡇⠀⡎⠆⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⡡⠊⠁⡠⠌⠀⡠⠃⡆⢀⡿⢟⠶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣊⠡⠭⠴⠶⢮⣤⡤⣮⠥⠼⠐⢡⠃⡠⠀⡇⢡⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣾⢂⠥⠒⠀⠉⣉⣀⣀⡀⠀⠀⠤⠄⢊⠥⠊⢀⠜⡠⢣⠈⠦
⠀⠀⠀⠀⠀⠀⠀⡆⠬⠺⢿⣓⠴⠦⠍⣐⠶⠤⠀⢀⡤⠤⠖⣊⠴⠖⠚⣓⠾⠛⡡⠊⢀⢷
⠀⠀⠀⠀⠀⠀⠀⡥⠍⠑⠐⢒⣈⡉⠥⢐⣒⡈⠭⠐⠒⠉⣁⠠⠔⠒⣉⠤⠒⢉⡠⠒⡡⣪
⠀⠀⠀⠀⠀⠀⠠⠕⠆⢡⠍⠀⠒⠈⣉⡀⠤⠤⠐⢂⣉⠡⠤⠒⣊⠩⠄⣒⣩⠤⠶⠛⠈⠀⠉⠢
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠉⠉⠙⠀⠐⠒⠒⠛⠃⠠⠒⠒⠙⠓⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡴
⠀⠀⠀⠀⠀⠀⢿⠈⠏⠀⢲⠂⠲⡖⠀⣤⠀⢤⠄⢤⠄⠠⡤⠠⡤⠰⡔⠐⠖⠀⠺⠁⠈⠁⢰⠇
⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⢸⠀⠀⡄⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⡇⠀⠃⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡇⠀⡇⠀⠇⠀⡇⠀⡆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⢁⠀⢠⠀⠀⠀⢀⠀⠸⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⡇⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⠀⢨⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠬⣀⣸⡀⣀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⣇⣀⡅⠼⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠰⢶⡤⠀⣤⡄⣤⠀⠐⣠⣀⠤⣄⣀⠤⠀⠄⠀⠤⠤⡤⢤⠠⠤⠄⣶⣄⣢⣴⢄⣰⡖⠶⠶⠒⠒⠒⢒⣲⣶⣶⡶⢶⣶⠶
⠈⡈⡡⠀⠠⠁⠢⠄⠜⣠⠴⢫⠥⡀⠉⠺⣩⢈⢳⣃⠜⡀⠀⠀⠈⠋⠁⠐⠚⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢰⠟⠻⠋⣴
⠀⡤⣠⠒⠉⠉⠉⠓⢤⠁⠈⠉⠁⢣⡀⠈⠐⠀⡰⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠍⣩
⠀⢧⠃⠀⠀⠀⠀⠀⢘⡦⡀⠀⠀⢀⠉⠒⠒⠎⠑⠁⠀⠀⠀⢨⢧⢻⢀⡈⢰⢴⡧⠇⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⢋⡏⣿
⠀⡿⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⢠⣶⢰⠉⡎⠀⢸⠁⠀⠀⠀⢀⣀⡀⠀⢀⡘⠒⢹
⠈⡇⠂⠀⠀⠀⠀⡼⠁⡰⢳⠀⠀⡸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣁⣁⡈⠉⠘⣀⣁⠀⠈⠀⠀⠀⠀⢎⠀⠈⢲⠋⢹⠀⢸
⠀⠞⠆⣄⣠⠴⠊⠀⡰⠃⡜⢀⠰⠁⠀⠀⠡⢦⠈⣷⣤⠀⡐⣶⠁⢹⣄⡀⠉⢃⢦⡑⡄⠀⠀⣠⠀⠬⢦⡀⠀⢀⠎⡀⠼
⠀⠀⡅⢺⠓⡤⠀⠔⠁⢠⢯⠏⠀⠀⠀⠀⠀⠋⢖⠡⡌⠀⡽⠊⢰⢸⡔⢽⠀⠸⢀⠃⡇⡹⠆⢸⣀⢀⠀⢙⠶⠊⢟⡬⠂
⠀⠈⡢⠸⣄⠀⠀⠀⢠⠓⠋⠀⠀⠀⠀⠀⣄⠗⡨⢠⡇⠰⠇⠀⠼⠸⠗⠸⣀⡗⣋⠞⠸⢧⣾⣼⣾⢸⡀⠘⠄⣀⡠⢣⢷
⢸⡄⡠⠸⠈⠃⡶⠊⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣴⣏⠁⣠⣯⠎⠸⠆⠀⠀⠀⠀⢺
⠈⣿⠡⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠚⢁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠰⠚⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡳⠀⠠⠓⠀⠀⠀⠀⢸
⠀⣇⠂⡞⠛⠚⠶⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠙⡇⠀⡔⠀⠀⠀⠀⢰
⠰⣹⢰⡇⠀⠀⠀⠈⢳⡥⠦⣄⣠⠤⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡈⣿⠀⠘⠇⢠⢈⡆⠀⠘
⠀⠛⡉⠣⣎⣉⠭⢽⣾⠀⠀⣏⣀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣀⠈⣉⠀⢀⠠⢄⠀⢀⠤⡬⢀⠋
⠀⠈⠐⠀⡇⣏⠉⠉⠛⠓⣾⠓⠛⢷⠢⠬⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠘⠲⠃⢰⠤⣬⠂
⠀⠠⠐⠚⡛⣿⠀⠀⢀⠀⣿⠀⠀⠼⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢅⡂
⠀⠀⠀⠀⠁⡿⠀⠀⢸⠀⡏⠀⠀⠇⠀⣎⣩⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠛⠋⠭⠭⠭⠭⠭⠉⠛⠃⢈
⠀⠀⡆⠀⢠⡇⠀⠀⢈⢀⡇⠀⢸⠠⡄⠀⠀⣀⡈⠉⠛⠛⠒⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⣡
⠀⡀⢘⢾⠋⣇⠀⠀⠀⢸⠁⠀⣈⢀⠃⢰⢰⠃⠙⠉⠓⠄⠒⠑⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⢸⡁
⠀⠀⠜⠒⠢⠭⠿⢿⣿⠛⠒⣒⠉⠸⠤⠬⠥⠤⠤⠀⣀⣀⣀⣀⡧⣀⠀⣀⠀⠀⠀⠀⢜⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢣
⠠⠀⠚⢿⠥⡤⠤⡤⠶⠶⣶⢖⡟⠉⣓⠠⠼⠿⠷⠶⠶⠶⠶⢒⡠⡿⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠁⠊⠙⠈⠀⠈⠃⠃⠊⠘⠘⠲⠊⠘⠀⠀⠒⠋⠟⠙⠂⠓⠈⠀⠓⠖⠀⠀⠲⠒⠒⠒⠒⠈⠉⠉⠉⠉⠁⠒⠒⠂⠒⠋
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⢛⣛⣛⡉⣉⠙⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢩⣖⣦⣶⣆⢸⣿⠃⢹⡇⠸⢷⣿⠀⣿⠉⠉⠉⠛⣲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⣿⢸⡟⠁⠟⢻⠈⠋⠳⠈⠁⠒⢚⣁⣀⣯⣀⣀⣀⣘⠛⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⡶⠀⠀⣻⣄⣡⣤⡤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠙⠋⠀⣀⡴⠃⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠠⠀⡇⢨⡄⠀⣼⣡⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⡆⠀⠀⠀⣹⣶⢶⡖⢲⢶⡶⡾⢯⣹⡇⠀⠀⣸⡎
⠀⠀⠀⠀⠀⠀⢸⡇⣇⢸⡀⠀⠉⠁⠀⢠⣤⡤⢤⠤⣤⢲⣶⢿⡁⢹⣌⣿⠀⠀⠀⠿⠋⠈⢷⠇⠈⠻⠃⠀⠙⠃⢸⡇⣿⡇⢠⣤⡄
⠀⠀⣴⢒⠊⠉⠙⠋⠛⠙⢓⠒⢦⡀⠀⢸⣿⡇⢸⣧⣽⠸⣿⠾⡇⠀⠋⠈⠀⠀⠀⠀⢸⡇⠀⢰⣢⠀⠀⣴⣦⠀⢸⣧⠻⠇⠈⠛⠉
⠀⠀⡧⢀⣀⢉⣭⡉⣩⣅⢠⣤⡀⢻⠀⠈⠈⠀⠈⠀⡁⠀⠁⠀⠐⣦⣀⢿⣠⢿⠀⢰⢟⣧⠀⣰⠿⡀⠀⢸⣻⣦⠈⠿⠀⢠⣦⣀⡀⠻⠃
⠀⠀⢷⡟⢻⣿⣸⣇⣟⣻⡿⢹⡇⡿⠀⠀⠀⠀⣶⣾⡿⣰⠀⠀⠀⠹⡉⣂⡡⠼⠀⣯⣵⡿⠀⣿⠃⢷⡀⣾⣭⣼⠇⠀⠺⣼⢿⣻⠅
⠀⠀⣸⣗⠀⣤⠙⠿⣃⠉⢠⣌⣻⠧⣄⢠⡖⠒⢻⣿⡏⢉⣳⡄⠀⡶⣄⢠⢺⠂⠀⢀⡀⣀⠀⢙⡓⠛⠁⠀⠀⠀⠀⢀⣀⡙⠋⠁⣀⢀
⠀⢸⠁⠈⠉⠓⠒⠚⣉⠉⠉⠉⠀⠀⠘⡇⢳⠚⠹⣿⡏⠉⣹⠁⣤⣷⣿⣿⣾⣧⠀⡸⠖⢶⣉⡳⣆⡵⠀⡶⠉⢲⣤⠟⠁⢸⡆⠀⠻⠟
⠀⢸⣴⢶⣄⡞⣷⣼⢻⡆⣾⢻⢠⡟⣦⣿⢸⡀⠀⣿⡇⠀⡟⠀⢸⣏⠋⠋⣭⡏⠀⠁⠈⠁⢀⣉⡉⠀⠀⣷⡀⠀⠉⠀⠀⣼⠃⣶⣤⡤
⠀⠀⣏⠈⠿⠃⠻⡿⠈⠷⣏⠈⢿⡃⣸⡅⠀⠣⢀⠛⠓⠚⠁⠀⠈⣿⣀⣴⣉⡇⠀⠀⠀⣰⠋⠀⠙⣦⠀⠈⠙⠲⢤⣠⡼⠃⠀⠻⠟⠁
⠀⠀⢿⠺⡧⢮⡥⣬⢤⡴⠶⢋⣛⣬⠾⠃⠀⣼⢁⢹⣠⡖⢒⡄⠀⠈⠉⠉⠉⠀⢀⡴⠒⣿⠀⠀⠀⣿⠞⠉⣶⠀⠀⣽⠁⠀⢀⡤⠖⠂⢤
⠀⣠⡀⠉⠓⠒⠒⠒⠒⠛⠉⠉⠀⢠⣤⡀⢠⡬⠽⡿⠻⣿⠏⣤⢰⣿⣤⣶⠀⣤⠞⠳⣄⢿⠀⠀⢀⣟⣠⠤⣿⡁⠀⠙⢦⠀⡞
⠲⡋⠹⡃⢤⢤⣶⣶⡾⣹⠀⡤⣄⢨⣿⡁⠸⡇⠀⣇⢠⡧⠀⢼⢻⣿⣿⡅⣸⠃⠀⠀⢹⣮⠧⣴⠻⡿⠁⠀⠈⣿⠀⠀⣼⠀⡇⠀⠀⠀⢠
⠘⠛⠉⠁⠘⠚⠉⢁⡀⠀⣠⢿⡅⠺⠾⠇⠀⣇⠀⣿⢸⠇⣀⣿⣸⣿⣸⠇⢻⡀⠀⢀⣾⡏⠀⢸⣿⡇⠀⠀⢀⡿⠀⠴⠃⠀⣸⠶⠴⠒⠋
⢸⠖⢦⠀⠀⣠⠚⣵⠿⠀⢑⣛⣁⡔⢰⠀⠀⠈⠉⠉⠉⠉⠁⣀⣀⠀⠀⠀⠀⠙⢶⠋⣿⡄⠀⣸⡿⠙⣦⡴⢛⣀⣀⡀⠀⢠⡇⠀⣸⣷⣶
⠉⠻⠁⠐⢊⣲⠗⠁⣴⠰⣿⣌⠿⠃⠘⢡⣾⠀⠀⠀⢀⡴⠺⣅⡽⢦⡀⠀⠀⠀⠀⠀⠈⢳⣤⠟⠠⠀⡄⡴⠋⠀⠀⠈⢢⠈⢇⠈⠛⡽⠋
⠘⠃⣠⡤⣤⣁⣀⣀⡈⠙⠋⠀⠀⢀⠴⢭⠭⠵⢦⠀⢯⢌⣓⣉⣫⣭⡽⠀⣔⠀⠀⠡⣠⠀⡅⢀⠃⠜⠐⡇⠀⠀⠀⠀⣸⠇⢸⡆⢠⣤
⠀⠀⣿⠀⠖⠀⢀⣠⡾⣷⣀⠀⠀⡾⢉⢚⣩⢉⡹⣄⢸⢸⣻⢹⢸⣿⠃⠀⣾⡆⠀⠀⠈⢳⡁⢀⠎⠀⠀⢻⣄⣀⣀⡴⠋⢀⡼⠀⠙⠛⠁
⠀⠀⢻⣆⣤⡾⠛⢋⣠⠾⣹⠃⠈⣶⣦⡭⡶⣤⡖⡟⠀⠉⠛⠛⠛⠁⡔⠀⠉⠙⠒⢄⡀⠀⣿⠀⠀⠀⢠⠞⠋⠁⠀⠀⣶⡄⠀⣶⣤⠄
⠀⠀⠀⠉⣷⣤⠴⢛⡵⠚⢡⣄⡄⠹⢾⣷⣷⣿⠼⠁⡠⣠⣶⣄⠀⢺⡄⠀⠀⠀⡀⣠⡗⠀⣿⡀⠀⠀⠸⡀⠠⣿⣖⠀⣀⣠⡆⠘⠁
⠀⠀⠀⠘⠧⠔⠚⠉⠀⠀⢮⢿⠗⠀⠀⠀⠀⠀⠀⠀⣱⢺⡟⡞⠁⠀⠘⡏⡏⣿⣏⣿⠃⠐⠁⠀⠀⠀⢀⡇⠀⠁⠀⣠⣯⡀⡟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣁⣀⣀⣀⣷⣿⣟⣛⣛⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣈⣀⣈⣃⣀⣀⣀⣀
⣿⣿⠛⡻⢛⡛⠛⣟⢛⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⣭⠇⠀⠀⠀⠀⠀⠀⠀⠘⢍⡹⠃⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠧
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣺⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢒⠢⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢠⠾⠥⠭⣭⣉⡆⠀⠀⠀⠀⠚⠶⠆⠀⠀⠀⠀⠓⢤⣀⣧⡇⠀⡀⠀⠀⠀⠀⣠⠖⠒⠒⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢯⡉⢉⠐⠒⠒⠢⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢰⠁⠀⠀⣠⠤⠞⢧
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠜⠉⠁⢀⠤⠼⡆
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡏⠉⠉⢢⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠳⡤⠊⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇⠀⠀⢸⠁⠀⣰⣷⡀⠀⠸⣷⣀⣠⠼⠁⣀⡀⠀⠀⢻⣆⠀⠀⡜⠀⠀⠀⠀⠈⠲⢤⣀⣠⠏
⠀⠀⠀⢼⠉⠑⠖⠁⠈⡇⠀⠀⠀⣿⠋⠉⠉⡿⠀⢠⡿⠀⣧⠀⠀⣿⠉⠀⠀⣿⠉⠉⢳⡀⠀⢿⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠸⣽⡆
⠀⠀⠀⠈⢦⡀⠀⠀⣠⠃⠀⠀⢰⣿⠀⠀⠀⡇⢀⣿⠋⠉⠹⡄⠀⢿⡄⠀⠀⣿⠀⠀⣠⠇⠀⢈⡿⠀⠀⠀⠀⢏⠓⣹⠂⠀⠀⠈⡆
⠀⠀⣀⠀⠀⠙⠢⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠁⠸⠏⠀⠀⠀⢧⠀⠈⠁⠀⠀⣿⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣴⡏⠙⠳⡄⠀⠀⢸⡇⠀⢰⣾⠙⠳⡄⠈⠉⢹⡏⠁⢀⣀⠀⠀⡀⢸⡇⠀⠙⡄⠀⠀⠀⠀⢶⡄⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠀⣾⠃⠀⢸⣟⣀⠴⠃⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠸⣷⠀⠀⢹⠀⠀⣀⠀⠘⣷⡀⢠⠇⠀⠀⡇
⠀⠀⠤⣀⡄⠀⢸⣿⠉⠉⠲⡄⠀⣿⠀⠀⢸⡟⠳⣄⠀⠀⠀⣼⡇⠀⣼⡷⠦⢼⠇⠀⣿⠀⢀⡞⠀⣼⠟⡄⠀⠘⣧⡞⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠈⠉⠁⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⠿⠖⠋⠀⣼⠯⠤⡇⠀⠀⢹⡇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠻⠦⠖⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠻⠀⣠⡀⠀⠀⢴⠏⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣦
⠀⠀⠀⠀⠀⣠⡀⠀⣀⡁⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⡞⠳⠊⡆⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠀⠀⠀⡇⠙⡖⠦⣄⡀⠋⠀⠀⠖⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣸⣄⣧⠤⠔⢲⠀⠀⠘⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡀⡇⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⡭⠤⠔⠲⣚⣉⠽⡆⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠰⡶⠀⠀⠀⠀⢡⠀⢣⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠖⠒⠉⠉⠀⠀⣀⣱⡀
⠀⠀⣀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⠀⠀⡧⣤⢤⣖⣲⡭⠿⠽⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠴⠊⠀⠙⠦⣀⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⢟⠏⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠞⠿⠛⠛⠻⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡾⠟⠋⣁⡤⠴⠒⠚⠉⠉⠉⠒⠲⠦⣄⡉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣺⠗⠉⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⡞⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⣌⢣⡀
⠀⢀⠤⠤⣤⠤⠤⡶⠿⠥⠾⠋⠉⠓⠦⠴⠚⠉⠀⠈⠙⠢⠤⠚⠉⠀⠈⠙⠒⠤⠤⠖⠚⠉⠉⠓⠦⣤⠤⠒⠛⠲⢬⣣⣱⠤⠤⡄
⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⢸⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢀⢿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡀⠀⠀⠀⠀⠀⠀⠀⡰⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠶⠒⠃⠀⢠⡀⠀⠘⠳⠤⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⢸⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡾⠃⠀⠀⠀⠀⠀⢸
⠀⡜⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⡴⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡱⠀⣠⠤⢀⣀⣀⡠⣄⠀⠐⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣗⠦⠇⠀⠀⠀⠀⠀⠘⠦⠖⢃⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⢸⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡇⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠇⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢸⠀⡇⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠳⠼⣄⡀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠉⠓⠺⢤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣩⠔⠚⠓⠢⣍⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡥⠒⠉⢀⣠⣼⣦⣄⡀⠉⠲⢌⡙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⣈⠳⢤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⠴⢋⡠⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⣌⡙⠿⣿⣿⣿⡿⠟⢉⠤⠒⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠉⠒⠤⣉⣡⠔⠊⠁⠀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⣧⣠⣄⡀⠀⢸⠀⠀⠀⢠⠿⢄⡀⠙⠲⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⠀⠳⢄⡈⠑⡶⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⠃⢸⠀⠀⠀⠀⠀⣀⣘⠀⢁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢿⡿⣿⣶⣿⠿⣶⣄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⠟⠁⠀⢸⠀⠀⠀⢠⠛⢅⣉⠀⢸⠀⣿
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣛⣻⣿⡿⢟⣿⣻⢿⣿⣟⣿⡿⣷⣤⣀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⢄⡉⠀⠸⠀⣿⣶⣤⣄⡀
⠀⠀⠀⢰⣿⡿⣷⣾⣯⣿⣿⣯⡺⠿⠿⠿⢿⣪⣿⣿⣾⣟⣿⣿⢿⡆⠀⠉⠓⠦⣄⡀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿⣷⣿⣾⣿⣿⠿⠋⠁
⠀⠀⠀⢸⣿⣿⣷⣭⣻⢿⣭⣿⢿⣷⣾⣶⢿⣿⣭⣿⠿⣻⣽⣾⣿⣷⠀⠀⠀⠀⠀⠙⠳⢤⣸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⢸⡏⠻⣿⣿⣿⣷⣯⣛⠿⣿⣟⣻⡿⢟⣫⣷⣿⣿⡿⠿⠋⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡿⠟⠋⠁⠈⠁
⠀⠀⠀⠘⠳⣄⡀⠉⠙⠻⢿⣿⣿⣾⡍⣽⣾⣿⡿⠛⠁⠀⠀⣀⣤⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠙⠻⢿⣧⡿⠟⠁⠀⢀⣠⣴⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⢸⠀⣀⣤⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⠀⠐⠂⠀⠔⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠈⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⢄⡄⠀⠉⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠴⠀⠄⠈⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣉⢨⢁⣀⡀⠀⠘⠄⠀⠀⠀⠌⠀⠀⡃⡆⠀⠠⠀⠐⠀⢒
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣀⠀⠀⠂⣂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢁⠈⢔⢤⠀⠐
⠀⠀⠀⠀⠀⢁⡹⠈⠉⠁⠠⣹⠀⠀⠉⠀⠈⡀⣄⡀⠀⠀⢀⡨⢃⠇⡈⠛⠛⠀⠀⠁⠐⠊⠀⠠⡀⠆
⠀⠀⠈⠀⠀⢒⠀⣄⠀⠀⠀⠚⠀⠀⠀⠠⢚⠧⠀⠣⠤⠦⠔⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠅⠀⠁
⠀⠀⠀⠈⠀⠀⠡⠌⠄⠂⠁⠀⠀⠀⠄⠁⢠⡤⠟⠒⠀⠀⠀⠀⠀⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⠟⠉⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣾⣿⠻⡆⠘⢿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⡿⠋⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⢱⣿⠿⠁⠀⠁⠀⠀⠻⣿
⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢸⣿⣿⣿⣿⣇⣾⣿⣿⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⢠⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡿⣿⣎⣿⣿⣿⣾⣿⡟⣸⣿⣿⣿⣿⠃⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡟⠻⡟⠀⠀⠀⠀⠀⡀⣤⡀⠠
⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣴⠏⠀⠀⠠⠂⠀⢀⣤⣠⣴⠞⣽⣿⣿⡏⠀⣴⡇⠀⠀⠀⠀⠀⡇⢹⡇
⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢠⡿⠃⠀⠀⠀⣠⣴⣾⣿⣿⣿⣣⣾⣿⣿⣿⠀⣼⣿⣧⣤⠀⠀⠀⠀⠁⢸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡆⡀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡿⣧⠃⠀⠀⠀⠸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⣼⣿⣿⣿⡿⢨⣿⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣧⠟⠀⠀⠀⡀⠀⠁
⣿⣿⣿⣿⣿⣿⣻⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣯⣾⣿⣿⣿⣿⡟⠁⢸⡞⣿⣿⣿⣿⣧⠀⠀⢠⣇
⣿⣿⣟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠿⣿⠟⠀⣿⣿⣿⡿⣿⠛⣿⣧⡄⠀⢇⠈⠻⢿⡇⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡟⠀⣠⢿⣿⣿⣿⣿⠀⠈⠻⣷⡀⠘⠆⠀⢸⣷⡀⠘⠀⠀⢻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠇⠀⡇⠈⣿⣿⣿⢹⡆⠀⠀⠹⣧⠀⠀⠀⢸⣿⣷⡤⠀⠀⠈⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣾⣿⣯⠇⠀⠀⠀⠙⡆⠀⠀⠀⢿⣿⣧⣇⠀⠀⢹⡆
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⠃⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⠀⠀⠀⠀⢰⡄⠀⠀⠈⢻⡿⣿⡀⠀⢼⠁
⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠟⠁⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠳⠀⠀⠀⠘⣇⣿⣧⠀⢸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣾⣿⡟⢸⣷⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣷⣀⠀⣀⣤⣴⣄⣀⣤⣴⣿⣿⠀⠸⡇⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⡗⠀⠀⣿⠟⠿⠛⠛⠻⠿⠿⠛⠛⠛⠉⠁⠀⢸⣿⡟⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⠸⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣟⠋⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⢦⣀⣀⣀⣀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⣰⡌⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡟⣿⣿⣿⡿⣟⡿⠛
⣿⣿⣿⣿⣷⡜⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⢿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⠂⣠⣤⣾⣿⣿⣿⣿⣿⠇⠿⣿⠿⠚⠉
⣿⣿⣿⣿⣿⣿⣞⢷⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⡖
⣿⣿⣿⣿⣿⣿⣿⣯⠻⣆⠈⠛⠿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣉⣉⣭⣿⣿⣿⣿⣿⠿⠟⠫⠐⠋⠁⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣷⣦⡀⠀⠉⠲⠬⣝⣛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠹⡄⠈⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠠⠷⠂⠀⠘⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣄⠀⠀⠀⠀⠀⠀⣠⠏⢱⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠈⢓⣦⣤⡤⠶⠋⢁⡴⠋⠀⢈⡷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠚⠉⣉⣀⣤⠤⠴⠒⠋⠀⠀⠀⡼⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠖⠁⣀⡤⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢰⠏⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⢠⠎⠀⠀⣿⣤
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⡞⠁⢀⡤⠀⠀⠀⠀⢀⡀⠀⠐⠚⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠟⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⣠⠏⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⠞⣠⣿⣽⠁
⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣆⣇⡇⠀⢀⠞⠁⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⢀⣴⣧⣾⠏⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡜⢿⡿⠛⣷⢚⡥⡄⠀⣠⡀⠀⢀⣼⣁⣀⣀⣤⣤⡖⠲⣿⣿⠁⠀⡟⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣆⠀⢸⡁⠀⢹⠋⠁⢹⡖⠋⠈⢻⠋⠁⠈⢻⠁⠀⠀⡇⠀⢰⠃⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⠈⡇⠀⢸⡇⠀⠈⡇⠀⠀⢸⠀⠀⠀⣾⠀⠀⢸⡇⠀⡾⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢳⠀⢳⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡿⠀⠀⢸⠀⢰⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠇⢸⡄⠀⣇⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣼⠀⡼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠃⠀⠻⠀⠀⣧⠀⠀⢸⠀⠀⠀⠇⠀⠀⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠉⠀⠀⠈⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠘⠇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠤⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡀⠀⢀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡃⢻⡋⣿⣖⢒⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣩⠿⣧⡼⠻⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣞⢙⣶⡋⣳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣤⠿⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡉⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠤⠀⠰⠶⠴⢿⠛⠋⠙⠂⠋⠀⠀⠀⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠣⠆⠀⠀⠀⠀⠠⢀⣰⠒⠛⠃⠀⠀⠀⠔⠒⠀⠚⠀⣠⣄⣬⠀⠀⢂⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣹⠇⠀⠀⠚⣿⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠛⠆⢿⣷⠀⠀⢀⡀⠜⠳⢄⣀⡴⠖⠲⣄⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠠⠏⢠⣦⡄⠀⠀⠈⠀⠻⠿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣻⣍⣁⠀⠀⠀⠀⢀⣰⡆⠠⠆⠀⠀⠀⣤⣀⡀⠈⠉⠉⠠⣴⠐⠀⠠⣤⡤⠖⠒⠚⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠉⠈⢡⠉⠀⠀⠀⠀⠈⠁⣾⠤⠀⢠⡖⠛⠉⠛⠀⣁⣀⠀⠀⠁⠈⣷⣶⡏⠀⠀⠀⠀⠀⠙⡷
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢻⣶⣾⠋⠀⠀⠀⠠⣾⡥⠄⣤⠈⡴⢄⠀⠀⠀⠈⢃⡹⠂⢀⡸⠇⢀⠀⠚⢿⣿⠛⠀⢀⡸⠛⢀⣠⣴⣿⠐⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠋⣸⣆⠀⠀⠀⣤⠃⠘⣷⡘⠧⠀⠀⢦⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⣦⡟⠁⠀⠈⠁⣭⣤⣌⣀⠀⠀⠚⡂
⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⢀⣄⣈⣉⠇⠠⠾⡇⢠⡄⠘⠁⡈⠃⠀⠐⠊⠁⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠘⠛⠀⠀⠻⣄⠀⠀⠀⠀⠈⣹⣙⠉⠀⠐⡀⠉⠲⠶
⡀⣀⣰⣆⠀⠀⠀⠀⠁⠈⠿⢧⣄⠀⠀⠀⠀⠀⠀⣻⢾⡇⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠘⢻⠀⠀⠀⠀⠀⢳⣤⡄⣸⣷⠶⠖⠂⠈⠛⢀⣾⣿⣦⠀⠀⢀⡀
⠀⠀⠙⠟⠀⢀⠀⠀⠈⠀⠀⠀⣹⡄⠀⠀⠀⠀⢀⠣⠈⠁⠘⠲⣄⠙⣿⣶⠶⠖⠲⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⣾⠃⠀⠈⢙⠀⠀⠀⠀⢢⡈⠻⠛⠁⠀⠀⣼⡇
⠀⠀⠀⢦⣤⠾⣳⠴⢀⡀⠀⠀⠉⠁⠂⠐⠆⠀⠀⠐⠀⠀⣀⣼⣿⡄⠀⠀⠀⠀⠀⢰⡿⠰⢀⣠⣄⡄⠂⠐⠂⠛⢃⣉⠀⠈⠁⡟⠀⠀⣤⡄⠸⠻⠇⢠⡔⠉
⠀⠀⠀⠸⡇⠀⠀⠀⠘⠁⠀⡀⠀⠰⠓⠀⠀⣀⢠⠀⢤⣠⡈⢉⣿⣥⡀⠀⡀⠐⣦⠈⠀⠀⠀⢹⣿⣤⡀⠀⠀⢰⣦⠙⢶⡌⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣇⠀⠀⠂⠀⠄⣀⣽⠿⠇⠀⢰⣾⡟⢣⠀⠀⠉⠛⢀⣄⡙⠟⠈⢀⣸⣿⡇⠀⣠⣀⣠⣷⣄⢡⡀⣤⡈⠛⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠛⢇⣸⠀⠀⠀⠀⠸⣿⣇⠀⠀⢿⣿⡄⠀⠀⠉⠹⠾⠿⠛⡛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⠣⢀⣠⣿⣄⡀⠘⠀⠀⠀⠈⡃⢀⠶⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠙⣻⡀⢀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠔⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡁⠀⡉⠠⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣗⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣿⠀⠀⣀⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢞⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠘⠁⠀⠀⡜⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⡠⠋⠀⠀⠀⡠⠀⠀⡇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠎⠀⠀⠀⠀⠔⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠁⠀⠀⢀⠔⠃⠀⠀⡠⠁⢠⠓⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢀⡦⠀⠒⠒⢂⢤⡎⠀⠀⢄⣤⠊⠀⠤⠋⡈⠐⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡐⠋⠢⣌⡠⠔⠊⠁⠀⣀⠤⠒⠂⠁⠀⠀⠀⠀⠀⠄⠀⠀⡄⠹⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣣⡈⠛⠤⢋⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠠⠁⢐⢦⠀⠱⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠈⠁⠒⠀⠤⢏⡀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⢀⣴⠡⡴⠊⠀⠆⠀⠃⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡒⠓⠤⠄⠤⠀⠀⠀⠀⠀⠈⠁⠲⠾⠤⠤⠀⠒⠂⢈⠉⠤⠐⠊⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⣑⡠⠤⠀⠀⠀⠂⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠀⠀⠀⢀⡀⠤⡴⠊⠀⠀⡰⠀⣰⠃
⠀⠀⠀⠀⠀⡀⠄⠖⠋⠙⡁⠀⠉⠐⠠⠄⠀⠀⠀⠀⠀⠠⠤⠄⠀⠒⠒⢀⡉⠁⠄⠂⠁⠀⠀⡠⢚⡠⢊⠆⢀⡀
⠀⠀⠀⠀⡊⡀⡌⠀⠀⠀⠈⠢⠄⡀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠐⠂⠉⠁⠀⠀⠀⠀⡀⠄⠒⡉⢔⡡⠐⠉⠢⠀⠈⠑⢂
⠀⠀⠀⠀⠑⡙⢳⣄⡀⡀⠀⠀⠀⠀⠀⠈⠁⠉⠄⠀⠀⠀⠀⠀⠠⡤⠀⠒⠂⢉⡁⠠⠐⠋⠁⠀⠀⠀⠀⢀⣂⢀⡔⠟
⠀⠀⠀⠀⠀⠘⢄⠡⡡⡘⡎⢶⠒⢤⠀⢄⠤⢄⡀⡀⢀⣀⠀⢀⠀⢈⣉⠉⢉⡀⠀⢄⡠⠢⡤⠂⡔⢰⢁⢃⢏⠨⠂
⠀⠀⠀⠀⠀⠀⠈⢂⠐⠜⠈⠄⢂⠀⠄⠘⡀⠈⠀⠈⠃⠀⢹⠀⠈⠁⠀⠸⠀⢨⠁⠰⠁⠀⠀⡜⠠⢡⢃⢂⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠌⠌⠄⢣⠘⠀⠁⠀⢃⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⡀⠀⠁⠠⠁⡘⢀⢃⢂⠆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⡌⠜⡀⠆⢁⠘⠀⠘⠀⠸⠀⠀⠀⢠⠀⠀⠀⢠⠁⡌⠀⠆⢰⠀⠀⠄⡌⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⡐⠐⠘⠈⡀⠃⠀⡁⠀⡄⠀⠀⢸⠀⢰⠀⠈⠰⠀⠰⠀⠆⠰⡘⠘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠠⠀⠃⠸⢀⠃⢁⡣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠬⣰⢠⠀⡀⢰⠀⢀⢀⠀⡂⠀⡇⢰⠀⡀⢀⠀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡈⠀⠉⠈⠈⠁⠀⠁⠈⠀⠉⠉
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣀⠒⠒⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣤⣽⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠙⠟⠛⠉⠁⠀⠀⠀⠈⠙⣻⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢛⡛⡟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⡀⢰⣤⣴⣾⣿⣍⡉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠹⠅⣹⠋⠀⠙⠻⠅⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⡿⠿⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⡠⠊⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⡀⢀⣠⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⣯⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⡴⣶⣿⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠚⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣿⣥⣼⣿⣿⣛⣋⡉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠳⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣿⣯⣈⢛⣋⠻⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⣄⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⣿⣿⣿⣿⣿⣷⣦⣄⡉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡏⢿⡿⠏⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⣀⣴⡾⠿⠿⢿⣿⣿⣿⣿⣿⣏⣤⣀⠙⢮⣉⣁⠀⣀⣤⣾⡍⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠞⠿⣋⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⠄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡿
⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⠛⠛⠛⠛⠻⣿⣿⣿⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣾⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⡿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣤⣤⣄⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⣾⣿⣿⣿⣿⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣞⢦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⡟⣭⡿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢸⣿⡇⣿⡇⣿⢱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢿⠇⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢞⡇⠀⠀⣿⠇
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⣿⣿⣿⣦⡀
⣿⣟⠀⣸⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣶⣷⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠐⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⡩⠄⠀⠀⢀⡴⢏⡨⠁⠀⠀⠀⠊⢄⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠀⠀⠀⠀⢠⡮⣕⠀⠀⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠋⠀⠀⠀⠀⠀⢰⠗⠥⠀⠀⠀⢈⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣀⠀⠀⠀⠀⠀⢀⠢⢀⠄⠀⠀⠀⠀⠀⠐⢠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠑⠀⡀⢀⠀⠀⠀⠀⠀⢠⠀⢃⠀⠂⠀⠀⠈⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⠄⠀⡀⠀⠀⣔⢂⣨⠜⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠦⡀⠀⠈⠲⠐⠤⠊⠁⠀⡀⢀⠀⠀⠀⠀⠀⠴⢆⣄⠉⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠆⠌⠀⠀⠔⠁⠀⢈⠦⡀⠚⠋⢄⠀⠀⠀⠄⠠⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠄⠄⠀⡠⠀⠀⡀⠐⠁⠀⢀⠰⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠈⠀⠀⠐⠈⠀⠄⠀⠈⠁
⠀⠀⠀⢠⠂⠔⡡⠀⡀⠄⡂⠠
⠀⠀⢠⣏⣀⡨⠔
⠀⠀⠚⠋⠁

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌⠀⢈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⢲⡖⠒⢦⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠘⣦⠤⢤⣀⠤⠤⠼⣄⡤⠦⠤⢄⡠⠦⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⡄⠀⢰⡇⢠⠀⢻⠀⠐⠃⢈⡇⠀⠒⠀⡷⣄⠉⢁⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠿⣧⣀⣸⡀⡴⡆⠘⡆⠀⣖⠋⣇⠀⢰⢚⢁⣸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠠⣏⢩⡏⠩⠙⣏⠉⣹⠉⠏⢻⠉⡙⡿⢉⢹⡌⢋⡹⠂
⠀⠀⠀⠀⠀⠀⠀⣇⣀⣘⣠⣏⣨⣇⣀⣸⠜⣆⣿⣰⣆⣼⣀⣡⢇⡴⣄⡿⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠁⢠⢿⠒⠒⠒⠒⢴⣾⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠹⡟⢁⣴⣦⡙⣆⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠠⠤⠤⢀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠳⡈⠻⠿⠃⣼⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠊⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠓⠲⣿⣿⣿⣷⣤⢇⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠒⠀⠒⠠⡈⠢⡀⠀⠀⠀⠀⠙⢿⣿⣿⠃⠀⠀⡅
⠀⠀⠀⠀⠀⠤⠀⠘⡄⠂⠀⠀⠀⠀⢰⣿⣿⠀⡞⠀⠀⠀⠀⠀⠀⠈⢢⠈⠳⢄⡀⠀⠀⠀⠘⡇⠀⢀⠎
⠀⠀⠀⢀⣄⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠉⣠⢺⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠉⠲⢄⡀⠀⢇⠀⡈
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠙⢄⠈⠓⠀⠐⠉⠀⠘⠄⠀⠀⠀⠀⠸⣿⡿⡠⠀⠀⠀⠀⠀⠀⢈⠗⠾⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠁⠂⠉⠦⡀⡀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⣠⠎⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠤⠀⠚⠄⢄⡀⠀⠀⠀⠀⠀⠀⠄⠰⠋⠁⠀⡀⡀⢀⠆⠀⠰⠀⠀⣉⠉⠁
⠀⠀⠀⠈⡀⠀⡀⠐⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠘⠂⡀⠄⠦⠃⠨⠇⠀⡰⠁⡘⢳⣘⠃⣴⠁
⠀⠀⠀⠂⡄⢀⠈⠎⠀⠀⣰⣶⣦⠀⠀⠀⠀⣰⣿⣷⡀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠙⠁⡀⢏⣉
⠀⠀⠀⠊⠀⠀⠙⠇⠀⠀⠹⢿⡿⢀⠀⣘⢀⡘⠻⠟⠀⠀⠰⠖⠁⠀⠀⠘⠃⠀⡀⠀⢴⠆⠀⠀⠀⠠⢴⣈⢳⠆⠉
⠀⠀⡁⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠁⠔⠂⠀⠀⠀⠈⠲⠶⠂⠀⠀⠀⠀⢀⣰⡦⠏⠁
⠀⠀⠱⢄⡀⠀⣀⠔⠁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠽⠁⠈
⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣉⣁⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣿⣞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡙⠟⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⠀⠀⠘⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣟⠀⠀⠀⠈⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣩⣤⡀⠠⠈⢠⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣮⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢀⣉⢻⣿⣿⣇⠙⢿⠟⢿⠏⠉⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⡨⢊⣿⣿⠟⠉⠭⣿⡇⣹⠀⠰⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠢⣀⢠⣿⢁⠞⠌⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠈⠁⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢃⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣒⡼⣦⣀⡀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠈⣹⠛⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⣴⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⣰⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣽⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⣷⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠿⠛⠀⠀⠀⠀⢸⣿⣿⣿⠿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣇⡀⠀⠀⠀⢀⣾⢧⣾⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⢷⣦⠀⠀⣠⣶⣿⣧⢻⣿⣿⠩⣾⣿⣏⣾⣿⣦⣄⠉⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣾⡿⠀⣾⣿⣿⣿⣿⡿⣿⡃⣿⣛⣿⣿⣿⣿⣽⣿⣧⣀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣯⣿⣿⢻⣿⠟⣿⣯⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣾⣿⣿⣾⢛⡿⣿⢸⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠹⢿⣿⣿⣇⣿⠈⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⠀⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡀⣀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠊⠉⠉⢁⣀⡀⣀⣀⣀⣀⣀⡀⠀⣀⠉⠉⠐⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⣸⠀⠠⠄⠀⢈⠁⠀⠀⠀⠀⢀⡰⠖⠛⠉⠉⠉⠉⠙⣦⣀⣐⡸
⠀⠄⠀⠀⠀⠀⠀⠀⡄⠸⠌⠃⠀⠀⠆⠊⢇⠰⠉⠑⠒⢤⡑⢢⡤⠔⠊⠁⣐⠢⠀⠔⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢀⣀⡠⠜⠋⣁⠶⣶⠖⢠⣬⡄⣨⣀⣀⠀⠀⠀⠈⠦⣀⣀
⠀⠀⠀⠀⠀⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢻⣧⣤⣶⣶⣚⣶⠁⠌⠲⠂⠻⣄⣀⣐⠜⠙⢯⡁⣶⡀⠀⠀⠤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⣠⠊⢻⣿⣿⣿⣿⡿⢄⡀⠁⠀⠀⣀⣀⡠⠤⠚⡀⠫⢍⠧⣉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⢀⣔⠵⠊⠁⠉⠀⠙⠛⢺⣟⢉⠑⡒⠒⠒⢲⣶⠟⠫⡄⠬⡉⢶⠰⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢸⣡⡄⠀⠺⡽⠁⢀⠔⠲⠟⠑⣎⢀⠟⠒⡆⠈⠀⠀⠴⢄⡈⠢⡷⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢺⠀⢰⡟⠉⠹⡆⠈⡇⢌⣠⡀⠀⠐⠛⠂⣶⢷⡴⣼⣿⣦⣰⣷⣽⡄⠀⠘⠊⠁⣠⡇⠀⡾⠉⠱⣶⠈
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣇⠀⠀⢱⠀⢳⡀⠘⠒⠖⠉⣦⣤⣾⣅⣳⢉⡿⣿⣁⡿⠐⣦⢠⠒⠉⠛⣸⠁⢰⠃⠀⢀⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹⡀⠀⢰⡀⠈⣏⠲⠎⢱⡤⠜⢲⠈⠉⠉⠉⠉⠀⠀⠀⢨⢩⠥⢄⢸⠉⡏⠀⢸⠀⠀⣼⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠛⠛⣡⢤⠈⠉⠓⠒⠀⠴⢿⣦⣤⣤⣤⣤⣤⣄⣄⠊⠛⠀⠚⠒⠈⠀⣀⢽⠓⠳⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⠤⠤⢴⠃⢠⠧⠤⠤⠤⠤⠤⢼⣄⣠⡆⠂⢠⣀⣠⢸⠦⠤⠤⠤⠤⠤⠼⡅⢸⣇⣀⠼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⣀⣠⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠠⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⠉⠧⣈⠿⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠙⠃⠐⢲⣠⠏⡏⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢠⣟⣀⡠⣀⣀⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠋⠀⠠⢄⠀⢹⡿⡟⢿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⡨⢧⣀⣀⠀⠀⠈⠉⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣼⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⡼⠀⠸⡆⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⠜⠀⢁⠀⠇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢀⣠⠔⠉⡄⢀⣨⡔⡃⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⡗⢛⣙⡗⠒⠒⢻⠁⠀⣆⡇⠀⡏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡽⠋⠀⠙⢆⠀⢸⠀⠀⡸⠁⣠⣇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡟⠀⠀⠀⠀⠀⠑⠚⠖⠊⢀⡴⠃⢻⡄⠀⢛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⢀⡾⢻⠁⠀⠀⠀⠀⠀⢀⠠⠐⣨⠏⠀⡌⠀⣦⠀⠘⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⣉⣉⣷⡤⣤⠤⣠⣛⠷⣾⣶⣤⠴⠒⠊⠉⠀⣠⠞⠁⣟⠋⠀⠀⢀⠀⠀⣇⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡌⠁⢸⣀⣇⡴⢃⢷⠀⣿⣿⣽⠖⣿⠿⠶⣻⣷⡶⠿⠀⠀⠀⠀⣼⠀⠀⡕⢂⢺⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠓⠶⡾⠋⠉⠙⡇⠈⢿⣿⣍⢻⣴⡇⠛⢢⠟⠁⠀⠀⠀⠀⠀⣠⠿⣦⣤⠏⡞⠘⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣀⠀⠀⣧⣀⠔⢠⠇⢀⣈⣿⡛⢷⣿⣾⣿⡏⠙⣆⢀⡤⠦⠒⣏⠕⠀⢸⡟⢀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⠉⠉⣩⡇⢠⡿⣄⡈⡟⢹⣩⠋⠁⠀⠀⠀⠀⠈⠙⣧⠀⠀⠘⣦⢴⠋⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢬⢿⠁⠉⣠⡀⣠⡇⠘⡛⢠⠲⡌⡶⠒⠀⠀⠀⠀⠀⢀⣼⡀⡠⢄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣻⣿⣿⠀⣿⣿⡀⠘⠚⠀⠙⣶⠒⠂⠀⠀⣰⠋⠸⣧⠝⠛⠚⠃⠀⠀⠀⢀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠈⠉⠟⠉⠀⡿⣿⣿⣿⣦⣤⣀⠀⠨⠿⣶⣾⣿⡿⠀⠀⠀⠀⢀⡀⠠⠀⠂⠈
⠀⠀⠀⠀⠀⢀⣈⡯⠉⠀⢹⡷⣤⣶⣶⡖⢢⣀⣰⡖⠒⢳⠙⣿⣮⣿⠻⠋⡋⠙⠑⠒⠒⠒⠓⠓⠛⠉⠋⣹⠥⡤
⠀⠀⠀⠀⠀⢀⣱⠄⣀⣠⡿⠞⣿⠿⣤⣙⣦⡀⢀⡀⠀⢸⡁⣡⣿⡏⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠐⠶⠒⠒⠒⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠈⣧⡼⠛⣯⡠⣾⡁⠶⠀⠉⠛⡿⡏⣻⠦⢼⣡⣘⡟⣁⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡠⠤⠲⣇⣠⣤⡘⢋⣩⣅⠒⠚⠒⢤⣀
⠀⠀⠀⠀⠀⠘⠙⢄⣉⣀⣱⡾⢻⠶⣤⣀⣀⣉⣿⣥⡀⠀⣨⠙⣿⣽⡿⠳⢦⣄⣀⣀⣀⣶⣶⣔⣺⡂⣅⣠⠐⣦⡟⢙⣦⣼⣛⡱⠌⣱⡤⢛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡉⠛⢶⣤⣼⠃⣶⠀⠀⠀⠙⣲⣍⣰⠿⣟⠘⢣⡟⠻⣿⣿⣿⡍⢫⠟⢿⠉⠀⠘⣆⣈⣿⡏⠉⢹⡏⢿⠋⡙⢳⣬⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣀⠸⢥⣤⡴⣿⠫⡍⠉⠀⠉⣆⣨⣷⣯⡐⠃⠀⠈⠉⢙⠛⢿⣾⣷⣿⢿⣧⠤⣤⠶⢲⠞⢷⣿⣬⡤⢚⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠨⡇⠁⠒⠒⠙⠻⣅⠘⣋⣹⡿⠶⢦⡤⣈⣱⠏⠀⢰⠆⣾⡿⢶⣍⣰⠧⢤⡮⣍⣹⣄⡋⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠑⠲⢾⣷⠛⣿⢶⠶⣎⠉⣩⠜⠳⣾⡧⠄⠺⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠀⠉⠳⠒⠂⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⣼⡇⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠰⣶⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣷⣀⣀⣻⣀⣀⣀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠟⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣻⣿⡇⢸⣿⣷⠈⣿⣿⡏⣿⣿⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠻⣿⠃⢸⣿⣿⠀⠻⠟⠁⣿⣿⡧⠀⢸⣿⣿⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠛⠟⠁⠀⠸⣿⡿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⡀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢸⠃⠀⣧⠀⣿
⠀⠀⣀⣠⡤⠴⠶⣶⣶⣿⣿⣿⡿⠿⢿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⣿⣧⠀⣾⣿⣿⣿⣷⡀⢹⣿⣿⣿⡏⠙⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⢰⣿⣿⣇⠈⠛⢸⣿⣿⣷⠀⠙⢻⣿⣷⠀⢸⣿⣿⠀⠉⣹⣿⣷⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣿⠏⠀⠀⠘⢿⡿⠃⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠋⠀⠀⠻⠿⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠲⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢀⠠⠤⠰⠖⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⠶⠖⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠶⠾⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣿⣷⣶⣶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣿⣯⣿⣿⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⣰⡎⣹⣏⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⣀⣻⠛⠙⠛⢸⠾⠇⢰⣿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⣀⠀⠒⠃⢀⣠⣾⡿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⡛⢋⢀⡴⠚⠉⣅⣳⣶⣿⣿⢧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢶⣿⣿⡿⠋⠀⠀⢀⣻⡿⣫⡿⣿⡾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⡺⣿⣧⡶⠚⢉⡔⣡⣾⣿⠶⠛⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣼⣿⣿⠟⠁⢀⡴⢫⡾⢻⣿⣶⣶⣾⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠍⠛⠿⣶⢶⡿⠓⣛⢛⠛⣿⢿⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣴⣦⣑⣈⠂⡀⢼⡿⣏⡑⣷⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢿⣦⣿⣿⣦⠀⣴⣦⣿⣿⡿⣿⣿⣿⡑⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⣿⡙⣿⡇⠾⢻⣿⠻⣿⡧⠙⣿⡏⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣧⢸⡇⡄⢸⡗⠀⣿⡇⢰⣿⠇⣾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⣸⡿⡇⣿⡇⢀⣿⠄⣿⣿⣼⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⢹⡅⣿⣷⢸⣿⢸⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠷⢾⣿⣿⣿⣿⣿⣿⠟⠋⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡷⣰⣄
⠀⠀⠀⠀⠀⠀⣰⠟⣽⣴⠛⠛⠛⢶⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢟⣋⡁⢀⣉⠻⣇
⠀⠀⠀⠀⠀⠀⣧⡟⠁⠶⠇⡴⢾⠈⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢪⣿⡄⢮⣧⡇⡿⣄
⠀⠀⠀⠀⠀⡰⡛⠓⠀⠀⠃⠘⠃⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡁⣀⠉⠄⢨⠉⣀⣠⣾⠂
⠀⠀⠀⠀⠀⠑⠬⣶⡀⠀⣀⠚⠀⣰⡦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⡹⡌⠑⠨⡠⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢑⣄⣀⣀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢪⡅⢩⠔⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠺⡀⢇⡸⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⢧⠘⣹⣷⣄
⠀⠀⠀⡀⣴⣾⣿⣿⣄⠸⠆⠀⠚⣸⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡙⣾⣷⢩⣿⣿⣧
⠀⢀⣦⣤⣿⣿⣿⣿⣿⣷⣶⡶⠋⢿⣿⣿⣿⣿⣷⣤⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣼⣷⢸⣿⣿⣿⡆
⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⠇⢸⢸⣿⣿⡆⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⡄
⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣏⢀⣮⣾⣿⣿⡇⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⠔⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠢⡀
⠀⠈⢩⠋⢩⢽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠩⡉⠹⡉⠀⠀⠀⠀⠀⠀⠀⢸⣰⡶⢹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⢶⣆⠇
⠀⠀⠘⠄⣨⠦⢐⠄⣽⣿⣿⣿⣿⣿⣏⠤⡀⠴⣁⠴⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣄⣀
⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠰⢄⠀⠀⠀⠀⠀⠀⢰⣀⡉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⢋⣈⡄
⠀⠀⠀⠀⠀⠶⠂⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡏⢻
⠀⠀⠀⠀⠘⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢢⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⡴⡿⠁
⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠘⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠋⠁⠴⠿⠿⠿⠿⠇⠻⠿⠿⠿⠿⠆⠈⠛⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⠿⠋⠉⠉⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠙⠛⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠐⣿⣏⠀⠀⠀⠽⠿⠁⠀⠀⢠⣴⡀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⢀⣶⣦⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠈⠺⣻⣷⡄⠀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠘⠀⢀⣠⣶⠾⠟⠛⠉⠛⠛⠙⠛⠛⠷⣶⣄⡀⠀⠀⠀⢀⣀⣤⣼⣿⣿⠿⠟⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⣶⡧⠄⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣶⡾⠿⠟⠛⠋⠉⢀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠁⠀⣰⡿⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⠿⠿⠛⠋⠉⢀⠀⣠⣴⣦⡐⣿⡛⠃⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣸⡟⢁⣀⣠⣤⣴⣶⠿⠿⠛⠛⠉⠁⢀⣀⣤⡄⣶⡀⢹⡇⢿⡇⠹⠃⢹⣧⡶⠄⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣀⣠⣤⣴⣿⡿⠿⠛⠋⠉⢁⢀⣀⠀⠀⣶⠟⣷⡌⣿⡁⣀⢻⣿⣎⣿⡘⣿⠀⣠⡌⣿⣀⣀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⣀⣀⣼⣿⣷⡾⠿⠛⠛⠉⠁⣀⣠⣄⠀⣶⡀⢻⡇⢿⡆⠀⢻⣇⢬⣧⢹⣿⠛⠈⣿⡘⢿⣧⠹⣧⣼⡇⠘⠛⠛⠀⢀⣀⣠⣤⣿⣷
⠀⢾⣿⠟⠛⠉⠁⠀⣀⡀⣤⡀⢸⣇⢻⡏⠹⣧⢹⣧⠈⣿⡘⣷⠀⠘⣿⡄⢻⡆⢿⣤⣶⠸⠇⠈⠛⠀⢀⣀⣠⣤⣶⣶⣿⣿⡟⠋⠉⠁
⠀⠘⣿⡄⠀⠀⠀⠀⢹⣧⢻⣿⣌⣿⡘⣿⠀⢿⡆⣿⡄⢻⡇⢻⣧⣶⠘⠿⠟⠋⠈⠁⣀⣠⣤⣴⣶⣿⠿⠛⠋⠉⠁⠀⣼⣿⡇
⠀⠀⢹⣷⠀⠀⠀⠀⠀⢿⡎⢿⡙⣿⣇⢹⣧⣼⡷⠘⠻⠟⠃⠀⠉⣀⣀⣤⣴⣶⡿⠿⠛⠛⠉⠁⣽⡟⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣷⠸⡧⠈⠛⠈⠉⠉⣀⣀⣤⣴⣶⡾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⢠⣾⠟⠀⢀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠉⣀⣀⣤⣤⣶⣾⢿⣿⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠐⢾⠿⠀⢀⣼⣿⡏
⠀⠀⠀⠀⣿⣧⣤⣤⣶⣾⣿⡟⠛⠉⠉⠀⠀⠀⠈⠛⠿⣦⣦⣤⣀⣀⣀⣠⣤⣴⣶⠾⠛⠁⠀⡀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠘⠛⠋⠉⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⣄⡀⠀⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⢻⢿⠁⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣦⣄⡀⠀⠉⠟⠇⠀⠀⢀⣦⣖⠀⠀⠀⣱⣿⠄⠀⠀⠀⢀⣠⣶⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣯⣰⣤⣀⡀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⢀⣀⣄⣰⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣾⣿⣶⣶⣶⣤⣤⣶⣶⣾⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠁


⡿⢿⠿⢿⠿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⡿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣝⣟⣽⣿⣦⣼⢿⠶⠛⠛⠉⠉⠛⠛⠛⢯⡉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣟⡛⠛⡓⠀⠀⣀⠀⠀⠀⠀⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠈⠁⠀⠈⡆⠀⠈⢻⣦⠀⠀⠰⠀⠉⠙⠳⣄
⠀⠀⠀⠀⢠⣄⡴⠋⠙⣝⠢⢈⠙⠛⠛⠛⠛⠉⠀⠀⡼⠀⢠⠆⠀⢸⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠌⠣⡀
⠀⠀⠀⠀⠀⡍⠀⢀⠀⠈⠑⠀⠀⠠⠄⠀⠀⣀⡴⠚⣀⡴⠋⠀⠀⡞⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡼⠂⠠⢄⣠⣤⣤⣤⣤⠶⠖⠛⠉⠀⠚⠉⠀⠀⢠⠎⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡄⢸⠀⠀⡀⠀⠠
⠀⠀⠀⠀⢨⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⡴⢋⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠘⢮⣁⠒⠒⢒⣒⣒⣋⣩⣤⣤⣶⣶⠿⠟⠉⠀⠀⣀⠴⠚⠉⠀⠉⣀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠇⠀⢰⡇
⠀⠀⠀⠀⠀⣠⠊⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠐⠊⠉⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⢀⡿⠀⠀⣤⡾⠀⢀⣾⠑⢄
⠀⠀⠀⢠⠞⠁⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠴⠒⠋⡁⠀⠀⠀⠀⢀⣴⡟⠁⠀⣰⡟⠁⠀⣼⣿⠃⠈⢣
⠀⠀⢠⠇⠀⠙⢿⣿⠋⢩⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⣠⡾⠋⠀⠀⣰⡿⠃⠀⠘⢀⡆
⠀⠀⢸⡀⢀⡆⠀⠙⣆⡀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠖⠛⠉⠉⢀⣠⠴⠞⠉⠀⢀⣠⡾⠟⠁⠐⠀⣠⣾⠁
⠀⠀⠈⣧⡘⣧⡀⠀⠈⠙⠛⠛⠛⠛⠋⠉⢦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⣤⣄⣀⣀⣀⣠⣤⠶⠏⠁⣀⣤⣴⣶⡿⠟⠁
⠀⠀⠀⠘⢿⣮⣁⠀⠘⠃⠀⠀⠂⠀⠀⠀⠀⠙⠛⠷⠶⠾⠿⠟⠛⠍⠀⡀⠆⠈⠉⡉⠉⠁⠀⢀⣠⠚⣿⡏⢰⡟
⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣶⣦⣤⣴⣷⣦⣄⡀⠀⢀⠀⠈⠀⠀⠀⣀⣤⣴⣶⣃⣀⣤⣤⣶⡾⣿⡟⢸⣿⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡄⢿⣿⡀⢸⣿⡟⠿⣿⣿⡿⠿⣿⣿⠿⢻⣿⠉⢹⣿⣿⠛⣿⡿⠀⣿⡇⣸⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣈⣿⡸⣇⢸⣿⡇⠘⣿⣇⠀⢸⣿⡇⠀⣿⣏⠀⢸⣿⠀⢈⣿⡏⠀⣿⡇⠀⣿⠀⣿⢇⣟
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣧⢻⡄⣿⣷⠀⢿⣿⠀⠘⣿⡇⠀⣽⣯⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇⢸⡿⢰⣿⣸⣿⣿⣶⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣧⢸⣿⡀⢸⣿⡀⠀⣿⡇⠀⢹⣯⠀⢸⣿⠀⢸⣿⡇⢀⣿⠁⣼⡇⣸⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡀⣿⡇⠀⣿⡇⠀⣿⣧⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⢸⣿⠀⣿⡇⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣿⣿⣷⣴⣿⣇⣀⣽⣿⠀⢸⣿⠀⢸⣿⠀⢸⣿⡇⣸⣿⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⠿⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠛⠛⠉⠉⠉⠉⠛⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠆⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠐⠀⠂

⠀⠀⠰⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣤⡀
⠀⠘⢣⠀⠀⠀⠃⢀⡒⠀⠀⠀⠀⠀⣄⣀⠀⣀⠀⢀⠠⠀⡀⠀⠀⠀⣀⣴⣟⣋⢭⢤⡀⠝⢋⣦⣜⠳⠄
⢀⠀⠾⠀⠀⢀⢡⡦⠁⠀⠀⠀⠀⠚⠀⠀⠌⠁⠀⠈⠀⠰⠀⠀⠀⢰⣿⣿⣿⣿⣥⡈⠳⢦⡀⠀⠫⢷⡀⠰⡀
⠂⠀⠀⠀⡄⠈⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⠈⠻⣶⠹⢆⠀⠹⢆⢄⢙⡇⠀⢷
⠀⢠⣦⡾⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⣤⣤⣴⡿⡀⠰⢄⢀⣻⣆⠢⣇⠀⠈
⣾⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⢴⠉⣷⠀⢳⢹⣿⣆⠹⠀⠘
⠑⠙⢾⠃⡀⠀⠈⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⢸⡀⣇⡇⣠⠘⣿⢜⠇⡆⢀
⠀⠀⢐⡀⢀⣟⡄⠱⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠐⠶⠖⡿⠒⠒⠒⠛⠃⣻⢿⡌⠁⣝⠄⠀⡷⣷
⠀⠀⢈⡁⠀⡜⣆⠏⣄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣷⠄⠀⠀⠀⠀⠻⣈⠟⢷⢈⣇⡀⢰⣟
⠀⠀⠈⢥⠂⠀⠈⠘⠀⢀⠀⠀⢃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⠀⠀⠎⠰⡀⢹⠀⠀⠀⢏
⠀⠘⠣⡀⠀⠀⠀⠁⠀⠳⠆⠀⠀⡀⠀⠀⠀⢘⣤⡀⠀⠀⠀⠀⠉⢠⠆⡠⢤⡴⢂⡜⣶⠀⠀⠇⣸⠀⠈⠐⠺⡄⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠐⢋⠆⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠏⠁⣾⡀⠀⠀⣀⠋⣸⣿⢒⣧⣤⣷⡾⢄⠄⠀⠃⠀⢂⡄⠐⢄⣂⡀⠀⠀⠘⠂⠼⠄
⠀⠀⠀⠈⢆⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠃⠁⢰⡾⠁⣴⠟⢿⡟⣼⣄⣈⠠⣀⠆⠀⡄⢳⠀⡀⢟⠣⠀⠙⠒⠂
⠀⠀⠀⠀⠈⠀⠀⣶⠀⠀⠈⣄⠀⠀⠄⠀⠀⠀⡀⠁⢀⠞⠃⠀⣼⠶⣷⡄⣿⣠⠼⣿⠓⢹⡆⢤⠀⠸⡆⠁⠈⠑⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠘⣋⠀⢠⡴⠁⠠⠃⠀⡀⠀⠠⠀⠰⠥⠀⢠⣀⣸⣿⣽⣧⣞⣹⡾⢷⣿⣄⠐⢸⠇⠸⣧⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠘⠁⠀⠞⠀⡀⠁⠀⠀⠀⠀⠀⠀⠐⠁⢠⠀⠁⠠⠘⣯⠿⠛⣿⣿⣽⣯⡶⢿⣿⣼⣿⠊⠇⡀⠡⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣷⡆⢠⡾⠁⠀⠀⠀⠀⠀⠁⠐⠁⠀⠈⠀⠀⠟⢛⡛⣟⣋⡿⢻⡟⢻⣶⣿⣯⣧⣿⠀⣀⠁⡄⠀⠀⠀⡀⠀⠀⠀⠿
⠀⠀⠀⡨⠁⠠⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣌⡀⢻⠛⢤⣼⣷⣿⣩⣧⣼⣿⣬⠀⠿⣦⠀⠠⢠⣄⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠐⠎⠀⣧⡀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠈⠀⠠⠈⢻⠲⢮⣴⡂⠠⢔⣵⣻⣿⡷⣾⣿⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠉⠁
⠀⢀⠀⠐⠒⣋⣅⠈⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠲⢟⡤⢽⣶⣿⣋⣭⠃⣵⡇⢿⠀⠀⠀⡀
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⣳⣾⠟⠛⣿⣷⣶⠿⢳⣿⡆⠺⣿⡇⠀⠀⢤⣶⡆⣦⡛⠰⠀⢃⠒
⠀⠀⣄⠀⠀⠀⠀⠔⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣻⣧⣄⢳⣾⣿⠷⣿⣶⠏⢰⡿⣄⠈⠁⢸⣷⣤⡉⠃⠉⠐⠆⠉
⠀⠀⢉⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠻⣿⢿⣿⡏⠜⠙⢧⠘⣇⡿⢦⡀⠈
⡀⠀⣬⠛⣤⠧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠾⠁⠀⠁⠀⢠⣬⣧⡉⣶⣿⣿⣵⠾⣥⣶⡌⢠⣿⡇⣀⡽⠦⣀⠀⠀⠀⠲⠄⠀⠖⠦⠤
⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢀⡔⢠⠀⠃⠀⠀⠁⠀⠀⠀⠀⣾⡁⢿⣷⣝⣟⣿⣟⠒⡟⠹⢧⣼⣿⣿⠿⠖⠛⢻⡻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠂
⠀⢅⠐⠊⢀⠗⠁⠀⠀⢀⣾⣼⡳⠋⠀⠀⠀⠀⠀⠀⠀⢘⡫⠿⠻⣷⣻⣏⣹⡿⣿⡦⢠⣼⣏⣀⠋⡀⠒⠦⣾⠁⠈⠻⣝⢳⠠⢀⡀⠀⠀⠀⠲⠀⠀⢰⠁⡄
⠀⠋⠠⢖⣯⠁⠀⡀⢠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣦⣴⡆⢰⡟⢡⣽⣆⣼⡇⢾⡇⢠⣿⡿⠋⣆⢸⠇⠀⠀⠀⠈⠻⣧⡀⠀⣉⡠⠖⢶⣤⣀
⠀⠀⠀⠀⠃⣀⠰⠦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠉⠿⠛⢡⣿⣯⣿⡍⠛⠑⢁⡼⠋⢁⢰⡏⣿⠴⠒⠶⠶⠶⠶⢞⣷⣮⣄⡀⠀⠸⡄⠉⠓⢦⣁
⠀⠀⠀⠀⢰⡁⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣀⣤⣤⣄⠀⢉⡀⠘⣠⣤⣴⠟⠇⢠⣄⣾⣇⢸⡆⠀⠀⠀⣀⡴⢋⢀⢻⡆⠉⠓⠤⣿⣀⣠⠴⠞⠛
⠀⠀⢀⡀⠈⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⣹⢿⣹⡟⣷⣀⣡⡏⣴⣦⣄⣿⣿⡏⢼⣦⣹⣄⡤⠞⠉⠠⠀⠾⠀⢿⡀⠀⢠⠼⡿⣄⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⡟⠠⡟⢁⣿⣋⠙⠿⣯⡄⣼⠋⢸⡷⡀⠹⣿⢳⣄⡀⠄⠀⠀⡾⠀⠈⣳⡴⠉⠀⠁⠈⠑⢤⡇
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀⠀⡇⠀⢩⡜⠻⣿⣢⣄⣼⢷⣿⠀⣏⠀⣿⠗⠻⠘⢯⠙⡦⠀⠀⣀⡠⠐⠛⢧⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⣚⠛⣽⠋⠙⣿⠛⣦⠟⠚⠻⢦⣄⠀⣾⣞⡴⠾⠛⠛⠳⢄⡀⠈⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢠⠀⠀⠀⠈⣿⠞⠹⣃⣼⢅⠀⠙⠣⣄⡙⣿⡏⠀⠋⡉⠀⡰⠆⠀⠀⠀⣉⣳⣬⣷⣄⡀⠤⠀⢒
⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⣿⠀⠀⠀⠀⠀⠖⠀⠀⠀⢉⠀⠀⢿⡆⠀⠀⠀⢻⡳⣄⢻⡜⠻⣤⣿⠶⠈⢫⠘⠷⠂⠀⢠⠐⠀⢀⣤⣄⠀⠀⠈⠁⠉⠉⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠈⠀⠈⡍⣄⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⠀⠀⠀⠵⢜⠳⣿⡆⢸⣇⣠⣀⣄⠋⠀⠂⠀⠉⡠⡄⠀⠀⠙⠆⠀⠀⠀⠀⠀⢀⣶⠁
⠀⠀⠀⠀⠀⠀⢀⠒⠀⣄⡜⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢿⣿⠈⣳⠊⠘⣦⠀⠀⠚⠋⠶⢧⣤⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠛⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⣣⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠰⠆⠀⠀⠀⣠⣴⠶⠖⣄⠀⠀⡆⠀⠃⢀⣁⠀⣠⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠑⠀⠀⠀⣼⠟⠋⠉⠛⠛⠃⠠⣧⣀⡁⠈⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠈⠀⠀⠀⠀⡤⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠀⠘⢋⠁⠀⠰⠗⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⣲⡁⠀⠀⠠⠈⠀⠀⠀⠦⠠⠆⢀⣴⢻⢢
⠀⠀⠀⠀⠀⠀⡈⠀⢀⡄⠀⠹⣿⣿⣿⣿⢻⣿⡍⠑⣾⡇⠀⠀⠠⠀⠈⠀⡸⠚⠷⢷⣁⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠠⠀⠹⣿⣿⣿⣼⠋⠛⢴⣿⣿⣶⣤⠀⣤⣤⣶⡌⠀⠀⠀⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠘⢻⡏⠀⠁⠀⠀⢹⣿⣿⣟⠈⠃⢹⣿⣿⠀⠉⣿⡇⠈⢿⣿⠄⠀⠀⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⢀⢀⡀⣸⡇⠁⠀⢀⣤⣸⣿⣿⣇⡀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢐⣿⡟⠄⠀⠠⠠
⠀⠀⠀⠀⠘⣿⢷⣾⡏⠋⠈⠘⠓⢻⣿⣿⣿⠀⠀⢘⣿⣿⠇⠀⣀⣀⡀⠀⢸⣇⠀⠀⠀⠈⠉⣸⠻⠦⠄⣠⠾⠂⠓⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣷⣷⣦⣼⣿⣿⣿⣷⠶⣾⠋⠀⣿⣿⣿⣿⣿⣿⠈⢯⠭⠿⢭⡴⠟⢻⣆⠀⠰⣃⣀⣈⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠙⡆⠀⠈⣿⣿⣿⣍⣙⣷⣏⣀⣀⣼⣯⣶⣶⣿⣆⠈⣩⡉⠉⣭⡄⠾⠁
⠀⠀⠀⢀⢆⠀⠀⠰⣤⡃⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠆⠀⢸⢻⣿⣿⣿⣿⡿⠿⠟⠛⠙⣿⣿⣿⣟⢄⣉⠸⠇⢈⣠⠀⢀⠄
⠀⠀⣠⣧⣄⣁⠓⠶⠋⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⡾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣷⣿⣿⠟⠀⠙⠉⠏⠉⠡⠀⠈
⠀⠀⠎⠉⠙⠛⠛⠓⠓⢛⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒⠚⣿⠈⡀⣼
⠀⠀⢀⣴⣀⠀⣀⠀⠀⠀⠈⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠃⢴⠿⠃
⠀⠀⠀⠉⠛⠻⣿⠀⠀⠀⠀⣇⢀⡀⢀⡇⠀⠀⠀⠠⠄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡀⠀⢲⡀⠀⠀⣀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠺⣿⡀⣠⣴⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⡍⡏⠛⠉⠮⠃
⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣷⣿⡿⠿⠛⠛⠛⠛⠋⠙⠛⠓⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⠒⠲⠶⠦⣤⣴⠟⠛⠒⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠀⣼⠁⠀⠀⠀⠀⠀⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠛⠀⠀⢹⡀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠉⣙⠛⠓⠒⠶⠖⠒⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⠃⠀⠀⠀⠀⠰⠛⠉⠁⠀⠀⠈⠉⠳⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡞⠉⠀⠀⠀⠀⠀⠀⠛⠉⠃⠀⣦⠘⠉⠓⢸⡇
⠀⠀⠀⠀⠀⢀⣠⠴⠶⠲⠶⣤⡀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⢠⠟⠁⢀⣠⣆⣀⠀⠙⣦⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⢀⡞⠀⠉⠙⠓⠦⣤
⠀⠀⠀⠀⡟⠀⠀⢀⣀⣀⣿⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣼⠀⠀⠀⠀⠀⡼⠁⠀⢴⣳⡄⠀⢠
⠀⠀⠀⠀⢷⠀⠀⢸⣅⣀⣀⠀⠀⣸⠃⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠲⠶⠤⠶⠆⠀⢀⡴⠃⠀⠀⠀⠀⣼⢃⡴⠶⠦⠉⠀⠀⡾
⠀⠀⠀⠀⠀⠣⣄⠀⠈⠃⠀⣀⡴⠋⠀⠀⠀⠀⠀⢸⡇⠀⣄⡀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⣰⢫⡏⠀⠀⠀⢸⡄⡼
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠛⠒⠒⡞⠋⠉⠀⠀⠀⠀⠀⠀⢰⠏⠀⣳⣄⣀⣠⡞⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣼⣧⡀⠀⠀⠀⠀⣠⠷⣄⡀⢀⡀⠀⠀⠀⢠⡟⠀⣸⠧⠬⠯⠉⠙⣧
⠀⣠⡴⠒⠒⠶⢤⡀⠀⠀⠀⠀⢠⡶⠚⠋⠉⣿⠉⠀⠀⠉⢦⣄⡴⠊⠀⠀⠀⣹⡏⠉⠛⠲⣤⠺⢦⣤⣿⣛⣛⡛⠀⠀⣿
⣼⠃⠀⠶⠷⣦⠀⢹⡄⠀⣠⠞⠋⣧⠀⠀⠀⠸⣷⣄⠀⠀⢀⣿⣇⠀⠀⢀⡴⡿⠀⠀⠀⢠⡏⠓⢦⡘⠧⠤⡤⠀⠀⢠⡏
⣷⠀⠠⣟⠛⡋⠀⢠⡇⣼⠃⠀⠀⢹⡄⠀⠀⠀⢻⡈⢷⣄⣾⠁⢹⣆⡴⠋⣸⠃⠀⠀⠀⡾⠀⠀⠈⢻⣄⣼⠁⠀⢠⡞
⠘⢦⡀⠉⠛⠁⣠⠞⠀⡏⠀⠀⠀⠀⢷⠀⠀⠀⠈⣧⠀⠙⣿⠀⢸⡟⠁⢠⡏⠀⠀⠀⢰⠇⠀⠀⠀⢸⡏⠉⠙⠛⠛⢶⡄
⠀⠀⠉⠙⠛⠋⠁⠀⠀⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠸⡆⠀⣿⠀⢸⡇⢀⡾⠀⠀⠀⢀⡟⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣤⣤⡀⠀⢻⡀⡏⠀⢸⡇⣸⠁⠀⣠⣤⣼⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⢀⡞⠁⠀⠈⢷⡇⠀⠀⣷⠏⠀⠀⠹⣆⠀⠀⣶⠀⠀⣼⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠈⢳⡀⠀⠀⠸⡇⠀⢀⡟⢿⢻⡄⣴⢋⠀⠀⣿⡀⢠⡏⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠹⣆⠀⠀⢻⡀⣼⢁⡾⠸⠿⣛⣭⣗⠀⣿⡇⣸⠃⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢧⡀⠈⣷⠇⣾⠀⠀⠀⠹⢖⣯⠀⣿⣷⡟⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣀⣤⠴⠟⠛⠙⣟⠋⠀⠀⠀⢈⣩⠟⠀⣿⢹⠃⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠷⠚⠋⠁⠀⠀⠀⠀⠀⢹⣤⠴⠖⠛⠉⠀⠀⠀⣿⠸⣄⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠓⠖⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣤⠶⠛⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣦⣶⣴⣶⣦⣴⣦⣶⣶⣴⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶
⣿⣿⣇⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠀⠀⠀⣀
⠀⠀⢀⡀⠠⠓⡀⠀⠀⠄⠀⠦⠊⠛⢲⠤⠀⢀⣀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡴⠛⠉⠋⠀⠄⠀⣐⠐⢀
⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠟⠁⠓⠘⠇⠘⠋⢲⠞⠒⠁⠾⠁⠠⠈⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣸⠟⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠅⠀⠉⠒⠂⠀⠰⠀⠀⢠⠤⠀⠦⠀⠀⠀⠴⠂⢤⠄⠀⠚⠁⠘⠉⠉⠁⠀⢀⠀⠀⠁⠀⢸⢥
⠀⠀⠀⠀⠀⠐⠀⠀⠚⠠⡬⠑⠀⠸⠗⠀⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢠⡀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠥
⠀⢀⣀⣤⣄⡤⠀⠂⠀⠈⠀⠀⠀⢀⠀⠀⠀⠉⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠫⡄⠀⠐⠂⠀⠲⠌⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠌⠀⠀⢄⠘⢁⠀⠀⠘⠁
⠀⠀⠀⡐⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⡐⣒⠀⠀⠂⢀⡀⠀⡄⢸⡆⡀⠀⢄⠈⠉⠀⠀⢀⡴⠀⠨⠀⠀⠀⠀⠇⠀⠀⠀⣠⡄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⡀⠄⠀⡔⡷⠀⠯⠼⣧⢼⢦⠼⠷⠄⠀⠀⡖⠀⠀⠀⠀⠐⠀⠀⠚⠂⢠⠀⠈⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠎⠀⠃⠞⠚⠀⠀⠂⡇⠀⠀⠀⠀⠀⡄⠀⠀⢠⡀⢠⠀⠀⠀⢀⠆
⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢖⡦⢀⢻⠀⢾⡘⠺⠈⢿⡚⠊⠓⡆⠀⠋⠀⠈⠀⠀⠀⠀⠀⠠⠈⠘
⠀⠀⡀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡀⠛⢀⡓⠀⣉⠀⠋⠁⢂⡑⠷⠀⠀⠆⠀⠂⠀⠀⠀⢀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢨⠅⠀⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⡀⣠⠀⠀⠀⢠⡄⠀⠙⣓⠃⣼⠃⠠⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡾⠀⠦⡀⠀⠠⠄⠀⠀⢀⣀⣀⡀⠀⠀⠐⠊⠛⠀⠀⠀⠈⠀⠠⢀⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠂⠀⠀⠂⠀⠚⠋⠀⠀⠀⠀⠈⠀⠝⠲⢤⣉⣀⡀⠀⠉⠀⡀⠀⠄⠐⢊⠠⠸⢀⡀⠀⠀⠀⣀
⠀⠀⠀⣮⢧⢆⣄⠀⠀⠀⠀⠀⠀⠈⠫⠉⠁⠀⠐⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⠁⠁⠀⠁⢐⢄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣼⡃⠠⠠⠀⠀⠀⠀⠀⠘⢞⡛⣭⡴⣄⣶⠀⠀⠄⠀⠨⠀⠀⡆⢸⠀⡆⡆
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠳⣧⣾⣗⣻⡇⡮⠀⠄⠠⠸⠀⠀⠛⠘⠀⠃⠃
⠀⠀⠀⠠⠄⠐⠆⠠⠤⠀⠀⠢⣀⠀⠆⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠷⠍⠗⠀⢦⡤⢲⡀⠠⣆⠀⠀⠄⠲
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠙⡇⠀⠀⢤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡤⠀⡀⠀⠀⠀⠛⠀⠀⠲⠄⠀⠀⢀⡤⠘⣷⠀⠀⠀⢀⠀⠀⠠⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢀⡠⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠹⣄⠀⠀⠀⠀⠀⠈⣆⠀⠠⠀⡔⠁⠀⢀⠂
⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⢀⠴⠉⠷⡄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡞⠁⠀⠀⠘⣄⠀⠀⠀⠀⢀⠸⠀⠀⢾⣀⠀⢀⡎
⠀⢀⠤⠂⠁⠀⠺⡄⢇⠀⠀⢠⠋⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢲⠂⣰⠆⢀⣈⣳⣤⠀⠀⢋⣀⣀⣤⠾⢄⠠⢎⣀
⠀⠃⢶⡀⠀⢀⠤⠓⠋⠀⠀⠾⡓⠆⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣩⠃⠀⠀⠈⠚⠙⠂⠁⠀⠌⢿⣷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄
⠀⠸⣈⠠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⢰⡁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠴⠶⢈⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠖⡚⠁⠉⠁⠄⢠⣧⠰⠀⠀⠀⠀⠀⠀⠈⠦⠤⠔⢻⠀⡘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠉⣉⠒⠒⠒⠒⣈⠙⡀⠀⢠⣪⠔⢉⠄⢀⡠⠔⢢⠞⠀⡇⢣⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡷⠆⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⠀⠟⠀⠀⠀⠀⠙⣀⠇⠀⡞⣡⠞⣁⠔⠉⠀⠀⣯⣶⣠⠛⡄⢇⡄⠀⠀⠀⠀⠀⠀⠀⡘⢰⢼⠀⠀⠀⢀⠃⠙⠢⢄⡀⠀⠀⢀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⡄⠂⠑⠒⠒⠒⠂⠉⠁⠀⠀⠀⠉⠓⠚⠁⠀⠀⠀⠀⠰⠘⢣⠀⢸⡘⡐⡀⠀⠀⠀⠀⠀⠀⠇⣸⣼⠀⠀⠀⡸⠀⠀⠀⠀⠉⠑⠲⠤⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢱⠀⠰⠀⡋⡲⣄⠀⡼⠀⣿⡏⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢣⡀⢀⡅⡁⠈⡶⠁⢠⣿⣇⡀⠀⡎⠀⠀⠀⠀⢀⣤⡤⣀⣀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢘⠟⠀⠱⡎⠀⠀⠀⠶⠉⢇⣜⡠⣊⢧⡒⢶⠙⠺⡷⢧⠰⠞⣢⣎⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⡘⠠⡆⠀⠘⢆⠀⠀⠀⣠⠎⣡⡼⣶⡞⣩⣽⡭⢿⡍⡶⢮⡽⣴⡡⣃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢤⠖⠁⠀⢠⠁⠀⣷⠀⠀⣀⣹⠦⣞⡹⢾⡰⢎⠽⡀⢩⠠⠼⠒⡟⠀⢀⡴⠋⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠉⠀⠀⠀⠀⠛⣲⠀⡟⠖⠋⠀⣂⡰⢣⢃⡜⡇⢲⣟⣹⣻⠀⠀⣠⠄⠊⠁⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⡆⠀⣠⠊⣘⡰⣫⣾⠴⠤⠦⠤⠄⠛⠂⠉⠀⠀⠀⠀⢠⠋⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢱⠎⠁⡴⢋⠼⠀⡗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠐⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⣰⠶⣲⡶⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡲⣄⣨⣶⠕⠊⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⡎
⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⣏⡴⠋⠀⡜⡝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⡼⣽⠃⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠊
⠀⠀⠀⠀⠀⣎⣀⣀⡴⠚⠁⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡴⠋⠒⠀⠒⠁⢤⣀⣀⡀⠀⠀⠀⠄⠀⠾⠤⠤⣀⣀⣀⠀⠀⠠⢊⡤⠔⠋
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠓⢄⣀⠀⣀⣀⠤⠤⠒⠂⠉⠉⠁⠈⠑⣄⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢐⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠤⠤⠤⠤⠤⠖⢚⣻⠿⢆⠀⣀⠤⠔⠒⠋⠀⠈⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⣀⡀⠤⠔⠊⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣁⣉⠀⠤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀⣀⡀⠀⣀⣀⠀⣤⣀⡀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⠂⠈⠉⠐⠀⠉⠉⠒⠀⠉⠁⠐⠉⠁⠀⠈⠍⠈⠉⠩⠚⠋⠙⠉⠛⠒