Harvest Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


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

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠒⠮⣉⡽⢁⠜⣰⠋⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⢞⠀⡞⠀⠉⣆⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠤⠒⠀⠉⢙⠗⢖⠋⠁⠀⠀⠀⠀⠢⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⡰⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡖⠁⠀⠀⠉⡰⠖⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⠻⣕⣲⠔⠓⠒⠉⠉⠉⠉⠉⠘⠁⠀⠀⠒⠂⠤⠤⠤⠄⠀⣀⣠⡀⠀⠀⠁⠀⡄⠀⠳⡶⠶⡏⠈⣶⠓⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢲⣼⡦⢬⣷⣀⢰⠀⢤⣀⣀⡀⠀⣀⣠⣤⣤⣤⠤⠴⣖⠈⠉⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⢠⠛⡋⠙⣏⠁⡿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢲⠤⡀⠀⠀⠉⠙⢦⡈⠁⠉⠉⠡⠉⠐⠀⠉⠉⠒⢤⣈⠁⠐⠂⠀⠀⣀⡀⠸⠊⣸⠦⣾⠓⡋⢻⡉⢹⣦⣼⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡈⠲⣄⠀⠀⠀⠈⠳⢤⡀⠠⠀⠀⠀⢀⠀⠄⠀⠈⠛⢿⡃⠀⠀⠀⣠⠖⠛⠛⠒⣿⡂⠙⠳⢾⣉⣤⣼⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠐⣄⠀⡙⢲⠤⣄⠀⠀⠑⣦⣄⣀⠀⠀⠈⡀⠀⠄⠀⠂⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⣯⠉⡤⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂⢾⡖⠓⠒⠒⢾⡀⢈⠂⠐⢈⠉⠒⢤⡈⠳⡉⠓⠦⣤⢀⡤⢤⣬⣠⣐⡠⣳⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠦⢿⠄⡟⢢⡆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⡗⠤⢄⣄⠨⠻⣷⠶⠶⠶⣛⡯⠭⠤⣼⣾⡇⠤⠤⣀⠀⠀⢀⡞⠁⠀⠈⠓⣏⣹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡊⠀⢀⠂⡁⠀⠈⢳⣄⣉⠁⠀⠈⢧⠀⡜⠁⠀⠀⠀⠀⠿⠄⠀⠀⠀⢱⣴⠟
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢧⡙⢦⣄⡀⠀⠀⠀⢀⠻⣟⠛⠳⠶⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠓⠤⣌⠳⣌⠛⢶⣀⣠⠂⢁⠈⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠤⣤⠴⠛⠁⠀⠀⠀⠙⠲⠼⣆⠀⠉⠙⠛⠶⠖⠞⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⣀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⣾⣿⣷⣤⣿⣿⡋⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠃⠀⠀⠛⠃⠀⢰⣦⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⣿⣀⣿⣿⡟⢻⣿⣉⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣤⠀⠾⠇⠀⢠⣤⠀⢶⠆⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣷⣾⣿⡿⠻⣿⣷⣿⣿⣿⣏⣈⣿⡿⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠉⠀⠀⣤⡀⠀⠁⠀⠀⠀⠿⠂⢀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣹⣇⣸⣷⣶⡿⣿⣿⣀⣿⡿⠿⣿⡄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⠗⠘⠿⠀⠉⢁⡀⠀⠾⠇⠀⣠⡀⢛⣯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⣶⡶⠾⠏⢻⡿⠿⣿⣤⣾⣿⡿⠿⣷⠶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠉⠉⢉⣉⣠⣧⠀⣠⡀⠛⠃⠀⠀⣀⡀⢉⣅⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠻⣿⣿⠀⠀⠀⠀⠑⠖⡻⢿⢹⣏⠷⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⢰⠀⠀⣸⣿⣿⣿⣷⣋⡥⣀⠆⠀⢂⡙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢱⣿⣿⡄⠀⠀⢀⠀⡀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠹⣿⠀⢠⣬⣥⣥⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢰⠀⢹⣿⠛⠚⠛⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠈⣿⣿⣿⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡆⢸⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠥⠤⠠⠠⠤⠦⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣽⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠤⢤⣦⣶⣴⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠀⠀⠈⢀⣠⠶⠶⣦⠈⠙⠻⠏⡟⣾⡆⠀⠀⠀⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡲⠋⠽⠁⠀⠀⠈⠀⠀⣀⡄⣀⣀⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣁⣴⣷⣾⣿⣵⣶⣦⠀⢠⣤⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠘⣿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⣿⣷⣽⣿⣿⣿⠛⠛⠁⠀⠀⠉⠉⠀⠈⠀⠀⢀⣤⣼⣤⡘⢿⠇⣴⣿⣿⣦
⠀⠀⠀⠀⣰⣧⣼⣷⣤⣀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠃⣄⠀⠻⢿⣿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⡀⣀⠀⠀⢀⢀⢀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢰⠿⠀⠀⢰⣇
⠀⠀⠀⠀⠙⢿⣿⠇⠀⣩⠀⠀⠀⠀⠀⠇⠿⠀⠳⠸⠺⠈⠇⠨⠇⠈⠳⠀⠇⠀⢠⢯⠇⣀⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⣸⠟⢰⣾⣿⣿⡆⣠⡀⠀⠀⠀⠀⢠⡄⣤⢠⡀⡄⣤⠀⠀⠀⠀⠀⢈⠁⢸⣿⡿⠛⣿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡋⠱⠟⠃⠀⠀⠀⠀⠘⠁⠛⠀⠁⠃⠛⠀⠀⠀⠀⠀⠌⢀⣼⣥⣠⣦⢈
⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢎⣤⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⠿⠛⠘⣿⣿⣿⢿⣿⢿⣿⣿⣤
⠀⠀⠀⠀⠀⠛⠿⣧⡻⣿⣿⣿⣟⣫⡿⠋⢀⣤⣶⠆⠀⠀⠀⠀⠙⠛⠉⠀⣰⡁⠈⠙⠻⡀⠉⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠋⠉⣩⣴⣾⣿⡿⠋⠀⠀⣄⠀⣆⠀⠀⠀⢠⣿⣷⠀⣿⠀⠡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠁⠀⠈⠀⠀⠀⢉⡧⢀⣤⣿⣿⣿⠀⢯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠛⠁⠀⠉⣓⠀⣀⠠⣶⠁⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠈⠙⠛⠁

⣿⡿⢿⣿⠿⣿⣿⠿⠿⠿⠛⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⢿⠿⠻⠿⢿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡏⠂⢙⠻⣿⠿⠶⠒⠊⡞⣿⠄⣉⣅⠀⠀⠿⠇⢀⠀⠈⡆⠀⢀⡄⠠⠃⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⢀⡁⡔⠂⠙⡴⢷⡈⠀⠀⠘⣿⣷⡤⢁⠀⠀⠘⠋⣀⡀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸
⣿⡇⣜⠋⠉⠑⠤⡄⠀⠘⠛⢦⠀⠀⠸⣿⠁⡏⠀⠢⠀⠀⠀⠉⢹⢶⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣿⣿⡉⡧⣀⠁⠴⠴⠛⠻⢧⠀⠲⡗⢠⠷⠀⠐⠢⠀⢠⠀⠀⠈⢿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡆⢻⣿⡗⡁⣸⣆⠠⠀⠀⢄⣿⣿⡴⠙⢏⠂⠀⢾⡄⡀⠀⢃⡀⣀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣬⡉⠁⠀⢹⣿⡇⠀⠐⢻⣿⡏⠀⡀⠈⠀⠀⠀⣀⠙⣦⣋⠈⠩⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠂⡀⠀⢸⣏⠈⠙⡥⠀⠄⠣⠀⠀⠀⠀⠀⠙⠁⠀⠀⣼⣿⢠⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡇⠀⠒⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠌⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⢰⡀⢀⣐⡿⢿⡞⠋⠛⣿⣷⣦⠀⠀⠀⡄
⣿⡄⠈⠀⠀⡄⡀⠀⠀⡀⠀⠈⢀⣾⠟⢿⣷⠀⢰⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⣿⠎⠀⠈⠛⣹⣆⣀⣈⡍⠀⣬⡿⠿⠖⠀⠀⠳⣦⡄⠀⠀⠀⠀⢰
⣿⣤⡴⠀⠈⠀⠘⢦⣤⠁⠀⢀⣼⣿⣶⣾⣿⡧⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡀⠀⠀⢀⣿⣿⠈⠀⠀⢀⣁⡐⡧⠀⠀⠀⣼⣿⡇⡀
⣿⡇⢱⣶⣝⣿⡤⠾⠠⠀⠆⠬⣿⡏⠙⠉⣿⣇⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡋⢴⠂⠤⠄⠤⢀⣀⣼⣿⣯⣀⣠⣴⣿⣿⠱⠷⠄⠀⠀⣝⡛⢪⠀⠀⠀⠀⢸
⣿⡇⠈⠁⢈⡏⠀⠀⠀⠀⠀⠘⠛⠃⠘⠀⠛⠃⠉⠉⠉⠛⠛⠳⠄⠄⢀⡀⠀⠀⠷⣮⣆⣀⡇⠀⠀⠀⠀⢸⠂⠀⠀⣾⠀⢠⣾⠂⢨⣿⢀⣸⣧⠄⠂⢀⣠⣤⣾
⣿⣇⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠉⠐⣆⣿⣿⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠁⠛⡟⣿⣿⣿⣿⡯⠇⢀⠈⠉⠉⡉⠈
⣿⣗⣤⠬⠥⣀⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⠲⢬⡒⢬⣑⠢⣕⡲⣅⣚⠙⢛⠁⢶⠀⠀⠄⠀⢠⡄⠀⠀⣤⠄⢴⣶⠟⢿⡟⠛⣿⠹⠉⠀⠀⠀⠀⢰
⣿⠗⣒⣉⡭⠥⠔⠒⣊⣉⠠⠤⠀⠂⢀⡀⠀⠀⠀⢀⣈⣳⣦⠽⠶⠞⠛⠋⠉⠩⠁⡀⡘⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⢸⣿⠀⣸⡇⢠⡏⠀⠁⠐⠀⠀⠀⠈
⣿⣏⣥⠤⠶⠒⣋⣩⡥⠴⠖⢒⣉⣩⣤⠴⠶⠚⠛⠉⢁⠠⠄⠀⠈⠉⠁⣠⠐⡶⠚⢣⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⣿⠇⢸⡇⠀⠀⢀⠀⠀⠀⠘
⣿⣧⠴⠖⠛⣋⣩⣤⠶⠖⠛⠋⠉⠀⢀⠀⠒⠁⠀⠀⢠⠴⠀⠘⠁⢀⡐⠃⠘⠃⠀⠸⢤⣅⠀⡀⠀⠀⠀⠀⡀⠀⠀⡇⠀⢸⡏⠀⣿⢀⣼⣠⠼⢠⣇⠄⠀⠀⢈
⣿⣧⠶⠞⠛⠉⠁⡀⠤⠀⠀⠀⠀⠀⠀⠛⢛⣿⣦⡀⠀⠀⠀⠀⢈⠀⢀⡀⡀⠀⠂⠠⣘⣿⠄⠀⠀⠁⠀⠀⠁⠀⠈⠉⠒⠋⣹⣿⠛⠉⠿⠇⠰⣿⠿⣄⡀⠀⢰
⣿⡇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢠⢤⡀⠀⠌⠛⠛⠁⠀⠀⠀⠄⠈⠿⠛⢂⠀⠀⠀⠀⡄⠀⠀⣤⣀⣦⣴⡇⠀⠀⠀⣸⣷⢨⠀⠀⡀⠐⠋
⣿⡇⠀⢀⡠⠀⠀⠀⠀⠀⠐⣦⣷⡤⠀⠀⠀⠀⣄⡀⡁⠀⠀⠀⠀⠀⢀⠔⢒⣁⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀⣉⠀⡰⠏⠀⢀⡼⢧⠀⠀⢠⣿⡿⣣⣆⡀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠀⠀⠰⠊⠉⠉⠓⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⣬⠒⠁⠂⠀⠉⠂⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⠀⠟⠀⠀⠁⠀⠚⢋⠁⠉⠉⠁⠀⣠⠘
⣿⡇⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⢰
⣿⣧⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⡿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠶⠖⠋⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢶⣶⣼⣆⠀⠀⠀⢘⣧⣤⡶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣠⠶⠛⠉⣩⡽⠛⠋⠉⠉⠛⠻⣭⡉⠙⠳⢦⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠟⠁⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⢷⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠹⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡏⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⣧⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡤⠶⠿⢦⡦⡼⠗⢦⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠛⣲⣦⣀⣟⠀⣠⢼⠷⠲⣄
⠀⠀⠀⠀⢰⣋⣀⣀⣾⠻⣣⠖⠻⣼⣁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⡝⢦⣰⠃⠧⠟⠹⠿⢻⡀⠀⠀⢿⡀
⠀⠀⠀⣾⠉⠁⣸⡽⠿⣤⡇⠀⠀⠸⣏⣠⣴⡒⠻⢦⣀⣀⣀⣀⣀⠀⢀⠀⢰⡓⠟⠀⠉⠀⠘⣿⣀⣀⣀⡀⠀⣠⣙⣦⢴⡞⠓⠲⢤
⠀⠀⣀⣼⣦⣞⣡⡤⠤⠤⣧⠀⡶⢶⠇⠉⠀⢹⠆⡴⠃⠀⢰⡏⠀⠙⢹⣷⣏⠀⣀⣀⢸⡳⣤⢻⣞⠁⠈⠉⠳⣿⠈⠀⠀⣿⠀⠀⣀
⢤⣬⡿⠉⠸⡅⠀⠀⠀⠀⢾⠳⠟⠀⠀⠀⢀⣼⡿⣥⣀⣀⣾⣅⡀⠀⠀⠁⣿⡶⠿⠈⠉⠁⠘⣿⡿⣄⡀⠀⠀⢸⠀⠀⣠⡾⠷⠯⣅
⠀⠈⢉⣙⣿⡳⣄⡀⠀⠀⠈⣳⣄⠀⢀⡤⠬⠗⠀⣸⠋⠉⠉⠛⢦⡀⠀⢠⡟⠀⠀⠀⠀⢀⣀⢸⡀⠀⠉⠿⣖⠚⠶⡏⠁⠀⠀⠀⢈
⠀⠀⠈⠙⠻⠶⢶⠭⠭⠿⠿⠏⠈⠓⢮⣽⣄⣠⠾⣅⠀⠀⣀⡤⣾⣥⠴⠾⠳⠶⣄⡴⣆⡞⠙⠞⠓⠒⠚⠏⠻⠛⠲⠿⠶⠤⠤⠖⠋

⠀⠀⠀⠀⠄⠀⠀⠀⠰⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⢸⣣⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠡⣼⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆
⠀⠀⡴⠀⠀⠀⠀⠠⢻⠐
⠀⠀⠂⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⢹⠆⠀⠀⢀⣤⣠⡏⠉⠃⠀⠈⡗⠒⠀⠐
⠀⠀⠀⠒⠶⡶⢼⡶⣶⣦⡀⠀⠀⠀⠂⠀⠀⠀⠂⢤⠤⣘⣤⡟⠲⡁⠠⠒⠱⠋⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⢅
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡌⢿⠄⠈⠀⠀⠀⠀⠀⠀⡸⢐⠛⠀⠀⢀⣄⠀⠀⣤⠐⠉⠁⠀⢠⣾⢻⣻⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣣⠀⡇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠈⠀⠀⠀⠏⠈⠲⠒⠊⠉⠙⠋⠁⠀⠀⠀⠈
⠈⠺⡄⠀⠀⠀⠜⡿⠾⡟⠦⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠄⠀⠀⠉
⠀⠀⠈⢩⠖⠀⠀⡅⠀⢀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠈⠀⠀⠀⠋⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠤⢰⡤⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠶⠀⠃⠆⠀⠇⠶⠘⠰⠆⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⢠⡴⠶⣶⠉⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠄
⢀⠔⠚⠂⠀⠈⠀⠀⠜⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⣤⣾⡛⠛⠯⣃⢄
⢸⠄⠀⠀⠀⢀⣤⣤⡄⠀⠐⠋⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣀⣴⡜⠛⠦⠀⠙⠦⡈⢳⣃
⢀⠀⠀⢀⣨⣿⣭⣷⠁⠀⠀⠠⢄⠀⠀⠂⠐⢀⡀⠉⠀⠀⠀⠀⠆⠠⢤⣿⣤⣔⠉⠀⠇⠀⠀⠑⠄⠀⠱⠄⣿
⠈⠟⠉⠁⠀⠈⠉⠀⠀⠀⢀⣀⠈⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢡⠈⢇⠀⠀⠀⠀⠀⠈⠆⠀⣧⡟
⠀⠀⡀⢀⠄⠀⠀⢠⠀⠀⠀⠁⣠⠎⠀⠀⠀⠠⠀⠀⠀⠀⠢⣀⡀⢈⠀⠀⡰⢀⣿⠄⠀⠐⠀⠀⠀⢸⡴⠋
⣤⣤⣥⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣤⣽⣶⣶⣿⣬⣥⣤⣵⣤⣤⣵⣦⣥⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⠂⣄⠀⠀⠰⠀⠀⠀⡄⢀⠀⢠⡀⠀⠀⠀⠄⢠⠄⠀⢀
⠀⡮⠷⠀⣠⠈⠀⠀⢀⡀⠀⠙⢆⠀⠈⠁⠀⡛⢌⡀⠀⠤⠀⠀⢻⡁⢲⠀⠈⠱⠀⢁⡁⠀⠺⠛⠁⢀⠖⠀⠘⠀⠀⠫⢠⣫⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⠺⠀⠠⠀⠀⣴⠼⠧⢹⠀⣁⠁⡀⠐⠆⠀⠂⠀⠀⠉⠐⠀⠀⠀⡀⡂
⠀⡐⢖⠩⢀⠀⠀⢀⠴⠒⠈⠉⠉⠓⠂⠀⠆⠀⣄⣀⣠⡄⠀⣈⠉⠉⠁⠀⣤⠀⠃⡀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣠⣀⠈⢉⡆
⠀⣚⣅⠤⠑⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢾⣿⠄⠀⠀⠄⠀⠀⠘⠀⠀⠇⠸⠀⡀⠉⠀⠄⠀⠠⡀⢉⠁⠀⠁
⠀⠠⡈⠁⡐⠀⡉⠀⠉⠉⠁⢻⠂⠉⠉⢁⣍⡁⠘⠒⠊⠀⢀⠁⠀⠤⠄⠀⡐⠂⣂⠀⠂⠁⠀⠀⠈⡀⡋⠁⠈⠏⣈⣁⠄⢶⢀
⠀⠠⣈⡁⠀⠀⢹⠃⠉⠀⠀⢸⠀⢤⠀⠨⢱⠀⠀⢰⢈⣄⠊⠀⠀⠀⠀⠀⠂⠀⠉⣉⠰⢢⡄⠀⢀⠁⠁⠀⠈⠱⠛⠓⠀⢠
⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡇⠀⠀⠀⠀⢈⠀⠀⢀⠀⢀⠄⣴⡀⠀⡀⡀⠀⡀⠘⠛⠃⠀⠀⡀⠠⣀⠂⠄
⠀⠠⠁⠀⡄⠂⠁⠀⢀⡀⢴⡸⠀⣀⠀⠠⠈⡇⠀⠁⠀⠀⠘⠀⠤⠚⠃⢀⣸⠁⡱⠀⢠⣴⠀⠹⢄⠀⠀⢀⠀⠀⠠⠐⠐⡀
⠀⢐⡂⠀⠈⠈⠀⠀⡉⠀⠀⡀⠘⠀⠄⠀⠠⠐⠄⠄⡀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣤⣌⡄⠀⠒⠋⠀⢀⣄⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠁⠐⠀⠺⠗⢀⢀⠁⠀⢀⠀⠠⠂⠀⢈⠂⠡⠀⠀⠀⠀⢠⠄⠀⢶⣦⣤⡄⠀⠀⠁⠀⢀⣶⡤⠐⢀⣉⢓⠄⠀⢀⠄
⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⠈⠂⠀⠁⠐⠀⠤⠐⠂⠀⠠⠀⠢⠄⠀⡈⠀⠀⠉⠀⢰⡇⠀⣄⢻⣺⣟⣃⣞⣿⣯⡄⢀⡀
⠀⠀⠀⠀⢂⡁⡀⠀⢦⠀⠀⠢⠘⠀⠀⡅⠀⠀⠂⠀⢈⠁⠀⢀⠢⠀⢐⡀⠂⠀⠀⠀⠀⠈⠁⠘⠉⠃⠈⡏⡍⠋⠈⠁⠑⠀⠁
⠀⢌⠤⠀⠈⣄⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢜⠀⠈⠀⠀⠀⠑⠀⡀⠂⠀⠀⡀⠀⣤⣄⡄⠀⠀⠃⠀⠀⠠⠀⠀⠦
⠀⠠⠎⡄⠀⠘⠀⠀⠒⠋⢀⠀⠃⠉⠘⠀⠃⠉⠐⠁⡀⠈⠁⠀⠀⠀⠀⡀⠈⢴⡥⠀⠀⠃⠀⠁⢛⠃⠀⠀⠀⠀⠂⡀⢠
⠀⢁⢚⡠⢡⠀⠀⠀⢀⠀⠉⢀⡁⠀⠁⠉⠁⢈⡁⠈⠁⣠⠘⠠⣀⣀⠶⠃⡀⣈⠈⠁⠀⠀⠀⡀⠘⠶⡄⠓⠃⠠⠀⠉⠠⠠⠆
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣀⠀⠀⠀⢠⠅⡊⠁⠀⠀⠀⠀⢉⡁⢁⠁⠀⠂⠀⠄⠠⣌⡀⠂
⠀⡎⠀⠀⠀⠆⠀⠰⣶⡴⣧⡄⠩⠤⠀⠀⠐⠋⢱⠀⠀⠈⢐⠃⠀⣀⠀⠐⠒⠁⠀⠒⠂⢠⠀⠀⢂⡊⠒⠀⠀⠀⡐⠀⠉⣀⡀
⠀⠀⠘⠈⠣⠀⠀⠀⠋⡏⠉⠇⠀⠀⠁⠄⠀⠀⢊⢄⠀⠁⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠇⠐⡁⠀⢠⠀⠀⠀⠩⠐
⠀⠀⠦⠀⠄⠀⠲⣒⠚⢁⣐⡇⠀⠀⠤⠀⠀⠄⠀⠽⠇⠀⠠⠄⠁⢀⠀⢀⡂⠈⡆⠙⠂⠁⢰⠘⠀⢩⢨⠅⠀⠒⠀⠀⠀⠀⠅
⠀⠀⣀⢠⠀⠀⢠⡌⠉⠉⠉⠁⠀⠄⣷⠲⠀⣠⢶⣖⠤⣄⠀⠲⠆⠀⠀⠶⢄⠀⠀⠀⠀⢤⠖⣆⠀⠒⠰⠂⠀⠀⠀⠐⠔⠁
⠀⠀⢘⠬⠆⠀⢈⠉⠢⠀⢀⠈⠀⠀⠀⠀⢨⣶⠋⠉⠙⢶⠆⠀⠄⢀⠘⠈⠁⠀⠀⠀⠀⢊⡗⢤⠀⠀⠂⠀⠤⣥⢀⢤⠀⠀⢄
⠀⠀⠈⠓⡯⠂⠈⠠⢀⠀⠀⠉⠀⠗⠀⠀⠈⢭⣷⣠⣶⡿⠂⠀⠂⢁⠀⢀⠀⠘⠉⠀⠀⠼⠧⣐⠀⠂⠀⢤⠀⠁⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠐⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠈⢑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠥⠚⠒⡶⠙⠏⢛⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡙⠒⠠⡖⠤⠃⠀⢢⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡠⠒⠉⠉⠉⠙⠳⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢹⠁⠀⠀⣠⠤⣄⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⡶⢘⡆⠀⠘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⡠⠞⠁⢀⠔⠁⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢶⡒⠒⠒⠲⢤⣀⡶⡇⡄⡼⠂⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢯⠀⠀⠀⠀⡇⠀⠀⣀⡀⠬⢧⣀⣨⣇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⣤⢤⣞⠥⢀⠀⢱⡋⠣⣀⣧⠔⠉⠀⠀⠀⠀⠈⢳⡇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢋⠀⢀⣀⡇⢀⠜⠛⠢⢌⣑⣾⠀⢈⠵⠊⠠⠄⡀⠀⠈⠑⠒⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢙⠞⣄⠀⠀⠈⣆⡼⢠⡇⡡⠔⠒⠒⠢⣽⡽⠂⠉⠐⢄⠀⠀⠈⠳⣄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⡏⢯⣱⠺⡥⡀⣾⣻⠏⢸⡀⠤⣐⠞⢡⠤⠽⢃⠉⠉⠲⣄⠈⢳⠀⠀⠀⠀⢳⡀⠀⠀⠈⢣⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠠⡁⠀⠁⠀⠀⠀⢣⢀⣹⡀⠀⡸⠙⣷⡶⠋⠀⡜⠁⠀⡎⠀⠀⠀⢣⠀⠀⠈⢧⢸⡤⠖⢤⡀⠀⢳⡠⠤⢀⠈⣇⡼
⠀⠀⢀⡤⠤⠴⠒⣳⡦⠤⣄⣀⣀⡼⣃⠀⣸⣧⠀⠀⢻⠀⠀⣸⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⢸⣼⡧⠂⠀⢱⠀⡇⠀⠀⠠⣽⠋
⢠⠞⠁⠀⠀⢐⠏⠀⢸⠤⣚⠉⠉⡱⠶⠭⣄⣈⠓⢤⡈⢦⠀⣇⠀⠀⠈⡇⠀⠀⠀⠀⡇⠀⢀⠞⠁⠱⡄⢠⡾⠒⠓⠶⡂⠀⠀⢧
⣏⠀⣄⠀⠀⡞⡲⠖⢻⢀⢈⠀⢸⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠼⣄⣀⠀⢱⡀⠀⢀⣰⡥⠖⠛⠶⠶⠶⠿⠿⡄⠀⠀⠀⢸⢄⡀⠀⡇
⠘⠳⠟⠀⠀⠯⠤⠄⠒⠛⠁⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠗⠦⢌⣀⣉⣂⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⠰⠯⣅⠀⠀⣤⢀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠖⠲⢿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠲⣆⣤⡀⠈⠋⠀⠒⠀⣘⣷⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⡋⠈⢷⣆⡀⠀⣴⣠⣼⠹⠛⠂⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠏⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⢆⡀⢉⠛⠦⣌⡛⠙⠳⠚⠶⣤⣖⠑⠀⠉⠉⢀⣄⠘⠀⣀⠀⠀⠀⠀⢆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣧⠀⠉⢀⡴⢆⡈⢻⣿⣦⣆⣀⡼⠟⢫⠑⠄⠹⠞⠇⠀⠀⠀⠀⢠⠂⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠾⣿⣿⣦⢀⡖⢁⠻⢿⣀⣈⡁⠼⠊⣽⣿⣷⣄⡀⠀⣶⣦⣴⡄⠀⣀⡄⠀⠀⡄⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠑⠀⢹⠑⣯⣧⣼⣾⣿⣯⡿⠈⢻⣿⠟⠉⠉⢛⣒⠉⠛⠉⠈⠙⠁⠀⠞⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⢸⠀⢈⣴⠞⠻⢷⣿⠟⢦⡘⠿⠀⠀⠉⠉⠳⣶⣦⠤⠀⡀⣀⣤⣞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⣼⣿⡭⢁⡀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢜⢻⠇⠀⣿⣿⠁⠹⣿⡶⠤⡤⠂⠛⠃⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⣆⣈⠗⢚⢿⡟⣄⠀⡟⠀⠀⠀⠀⠀⠀⠀⢶⠷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⠻⠀⠀⢨⣼⠇⠘⣶⠁⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⣿⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢻⡄⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢷⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠷⠤

⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⣀⠀⠀⠠⠀⣈
⠶⠶⢄⢆⣺⣯⠀⠉⢻⢿⣧⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⡓⠒⠐⠓⠂⠀⢠⡄⠀⡀
⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠉⠉⠒⠒⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠀⠁⠀⠠⣀⠑⣾⣾⠃⢀⣧⢰⡄
⠀⠀⠀⠂⠂⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠛⠻⠷⣶⣤⣀⢠⠀⠀⠀⡂⠀⠈⣦⠀⢹⣧⠘⣿⠀⣸⡏⢸⠇⠈⠋⠉
⠀⢀⢀⠀⠀⠄⠂⣀⠀⠈⠐⢄⡈⠑⠀⠀⠀⠀⣀⣀⡤⠼⠟⠛⠛⡄⠀⠀⡆⠀⠀⢻⡇⠀⢿⡆⢿⠠⢿⣁⡿⠀⠀⠀⠐
⠀⠀⢐⠀⡀⠠⠑⢀⠂⡄⡡⢄⣙⡦⠴⠒⠊⠉⠁⠀⠀⠀⠀⣠⡀⢃⠀⠀⢧⠀⠀⠸⣿⢀⠘⠣⣧⠀⠀⠈⣶⡾
⠐⢰⠠⠁⠊⡀⢂⣀⡦⠖⠛⠉⠀⠀⠀⠀⠀⠀⠁⠈⣜⠀⠶⠺⠥⣄⣢⡀⠈⠄⠀⠀⢿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠤⡉⣅⣮⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⡀⠈⠁⠀⠂⠐⠂⠀⠀⠈⠉
⠴⠛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠈⠛⠛⠛⠓⠀⠠⠀⠀⠀⠠⠀⠀⠀⡜⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠀⠀⢠⣀⠠⣿⣿⠀⠀⢨⣶⣦⣀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢶⡿⠀⠀⢘⢿⣷⣿⣯⣶⣶⠀⠛⢿⣯⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠘⣾⡷⠂⠀⠛⣻⡿⣿⣿⣯⡀⠰⢶⣿⠿⣇⣴⣤⡦⠹⣿⠇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⠚
⠀⠀⠀⡀⠀⠀⣠⣾⠀⠈⠀⠘⠃⢩⣤⣤⣴⡄⠀⠉⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠃⠀⢢⠇⠀⢀⠄⠀⢀
⠀⠀⠀⣿⣧⣰⣿⠃⠀⠀⠀⣤⣾⣿⣿⣿⠟⢀⣴⣾⣯⡀⢰⣿⣧⠀⠀⠀⠠⡀⢰⠁⠈⠣⣀⡼⠒⠋⠁⡠⠏⠁
⠀⠠⣤⣼⣿⣿⣷⣶⡷⠂⠀⠛⠛⠟⠛⠉⢠⣿⣿⣿⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠘⠢⣀⡀⢸⡇⣀⠤⠯⣤⠤⠤⠄
⠀⠀⠀⠀⠉⠻⣯⡀⠀⠀⢼⣿⣦⣶⣿⠀⠀⠉⠙⠻⠿⠛⣀⣧⣀⠄⠀⠀⠀⠀⠉⠙⠉⠙⣾⡿⠁
⠀⠀⠀⠀⣠⣤⣄⡁⠀⢀⣼⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⠀⣺⣷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣆⠈⠛⣿⣿⠟⠉⠀⠀⠀⠀⢿⡿⠀⢺⣿⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⡉⠉⠉⠉⠀⠀⠙⠁⢰⣤⣄⠀⠀⣤⣬⣶⣆⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠾⠟⠣⣦⡿⢿⣠⣤⡤⠀⣾⣿⣿⡇⢸⣿⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠛⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠈⣦⣤⡄⢀⡀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⡦⠀⠀⢤⣬⣧⢠⠶⡖⣐⡁⠈⣻⣶⣕⠙⢷⣢⣤⡀
⠀⠀⠀⠀⠀⠀⢾⠄⣼⡧⠥⡴⠻⣾⣿⣿⣿⣿⣿⠿⠀⢾⣿⣿⣞⠷⣄⠻⣿⣿⣆
⠀⠀⠀⠀⠀⣠⣿⣷⣿⣷⡠⣟⠀⣽⡏⠀⠀⣿⣯⠀⠀⠀⣿⠟⠻⠷⣧⡴⡽⣿⣿⣆
⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡷⠂⠀⠛⠛⠿⣶⣾⡇⠀⠀⠀⢹⣯⣿⡌⠻⢿⣁⡀
⠀⠀⣿⣿⣿⢿⣿⣿⣛⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⠀⠈⢻⣿⣦⣴⣶⣿⣯⣿⣿⣓⣄⣈⣷⣀⣀⣤⠄
⠀⠀⣿⣿⡏⠒⠺⣿⣿⣶⣿⣿⣿⡷⠶⣰⣿⣟⣧⠀⣀⣼⣿⠟⠛⢻⣿⡿⠍⣩⣉⡉⠙⠫⣡⣴⠚
⠀⠀⠸⣿⣿⣷⣾⣿⣟⣛⣛⠋⣠⣬⣿⣿⣿⣿⣿⣿⣭⣿⣿⣶⣶⣾⣛⣿⣿⣿⢿⣿⣶⣦⣿⡿⡄
⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⡿⠦⠿⠻⠷⡿⡯⠽⣛⣛⣿⣷⣳⣭⣉⣿⢿⣟⢿⣿⠟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⡲⠂⡀
⠀⠀⠀⠀⠥⠂⠀⡞⠁⠂⠀⠀⠀⠀⢸⣁⡴⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠀⠚⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡘⢷⠁
⠀⢹⠰⡆⢳⡄⢀⠰⡆⠀⠀⠀⠀⠀⠐⠼⠉⠀⢀
⠀⠈⢗⣻⣽⡳⣧⠀⣯⠀⠀⠀⠀⠀⠠⣄⠦⠀⠀⠈⠀⠂
⠀⠀⠘⠛⠃⢻⡧⣸⠃⠀⠀⠀⠀⠀⠠⠟⠃⠀⠀⠀⡄⠀⠈⠲⣁⣀⡁⠀⡀⠀⠀⠀⠀⢠⠀⠂⠀⠁⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢢⣰⣅⣾⢠⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣤⣤⣸⢟⣼⣾⣥⣯
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠀⠤⠒⠁⠑⠠⠀⠀⠀⠀⠀⠀⠘⢟⠛⠛⡋⠛⠙⠻⠝
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⠀⢸⡄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠑⣄⣀⡀⠀⠀⠀⢀⣀⣀⠒⠁⠀⠀⠀⠀⠳⠦⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠀⠉⠒⠈⠁⢰⠦⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⢠⣤⣴⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠂⢀⢠
⠀⠀⣿⣿⡿⠛⠉⠀⠀⠀⠈⠙⢷⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⣴⣷⠀⢸⣿
⠀⠀⣿⣿⣃⣀⣤⣤⣻⢿⣦⣀⡀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠄⢰⠆⠀⣤⡄⠀⠀⠀⠉⣤⣴⢴⣆⣠⣆
⠀⠀⣿⣿⣿⣿⣿⠳⣯⡻⣮⡻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠀⠀⠀⠀⠀⠀⠉⢔⣹⣿⣿⡿
⠀⠀⠉⠀⠀⠻⣿⣷⣿⣿⣾⡯⠊⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⢘⣀⡠⠤⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠊⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠊⠀⢀⢤⡤⠆⢁⠠⢄⣰⡭⡄⣤⡤⣌⢑⡄⠀⢠⠀⠀⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣸⠉⠈⣖⠁⢹⢊⠇⢸⢪⡀⠀⣇⠀⢰⡏⠀⠘⠁⠘⠆⠉⡶⠂⢻⠤⢖⢃⠠
⠀⠀⠀⠀⠀⠀⠘⡤⠶⠀⢿⣧⠀⣽⠀⣜⢸⠀⡏⠁⠇⢠⠇⡇⢸⢹⠀⡴⠀⢀⡆⠀⡟⡄⢠⡄⠸⠂
⠀⠀⠀⠀⠀⠉⢨⠸⠸⠀⢸⡏⠀⣿⠀⣇⣾⠀⢧⠀⡇⢸⠀⡇⢸⢸⠀⣧⠃⠸⡟⠀⢷⠃⢸⠃⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠑⠊⠓⠤⠣⡀⢀⡀⠈⣿⠀⠈⠲⡇⠀⠉⠀⠈⡎⠀⢹⡀⢀⡷⠤⠺⢤⠎⢉⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠉⠙⠈⠢⠤⠔⢉⠒⠊⠒⠊⠑⠒⠁⠍⠉⠂⠀⠀⠀⡐
⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠰⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠂⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⢀⠄⠁⠀⠐⢀⣡⣿⡿⠀⠀⠀⠀⠀⠉⠆⠀⠀⠈⢀⠀⠀⢀⡀⠀⠘⡆⠴⠀⢄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣾⣿⠋⠁⠀⠀⢀⡀⠐⠃⢠
⠁⠀⠀⠰⠋⠙⣾⣿⠃⠰⠀⢀⡄⠰⠀⠈⠂⠀⠀⠀⢄⠀⢀⡃⠀⠀⠁⠀⠀⠀⠈⠁⠀⠂⠉⠀⠉⠀⠀⠀⠁⠀⢼⣿⠛⠛⠲⠒⠂⠈⠀⠀⡠⠄
⠀⠄⠁⠀⠀⡐⠉⠉⠓⠂⠀⠀⠀⠀⢢⠀⠀⠑⢤⣀⣸⣷⡏⢁⠀⠀⠀⠀⠉⢀⠀⠀⠀⠐⠦⡈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⣀⡀⠠⠔⠂⠀⠀⠰
⠃⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠈⠻⣿⡇⠀⠀⠀⢾⣶⣤⣌⣀⠆⣀⡀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠈⢀⢄⡀⠀⠀⠀⠀⠀⠉
⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠙⠃⠀⠀⠀⠐⠸⡿⢿⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⣈⣀⣨⣼⡿
⠈⠒⠀⠀⣀⠄⠀⠀⠀⠀⢀⡄⠀⠀⠔⠒⠁⠀⠀⠀⠀⠄⠀⠋⠀⠄⠈⠘⢇⠀⠈⠐⠀⠀⠀⠀⠠⢀⠆⠀⠜⠀⢀⠀⠀⠉⠀⢸⣿⡿⠀⡄⠀⠈⠁
⠘⠁⠀⢀⣀⠀⠈⣠⠀⠀⠀⠀⠀⢀⠀⢀⡠⠀⠀⠀⠐⠐⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠂⠀⠀⠀⠀⠌⠉⠀⠓⠂
⠀⠘⠢⢀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠀⣲⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠐⠆⠀⠀⠂⡀⠀⠀⠑⡤⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠁⠀⢀⠀⠀⡠
⠀⠀⠀⠈⠀⠀⠀⠐⡡⠈⠃⣠⣴⣿⣿⠖⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠀⠈⠂⠀⠘⠃⠀⠈⢀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠁
⠀⠀⢀⠀⠀⠘⢆⠀⠄⠃⠈⠙⠋⠉⠺⡤⠄⢀⡀⣀⠀⣀⡀⠀⠀⠀⠀⠈⢁⣠⠄⠀⠀⠄⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⡑⠀⣀⠀⠀⠀⢀⠀⠀⡆
⠀⠀⠀⠀⢶⣦⣿⡄⠀⠀⢀⠀⠀⢄⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣑⡄⢁⣀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠠
⠀⠒⠤⠠⠞⠻⠛⠿⠿⠀⠈⠁⠀⠀⡁⠀⠉⠀⠒⠀⠉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⡿⢿⡟⠐⠀⠀⠐⢂⡀⠀⠀⠀⠀⠀⠐⠂⠄⡀
⣀⣀⡀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡁⠠⠆⠉⠀⠰⡀⠀⢄⠀⠀⠸⠂⠀⠀⠀⠀⠀⠄⠃⠀⢨⠆⠀⠀⠀⠀⠎⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠄
⢀⡍⠀⣈⠀⠀⠠⠄⠀⠀⠰⠄⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠈⢀⠘⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⠀⢀⠀⠀⠀⠀⠀⠈⠀⠒
⠀⠀⠔⣿⡇⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢠⠄⠁⠀⠀⠀⠂⠀⠠⠆⠀⡀⠀⠦⢈⣷⣤⠤⠊⠀⠀⠀⠀⠔⠃
⠈⣠⠾⣿⣿⣂⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⢰⡀⠀⠡⠀⠰⠀⠈⠀⠀⠐⠊⠀⠄⠂⠀⠀⠀⠀⠀⢠⣼⣿⡿⢄⡤⠀⠀⠈⠀⢀⠆⠀⢐
⠠⠃⠀⡸⠁⠈⢡⠀⠈⢲⠀⡀⠀⡀⠀⠈⠢⢀⣠⣿⣶⡯⠀⠀⠀⠀⠀⢀⣀⠀⠘⠂⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⠛⠀⡀⠀⠀⣀⠀⡠⠆⠀⠀⢠
⠂⠀⠀⠐⠀⠀⠈⠀⠀⠘⠀⠀⠀⠙⠤⠄⠀⠊⢀⠋⢻⣷⡌⠀⠀⠃⠠⠝⣿⣦⣌⣠⠀⠀⠐⢆⠀⠀⠀⠃⠀⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠀⠤⠀⠈⠁⠀⠀⠀⠀⢠⠟⠻⡏⠁⠑⠄⠀⠀⠁⠀⣀⠀⢠⠖⠀⠀⢀⡈⢄⣤⣿⢇⠀⠀⠀⠘
⠀⠀⠐⠀⠀⢀⡀⢠⠄⠀⣀⠀⠀⠀⢀⠀⠀⠀⠘⠒⠠⠀⠈⠁⠀⠂⠀⠸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⢀⡔⠈⠙⣿⠿⣿⠀⡁⠀⠠⠄
⠈⠐⠛⠀⠀⠁⣠⠀⠀⠀⠀⢤⣤⣀⣨⣐⡦⠠⢀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠸⠃⠀⠰⠀⠀⢀
⠂⠀⠀⠀⠠⠀⢀⣤⡄⢀⠀⠨⠙⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⡀⠀⠀⠀⠀⠀⠋⠀⡄⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⣀⠄⠻⢤⣾⣿⡟⠅⠉⠀⠀⠄⠸⡄⠀⠉⠐⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠁⠒⠀⠈
⠀⠀⠀⠀⡘⠋⠙⡄⠀⠀⠀⠂⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⢀⠄⠀⠀⠠⣺⣿⠀⠀⠃⠀⠀⠀⠀⢄⡀⠀⠴⠅⠀⠊
⠀⠀⠀⠊⠀⠀⠘⠀⠀⠠⠀⠀⠀⢦⡀⠀⠑⠠⣀⠀⠀⠸⠁⠀⠘⠁⠀⠀⠐⠂⠀⢀⠴⢾⣿⣷⠀⠆⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠋⠀⠂⡀
⠀⠀⠀⠀⠀⣀⠁⠀⣠⠀⠀⠙⠀⠀⠀⠐⠂⠀⠈⠀⠀⠒⠀⠀⠀⢀⠀⠘⠁⠀⠀⠁⠀⢰⠟⠙⠲⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠉⠐⠀⠈⡇
⣆⠀⠀⢀⡔⠀⢠⠔⠁⠀⠀⠀⠀⠘⠂⢀⠤⠆⠁⠉⠒⠁⠉⠀⠀⠉⠀⡇⠀⠐⠀⠀⠀⠄⠀⠀⠸⠀⠀⣸⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⢀⠐⢢
⠀⠉⠈⠁⠁⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠐⢶⠀⠀⠀⠄⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢀⣠⣏⠱⡄⠀⠀⠀⢰⠁⠀⠀⠀⠈⠂⠀⠀⠀⢀⣦⣄⠀⠀⠀⠀⠾⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠻⡟⠀⠀⠀⠀⠀⠀⣀⠘⠀⢦⡀⠀⢀⠞⠛⢿⣍⣰⣦⡤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣹⡇⡼⢁⣼⣧⠉⠀⢀⢀⠛⣢⡀⢠⣇⠐⠁⠂⠀⠀⠏⡹⠃⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠇⢁⣀⣼⡋⢈⡄⠀⡯⠃⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠈⠐⢥⣞⡀⣤⠀⢰⣤⠤
⠀⠀⠀⠀⠀⠀⢨⠠⠀⢗⠏⠛⠛⠳⠀⢉⠀⠀⠀⠀⠀⠀⠀⡴⠶⠃⠀⡿⠷⠰⠁⠠⣿⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠⡄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣴⣤⣀⢰⣦⣷⣴⣿⢀⣤⣿⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⢻⣷⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡿⣻⣫⣿⣿⣿⣿⣟⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠻⣿⣿⣿⣿⣿⡷⡷⣟⣿⣼⡟⣫⣿⠟⣿⡝⣭⡽⣵⣿⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡾⠿⠷⠶⠛⠛⢯⣾⣿⣼⣿⣿⣿⣿⣿⣿⣧⣿⢇⢿⣎⠵⠺⠟⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢡⣵⣄⡦⠴⣶⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣶⣤⠘⠢⠶⢪⡉⠙⠠⠀⢘⣿⣿⣸⠟⠻⢿⣿⣿⣿⢿⠿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⣏⠊⠉⠀⢙⠩⣶⠀⠀⠀⣽⣿⢠⣀⣀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠰⢑⠢⢀⡀⢡⠀⠀⢸⣿⣃⣀⣠⣴⣿⢧⣿⡄⠀⢠⠾⠟⡪⣿⣿⡿⢛⡵
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⠀⡇⠀⠀⠀⠉⢩⠉⠈⢹⡍⠈⣿⡆⢰⣿⠀⣼⣠⢼⣿⣿⠀⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡏⠀⠀⠀⠀⠀⠉⠀⠀⠈⣟⡩⢿⣻⣿⣿⣿⣻⡱⠞⠛⠛⠒⠿⢃⠐⣾⣶⣿⣶⣆⠀⠐⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡉⢑⠂⠀⠀⠀⢠⠀⠀⢠⣴⠞⠂⠀⢸⡃⠈⠈⠙⡷⠲⠆⠀⢰⠶⠗⠈⢻⣿⣿⣿⣷⡀⠦⠤⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⢈⠀⠀⠉⠀⠀⠀⠂⠀⠉⠁⠠⣄⠛⠻⣿⣆⠘⢿⣷⠂⠘⣿⡟⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⡀⠀⠀⠀⠘⢀⡠⠀⠀⠀⡀⠀⠀⢘⣦⠀⠘⣷⡄⠘⣷⠀⢹⣿⡆⠀⢻⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⡤⠇⠀⠀⠀⠈⢿⠁⠀⠀⠀⡇⠀⠀⠀⣿⡆⠀⢸⣿⡀⢹⠆⠰⣿⡇⠀⢸⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⡦⢀⠀⠀⠀⠀⠀⣇⠀⠀⠐⡏⠀⠀⠀⢽⣷⠀⠈⣿⡇⢸⠁⠈⢻⡇⠀⢸⡿⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠈⠀⠀⠃⠸⡄⠀⠀⢟⡀⠀⠀⠨⣿⠀⠀⣿⡇⡼⠀⠐⢾⡇⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠘⡁⠀⠀⠐⣿⠀⠀⠿⠋⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡵⠀⠀⠀⠀⢀⣼⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⠞⠀⠀⠀⠀⠀⣾⡏⢸⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⢸⣿⢠⠃⣰⡟⡸⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢠⠜⣿⡇⡠⣾⡧⠀⠀⠀⢸⣿⠏⢠⣿⣳⠃⠀⠀⡤⣤⡠⠊⠀⣠⠔⠊⢉⡴⠋⡾
⠰⡿⡢⠖⣄⡀⠀⠀⢿⠟⣰⣿⢃⣴⢦⠀⢸⣿⠀⢸⣿⠁⠀⢸⠃⢩⣿⠃⠀⢰⠃⢀⡴⠋⠀⢐⡇
⠰⣉⡘⠢⣁⢾⠖⢦⠀⠀⣿⡏⢸⣯⠜⢠⠏⠘⠛⢹⣿⠀⣠⠋⠑⠚⠋⠀⢀⡤⠛⢯⣀⣀⡤⠎
⠀⠺⠄⡤⠈⠷⣄⣚⠆⠀⠻⠧⠜⠷⠔⠁⠀⠀⠀⠘⠿⠚⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠴⠂⢤
⠀⠀⠘⠦⡤⠛⠃⠉⠲⠄⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⠠⠀⢀⣀⠤⣤⡤⢲⣦⠀⠘⢄⣀⡤⣿⡆
⠀⠀⣠⡤⡀⠀⠀⠀⡠⠒⠒⠛⠒⠶⢶⣿⡷⠴⠴⠶⠚⠋⠁⠀⠀⣿⡏⠀⣿⠃⣼⡟
⢀⣾⠋⣠⣿⠀⠀⣀⡀⠀⢀⣀⠀⠀⢸⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⠁⠀⠛⠀⣿⡇⠀⣸⣷⠴⠲⣦
⢸⣯⠔⣿⡏⠀⣰⣿⠃⢀⣾⣯⠀⢀⣾⣿⠀⣰⣿⠀⢠⣿⡇⠀⡸⠁⠀⠀⠀⠀⣿⡇⠀⣿⡏⠀⢀⣿
⠀⠀⠀⣿⣇⡴⢻⣏⡠⢛⣿⡇⢀⠞⠀⠙⠋⠘⣿⣀⢼⣿⠀⣰⠃⠀⠀⠀⠀⠀⢽⡇⢠⣿⠇⠀⣾⡟
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠘⣿⣧⠏⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠓⢄⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠉⣐⠀⠈⠘⡄⡴⠊⠗⡙⢉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠂⢄⠉⠰⠃⡰⢧⢇⡁⢸⠆⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡕⠒⠒⠪⢕⠤⡀⠀⢿⡟⡇⠀⠀⠀⠈⠫⣍⠉⡴⠊⢨⠄⠀⡵⠂⠸⠥⢲⡒⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⡎⠙⠻⣶⡀⠀⠉⠪⡳⢌⢯⣿⠀⠀⣀⡤⠴⠞⡗⢳⡒⠛⠚⠳⠠⠆⣀⣤⣊⠀⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡇⡁⠀⠀⠘⣵⠀⠀⠀⠈⠳⣽⣝⣷⠋⠁⠀⡠⠊⠁⠘⡀⠁⣬⣀⠃⠠⠀⡶⢭⣀⣐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠱⡳⣄⣀⢴⡝⠀⠀⠀⠀⠀⠈⣯⠞⣆⠀⠀⣅⠄⠈⠐⢙⠀⢧⢸⡀⢒⠀⠈⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣝⣛⡟⣆⠀⠈⢆⣰⡀⠚⢢⣈⠎⢦⠮⣡⣹⠁
⡰⠋⠑⠂⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠫⡏⣀⠹⠊⢧⡀⠀⠁⠙⠢⠇
⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣤⣴⠾⣾⣷⢦⣤⠿⠛⠷⠻⠿⣦⣤⣤⣤⣤⣀
⠘⢦⣀⣀⡤⠞⠁⠀⠀⠀⢀⡴⣛⡉⢢⡀⠄⢡⢬⡸⣌⣛⡿⠀⠁⠔⡠⣒⡪⡔⠘⡆⢉⢰⠋⢨⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡏⣿⣷⠄⡇⣰⠿⢀⠅⣂⢀⢀⡈⢿⡜⣇⠳⠟⢣⣴⠣⠘⣾⡀⠻⡿⢃⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢄⠑⠬⠵⠚⣰⠯⡡⢀⡈⠄⠀⠃⠀⢸⡇⡈⠙⠋⠉⡲⠓⠓⢾⡝⠲⠒⠋⠂⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠂⡬⠀⡀⣾⡟⢢⠐⠀⡠⠚⠉⢉⢉⢺⡇⢀⢄⠰⠶⢇⠿⣿⠀⣷⡠⠖⢛⠓⣅⠾⣇
⠀⠀⠀⠀⠀⠀⠀⣼⠋⢅⣁⡤⢴⡀⣿⠿⠠⠀⠀⡇⢴⣫⢯⢣⢸⡇⠁⠣⡠⠄⡀⢝⠩⡀⣿⠡⢸⣟⡿⢸⢆⢻
⠀⠀⠀⠀⠀⠀⠀⢻⠇⡔⠁⣴⠲⡌⣿⠦⠴⣥⠤⡱⣤⣉⣩⢼⢸⣇⠔⠋⡉⠑⣔⣘⠀⢈⣿⠀⠘⠲⡖⠁⠜⢻⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧⠀⡳⢭⠖⣿⣤⣦⡄⢱⠈⠂⢠⣴⡅⣿⡇⠀⡎⣟⡇⣸⣀⣪⣦⣿⡢⠂⡻⠋⢋⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢙⠲⠤⠤⢿⣜⣚⣃⠜⢀⠄⢀⢠⠡⣺⠇⡁⡑⣢⢒⡏⣡⣤⣨⡏⣴⣕⠐⢈⠚⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠖⡡⢌⡘⡇⢩⠝⡋⠉⠑⢦⡌⡄⣿⢀⠂⠐⠙⠉⢣⣙⣛⣼⠏⣤⣌⠑⣬⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣴⣶⣁⣹⢏⡀⡔⡭⣷⢈⡗⡈⠃⡸⣋⡙⢦⡕⣠⠀⡸⠁⡧⣝⣝⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢤⣧⣉⣡⣞⣀⣤⡾⢧⣿⣿⣀⣏⣥⡶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡄⢲⡾⣧⡠⢀⣀⠐⣀
⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠢⢤⣁⡀⢂⣴⣂⣄⣇⢦⣯⣷⣿⡗⣣⡍⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢤⡄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣵⢿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣶⣿⣾⣶⡿⣶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠡⠀⠀⠀⠀⠀⠀⠂⠀⡒⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠃⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⡦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇
⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠟⠀⠀⠀⢠⡒⠶⣮⢺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠡
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⣄⡀⠀⠀⠈⠀⠀⡾⠻⠝⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⢰⡟⠉⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣤⣶⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢾⡯⣿⣿⣿⣿⣿⢿⠿⣿⠋⣽⣾⣿⣿⢿⣿⣿⣿⣿⠻⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠷⢿⠿⣟⡿⠿⣿⣿⣿⣿⣿⣍⡬⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠀⠄⠱⠏⠉⠀⠂⠀⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⡤⢤⣴⣶⣷⣿⣿⣶⣶⣿⣶⣖⣶⣶⣶⣾⣶⣶⣶⣤⣦⣤⣦⣄⣀⡀⠀⠀⠀⡀⣿⣿⡇
⠀⠀⠀⠀⢤⣠⣦⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣟⣋⣇
⢀⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀
⠘⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢃

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⢈⣑⣿⣿⡇⠀⠀⢠⣤⣄⠀⠐⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠖⠀⠘⢀⣤⠟⠀⡀⠀⠀⢺⣶⣄
⠀⠀⠀⢀⣾⣿⡿⣿⣶⣂⡄⢘⣿⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⢠⣤⠄⠀⠀⠂⡠⣿⡿⠋⠐⠿⠀⠽⢿⡉⢉⡁
⠀⠀⠀⠘⠟⡁⠀⣮⠈⢃⣀⣤⣈⠀⠀⠀⠀⠀⠠⣶⣾⣧⠀⠈⠀⠀⠒⠀⠀⠉⠀⡀⠀⠀⠣⠀⠀⠉⠀⠀⠀⠈⠁⠈⠀⠀⠄⢴⣾⣶⣤⡑⠀⠊
⠀⠀⠀⠀⠀⠀⢸⣼⣿⣶⣿⣷⣿⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⡀⠀⡄⠀⡈⠀⠈⣿⣷⠀⠀⡆⠠
⠀⠀⠀⢀⠀⠀⡀⢈⣿⣧⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢻⣴⣿⣶⣷⣿⡟⠀⣀⠧⠖
⠀⠀⠈⠛⠿⠀⠁⠀⠻⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠙⠛⠋⠉⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢀⣀⡤⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣰⡄⠀⠀⠒⠈⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠰⡶⣴⠁⠀⠋⠉
⠀⠀⠀⢸⣿⣿⠄⢠⡄⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⡾⣤⡀
⠀⠀⠀⠈⠙⠋⠀⠈⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣧⡀⠁⠀⠀⠘⡅⣻⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠃⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠀⠀⠀⠀⠀⠀⠀⢾⣷⢸⡖⠀⠳⣤⡽⢀⡄
⠀⠀⠀⠀⠀⠀⡠⠀⠾⠁⠀⣤⣠⠀⢀⠀⠀⠀⠀⢸⡃⠀⠤⢀⠀⠀⠀⠀⠐⡄⠀⠀⢀⣄⠈⡧⣀⢋⡤⠅⠀⠀⠀⠀⢀⠀⢈⡀⢉⠠⣤⡀⡄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢠⡄⠀⠈⠀⠉⠛⠛⠃⢀⣈⡴⠚⠠⣿⣧⡬⠿⠁⠈⠋⠀⠀⠃⠀⠠⢔⡀⠀⠀⡒⣀⠀⠸⠃⠨⠇⠘⠛⡀⠀⣟⠉
⠀⠄⠀⠀⠀⠀⠀⠀⠋⠀⣴⡶⡴⠾⣷⣶⠀⠀⠀⢀⣾⣴⣿⡋⠀⠀⢰⠃⠀⠁⠀⠀⠠⠀⠳⠀⢠⢶⠀⠀⠀⠀⣦⣻⣁⣺⣿⣤⣶⣶⣶⣄⣁⡆⠈
⠀⠀⠀⠀⠁⠁⣀⣰⢿⣄⠙⣻⣆⠟⢿⣿⡇⠀⣼⣾⣿⢿⣿⡷⡖⠀⢰⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡉⠉⠻⣿⣿⠿⣿⡟⠀⢔
⠀⠂⠀⠀⠸⠏⢉⣤⠂⠁⠽⠀⠀⣮⠑⠡⠛⠂⠉⣿⣿⣿⢿⣷⣳⡤⢾⡄⠀⢠⡤⠀⠸⠆⠀⠀⠀⠀⢀⡄⣀⣰⡿⡿⣻⣤⣤⣼⠃⠀⠚⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠥⠚⠀⠛⢿⢸⣿⣠⠀⠘⡄⠸⠉⠉⠁⣶⣿⣟⠻⠿⢷⡮⢿⣷⣤⣠⡀⣠⣧⣴⣶⣾⣿⡏⡡⠇⠃⢽⠏⣭⣄⠾⠟⠇⠂⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠚⠂⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣀⣤⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⢀⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣏⠒⠢⢄⡀⢻⣧⣶⡄⠀⣰⠁⢀⣀⣠⠤⠶⣾⣯⣑⠒⠤⣀
⠀⠀⠀⠀⠀⠀⣠⣶⣚⣏⣣⣷⣿⣿⣿⣶⣶⣿⠟⣿⣿⡤⠀⡿⣿⢿⣿⣿⣿⣿⣟⣛⣛⡛⠻⠿⠿⢶
⠀⠀⠀⠀⠀⠀⢼⣿⣟⣛⠛⠉⢉⣿⢿⠉⡆⣷⣀⢌⠻⠷⠊⢤⣷⢸⣸⡇⠉⠻⣿⣿⣖⣒⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢽⣿⣟⡯⠅⢀⣾⡃⠈⣇⢹⣿⣤⣄⡄⣀⣀⣀⣀⣸⣿⣷⢀⠀⠈⠻⣿⣿⣷⣄⡀⢸
⠀⠀⠀⠀⠀⠀⣼⣿⡿⠊⢡⡾⠇⠃⠀⢸⢸⡗⠇⠀⡵⠚⠒⠤⣀⠁⠘⢻⣼⠀⠀⠀⠙⢿⠫⠈⠉⣿
⠀⠀⠀⠀⠀⠀⣾⠿⠿⠿⢿⣧⡤⠤⠤⠷⠾⠭⠤⠼⢖⡡⠀⠀⠀⠈⠉⠉⠻⡍⠳⡦⡍⠙⢳⡞⢳⣾
⠀⠀⠀⠀⠀⠀⣿⠛⠛⠿⠯⡈⢻⡿⢿⣛⠛⠛⠛⠓⠈⠳⡁⡶⠶⠶⣄⡀⠦⣽⡄⠘⠈⠀⠀⣷⠀⢾
⠀⠀⠀⠀⠀⠀⣿⢛⣛⡛⠛⡏⢀⠰⠑⢌⠫⢭⣉⣀⣀⠀⣀⡀⠈⠛⠛⠛⢷⣏⣀⡀⢀⠀⢀⡏⠐⣻
⠀⠀⠀⠀⠀⠀⢹⣿⠟⢛⣈⢳⠂⠀⠈⠀⠀⠀⠀⣠⠀⢀⠀⠠⡝⣯⣉⣉⣿⣿⣿⣾⣿⣶⠾⠛⠛⣿
⠀⠀⠀⠀⠀⠀⣿⣶⠞⣩⡤⠒⠓⣔⣠⣖⣇⡲⣎⣩⠔⠒⣌⡳⠊⡩⠤⠬⠭⠯⣙⣻⣿⣿⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⣟⠉⠉⣿⣤⣶⣧⣼⣞⣮⣵⣼⣯⣋⣩⣽⣧⣤⣶⣈⣠⣭⣶⣾⠯⠉⢻⢸⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⢄
⠀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠀⢹⠀⡀⣀⠀⠀⠀⠀⠆⣊⠑⣢⢉⢛⠐⢺
⠀⠀⠀⠀⠀⠀⠈⢳⣿⡒⠂⠀⠁⠀⠀⠀⠀⠀⣄⣀⡈⠢⢄⣿⣷⠲⠋⠀⠀⠀⠈⠸⠬⣱⣇⠸⢸⣂⠉
⠀⠀⠀⠀⠀⠀⠠⠊⠃⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠙⠒⢷⣀⣡⡦⠤⣀⣄⡄⠀⠀⠘⠒⠋⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠖⠀⣄⣬⣄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠘⡳⠤⣤⡀⠪⠑⠂⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠢⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠠⣨⠆⠁⠄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡀⠈⠑⣃⠴⢁⠂⠐⣢
⠀⠀⠀⠀⣐⠀⠀⠑⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡛⣫⣕⣶⡆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣞⣀⣣⡊⠑
⠀⠀⠀⢐⣀⡀⠠⠑⠖⢨⠁⠀⠀⠀⠀⠀⢀⣀⢉⡚⢬⣭⡼⢿⣜⣇⠀⠀⠀⠀⡠⡀⠓⣤⢵⣿⡿⢇
⠀⠀⠀⠠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⢴⣿⠟⡁⡏⢩⡟⠈⠀⠀⠀⠀⠀⠜⠐⢋⣱⠗⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠩⠀⠖⡀⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠁⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⠤⠒⠒⠉⠉⠑⠒⢤⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡜⠁⠠⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠈⢦⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠈⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠏⠘⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⡀⠀⡁⢃⠐⠉⠋⡀⢀⢀⣨⣠⢄⡠⢤⠓⠊⡉
⠀⠀⠄⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⡉⣀⠉⡉⠈⠙⢀⠁⣈⠃⡈⠠⠀⠠⠴⠒⠈⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡉⠀⠀⠀⠇⠀⠀⣈⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠀⠀⠀⡖⠀⠀⢐⠃⠀⠀⠇⠀⠀⢀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠠⠀⠀⠚⠋⠽⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠀⠐⡗⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠙⠀⠀⠀⠀⠰⠆⠀⠰⠄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠰⡄⠄⠦⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠭⣆⣳⣄⣲⣀⣆⣰⡄⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

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

⠀⠀⠀⠀⠀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠱⡱⡀⣰⡆⠀⠀⠀⡀⠀⠀⡐⠘⢢⠀⠀⠀⠄⠀⠔⠐
⠀⠀⠀⠀⠀⠠⡑⢵⠫⠃⠐⠠⠶⠂⠒⢌⠀⠀⢨⠠⠠⢄⠌⣼⠃⣁
⠀⠀⠀⠀⢐⠤⠋⠐⠶⢀⢍⣆⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⣰⠠⡤⢀⢂⡀
⠀⠀⠀⠠⠁⠔⠀⠀⠄⠉⠉⠉⠂⣁⠶⠉⢀⠜⠋⠁⠁⢎⠀⠈⠑⣉⡖⠙⠒⣆⠀⠀⠀⠀⠀⡀⠠⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠀⠐⠀⢀⠀⢴⠈⡤⠊⠀⡑⢔⠰⠁⢀⣀⠀⣁⠀⠀⠁⠀⢀
⠀⠀⠀⣜⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠓⠒⠒⠚⠒⠒⠀⣐⡁⠒⠨⠉⠁⠐⠂⠀⠀⠁
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠃
⠀⠀⠀⠀⠰⠄⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⣀⣀⡀⢠
⠀⠀⠀⠀⠀⠀⣨⡦⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⡜
⠀⠀⠀⠀⠀⠰⡇⠻⠆⣽⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠙⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⠴⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠳⠚⡄⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠋⠀⠀⠑⡀⠘⡄⠀⡄⢁⠀⠀⢠⠎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠉⠐⠢⢌⡢⣐⣀⠁⡌⠀⡰⠃⢠⠯⠒⠈⠉⠁⠉⠒⠤⣀⣠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⠆⢀⣀⡨⠘⢣⡎⠀⡰⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⡔⠙⡄⠀⠀⠈⢢⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢀⣀⣀⡠⠔⠁⠐⡴⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠇⠀⠀⡠⠊⠇⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡄⣄⢀⣀⠀⠠⠃⠀⠀⣃⣀⣤⣄⣐⠒⠒⠒⠀⠤⢄⣀⠀⠀⡁⢀⠇⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⣀⠤⠛⠛⣄⣀⢠⡃⠀⠀⠀⠀⠀⠉⠐⠠⣀⠀⠀⠉⠲⢍⠁⠀⠀⠀⣠⠤⠤⣀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢰⠁⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⢄⠀⠀⢅⣀⠠⠚⡆
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢢⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢣⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠜⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠎⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣀⣣⣀⡀⠀⠀⠀⠀⡜⠀⠀⢀⠔⠁⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠄⠠⠓⠒⠂⠉⠉⠀⠀⠀⠀⠀⠉⠑⠒⠾⠤⠤⠞⠕⠒⠈⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⠔⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⢀⠀⠀⢀⠂⢠⡎⣰⣾⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠻⣷⣲⡦⣤⣿⢉⡻⣿⠏⣁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠤⣥⣿⠑⢶⡿⣸⠷⡋⡉⢐⣤⣆⠁
⠀⠀⠀⠀⢀⣀⢠⠾⣍⣄⣿⣺⣠⡳⣿⣧⣿⡾⠿⠓⠈⣀⣀⣀
⠀⠀⠀⢴⣎⢿⣯⣠⡀⢿⣿⢟⢷⣗⣽⣛⢿⣣⢖⣶⠟⠁⠀⠈
⠀⢀⣴⣷⣿⣿⣿⣿⠖⠂⢹⡗⢌⢻⣿⣿⢛⠻⡅⣃
⠀⠈⠁⣻⣿⣿⣿⢉⡈⠙⠃⠳⣾⣷⢼⡿⣿⡴⢛⠳⠔⠂
⠀⠀⠀⢭⣯⣝⣿⣵⠄⠀⠀⢲⢱⣹⣿⣷⢲⣾⣿⢀⡀
⠀⠀⠐⣾⣼⣿⣿⢟⡁⠀⠀⠙⣬⣿⣏⠹⣿⣿⣿⡉⠏
⠀⢀⣼⣿⣿⣿⣿⣿⣇⠄⠴⣏⣾⡻⣿⡽⣿⢟⣻⡟
⠀⠛⠉⠛⠛⠛⠟⠛⠙⣁⢠⣠⢿⣿⣿⣧⠻⢩⢰⣷⢖⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣽⢻⣿⢻⣍⠟⡆⢹⣆⣿⡈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⢾⢏⢸⠿⣰⣧⣘⣿⣿⣷⣷⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢁⣻⣟⣿⡿⣷⡐⣿⣿⣿⣿⣿⣿⣇⣿⣧
⠀⠀⠰⣵⠞⢈⠭⡻⢿⣿⢿⢿⣷⢿⣿⡞⣿⣿⣿⣿⣾⣿⣿⣯⡤⢤⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣷⠃⡎⠀⢠⡏⣆⡆⣿⠙⢿⣷⣾⣯⣺⣿⣿⣿⡿⢁⠄⠠⠈⠉⡟⡍⠛⣆⠀⠀⠀⢀⠀⢠⠊⠁
⠀⠀⠐⠀⡙⣽⡅⣴⢿⣛⠋⠛⠑⢶⣾⣬⣿⡿⣿⣿⣿⡿⣷⣸⡤⡇⣀⣼⣡⣇⣷⣿⣰⣷⠶⣗⡘⠾⠂
⠀⠀⠀⠰⣟⡿⠋⡙⠋⠀⢲⡈⣦⣿⣍⣛⡉⡑⢘⠿⢫⣵⠚⠉⠦⣿⠉⣴⣿⡿⣿⣧⣤⣌⠑⠾⠃
⠀⠀⠀⠀⠀⢁⢡⣹⡘⢦⡤⢿⣙⣷⣤⣤⠾⠵⠿⠛⠚⠉⠀⠀⠀⠈⠉⠁⠩⢭⡍

⠆⠙⠳⣿⣆⠠⠄⠠⣔⢀⡀⠈⢿⠇⠀⠐⡀⠀⠘⠣⠀⠈⠢⠤⠀⠀⠈⠐⣧⡀
⠀⢀⣐⡀⠀⡰⠶⡄⠁⠘⣿⡦⢈⡀⠀⠓⡄⠂⠁⠀⠀⠀⠀⠀⠐⢃⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢰⣅⠀⢵⠀⠀⢈⣸⣦⠀⢹⡇⢃⠈⣐⠀⠀⠘⢳⣄⣀⠄⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⣿⡇⠾⢰⡈⠈⠀⣨⣦⡸⠦⠁⠠⣌⠀⠀⡀⠀⢻⣿⠀⠀⠀⠁⠀⠀⠐
⠠⢍⠁⠀⢸⡿⢀⠒⢿⡏⠀⠀⠁⢀⡀⠑⢤⣁⠩⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠘⠇⠈⠒⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠂⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⠀⢠⠜⠛⠁⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠀⢀⣀⡾⠿⠛⠘⢿⣷⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢁⣷⠆⠘⠀⠟⣫⠋⠀⢀⣿⡄
⠀⢀⣤⠂⠀⠈⠲⡄⡈⠀⢠⣿⣦⣾⣧⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⠉⠄⢀⣼⣿⣀⣠⣴⡿⣸⡄⠀⠰⠿⡀
⠀⠀⠿⠐⠫⡗⠘⠃⠀⠀⢸⣏⢉⢹⡷⠾⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣠⣄⣀⣀⣀⣆⣀⣰⣄⣴⣷⣠⣿⣤⣧⣗⣠⣤⣴⣶
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣤⡤⣀⣀⡀⢀⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠒
⣐⡒⠬⠥⣀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡒⢄⡢⢄⡢⢔⡠⢀⠠⣈⢑⣲⡤⠴⠞⠛⠛⠣⡴⠄⠤⠀⠄⠀⡤⠀⢻⠏⢿⡿⢿⡟⣿⢿⠇⠎⠄⠀⠤
⣒⣲⠭⠕⣒⡩⠭⢐⣂⠠⠄⡂⠀⠀⠀⠀⠀⠀⠈⠲⣍⢲⣍⡶⠽⠒⠛⠉⠁⠀⠀⠀⢀⠀⠒⠙⠀⠆⠀⠀⠀⠀⠂⠀⢸⠀⢸⡇⣼⠁⡟⠀⢀⠄⢀
⠥⢖⣋⡭⠖⣒⡭⠴⣒⡪⠥⢒⣂⠥⠀⣀⣠⡤⠶⠚⠋⠁⠀⠀⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⣶⠐⠀⠀⠀⠀⠀⠸⠄⣾⠦⣿⠴⣷⢡⣾⣶⠁
⣛⣭⠴⣚⣩⠵⢒⣫⠥⠖⣋⣩⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⢀⡀⠀⠐⠚⠂⠀⠀⠙⠛⠂⡄⠀⠀⠀⠀⠠⠀⣤⣴⠃⠀⠀⣶⡍⠈⠁⢠⠐
⡥⠖⣛⣭⠶⢚⣩⡴⠖⠋⠉⠤⠒⠀⠁⠀⠄⠀⠀⠀⡀⣶⡷⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⢄⠠⠄⢀⠀⠀⠀⠀⠀⠠⠄⠘⠁⢠⠜⠇⠀⣰⡿⢃⣤⡄
⡶⢛⣩⡴⠞⠋⠁⠰⠒⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠶⠿⠇⠀⠀⠀⠖⠈⠀⠀⠀⡠⠀⠀⠀⠀⡀⠃

⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⢸⣍⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡇⠀⠀⣀⠤⠒⠒⡷
⠀⠀⠀⠀⠀⠀⠀⢽⠣⡼⡄⠀⠀⢋⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⡇⠀⢳⠀⢰⣡⠄⢀⡜
⠀⠀⢀⡠⠤⠤⢄⡀⠹⡒⠋⣆⠀⣏⢩⡂⠀⠀⠀⠀⠀⠀⠀⠘⢫⣵⣇⣀⣀⣀⠀⠙⢤⣼⣴⣊⣑⡚⠁
⠀⠀⠘⢆⠀⠀⠤⣼⣄⠘⢯⢬⢣⢏⡡⢃⠴⠶⢄⠀⠀⠀⢠⠞⠉⠈⠉⠀⠀⠀⠙⢦⣠⠎⠻⣄⣀⣉⣢
⠀⠀⠀⠀⠉⠒⡫⠛⠝⡟⠒⠥⡣⡀⡄⠀⢣⠀⣸⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⠉
⠀⠀⠀⠀⠀⠘⠓⣚⠭⠔⠒⠒⠋⠛⠓⠲⣼⠀⣿⣖⡒⠛⠉⠙⠓⠒⠤⣄⠀⠀⢀⡤⠷⠦⠤⢤⣇⣀⣀⣀
⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⡠⠔⠒⠉⢉⠝⠉⠙⢦⡀⠉⠉⠓⠢⣄⠀⠀⠀⠑⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⣀⠴⡄
⠀⠀⢀⡜⠁⠀⠀⣠⠞⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠙⢦⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣦⠞⠁⡰⠁
⠀⠀⡜⠀⠀⢀⡞⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢳⡀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢠⠏⠀⠈⢁⡔⠁⢙⡷
⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⢀⣀⠤⠤⠔⠲⠼⢤⣠⠴⠟⠒⠒⠚⠶⡄
⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⣀⠴⠋⢡⡀⠀⠀⠈⠂⠀⡀⢹⣤⡀⠀⠀⢠⣖⣁
⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⡴⢪⡁⠀⠀⠀⠀⠀⠰⡄⠀⠀⢁⠾⡀⠈⠳⣄⠀⠀⠉⣉⡳
⠀⠀⠀⠳⣸⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠖⠁⠀⠀⠁⠀⢠⠀⠀⠀⠀⣡⠴⠚⠁⢠⡃⣠⢤⠀⠑⠦⣌⡓⠤⣄
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⠰⠄⠀⠀⡀⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⠀⠀⠉⠀⠀⠣⡴⠉⠓⠒⠖⠚
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣰⠁⠀⠀⣀⣀⣀⠤⠷⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠄⠠⠯⠁⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡠
⠝⠁⣲⠀⠒⠈⠀⠀⠉⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠠⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠄⠈⠀⠃⠀⠘⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠃⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠁⠀⠎⠀⠉⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠡
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⢀⠈⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⢀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡀
⠀⠀⠁⠀⠑⠠⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⢳⠀⠈⠀⠀⠔⠀⠀⠀⠀⠀⠀⢄⠐⠂
⠀⢀⡤⣄⢲⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠉
⠀⡀⢈⠙⠙⠃⠀⠀⠀⢀⣀⢀⢀⣀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⢀⡀⢀⣀⡀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⡶⣤⣄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠀⠀⠀⠀⠀⢠⣑⢟⡑⠣⣴⠀⠀⠀⠀⢐⣿⣽⣟⣿⣹⢶⡆
⠀⠀⠀⠰⣇⠀⡄⠀⠀⠀⠀⠀⠀⡜⠆⠈⢦⠄⠀⠀⠀⠀⣲⣡⠹⡏⣁⣼⠃⠀⠀⠀⠸⣻⣷⢿⣏⣿⢿⠅
⠀⠀⠘⣦⢛⡼⠃⠀⠀⠀⠀⠀⠀⠢⡰⡆⠖⠀⠀⠀⠀⠀⠘⠳⢙⡟⠓⠃⠀⠀⠀⠀⠀⠙⠽⢿⡿⠝⠁
⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠰⠞⠶⠀⠀⠀⠀⠀⠀⠀⠰⠶⠷⠆⠀⠀⠀⠀⠀⠀⠰⠶⠷⠆⠀⠀⠀⠀⠀⠀⠀⠰⠾⠳⠆
⠀⠀⠀⢀⣤⣶⣄⡀
⠀⠀⢐⣿⣿⣻⣿⢾⡄⠀⢀⣤⣤⡰⠶⣲⣀⠀⠀⠀⠀⠀⣤
⣠⣿⠼⡿⣟⣿⢿⠟⠀⠀⣀⣂⣀⣀⣀⣃⣁⣀⣃⠀⠀⢰⡷⣴⣶⢶⣶⢶⣶⠀⠀⠀⣖⣒⣒⣒⣒⣲⢠⠄⠄
⢻⣷⠀⣀⠉⡟⠁⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⠉⠀⠀⣿⣧⢰⣿⣾⣿⣾⣿⡆⠀⢀⣒⡒⣒⣒⣒⣒⣸⣷⣾
⠘⠛⠂⠿⠃⠗⠀⠀⠀⠀⠀⠘⠻⠛⠟⠻⠚⠃⠀⠀⠀⠋⠘⠘⠿⠿⠿⠿⠿⠃⠀⠀⠈⠘⠟⠉⠉⠉⠉⠻⠛
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⢀⡈⠳⣤⡤⣤⣤⣤⡀⠀⠀⠀⢀⢔⣬⣡⡖⢄⠀⠀⠀⠀⡤⡒⠒⠢⡄⠀⠀⠀⠀⠀⢀⣀⣜⣍⣸⣡⣀⡀
⠀⡀⢡⣇⠞⠈⠓⡄⠉⠀⠀⠀⡇⣿⡟⢹⣿⡋⠀⠀⠀⠘⠀⠀⠀⠀⠘⣠⣾⣧⠀⠀⠸⡄⠀⠀⠀⠀⠠⠇
⠀⣠⠟⠹⣄⠀⢀⠆⠀⠀⠀⠀⠐⢝⠿⠿⣏⠝⠀⠀⠀⠘⢄⡀⠀⣠⢾⣿⣿⠇⠀⠀⠀⣷⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢠⣠⡀⠀⠀⠀⣠⠤⡆⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣄
⠀⡴⠲⠖⠲⢿⣭⠯⠀⠀⠀⢳⣀⣧⣤⣴⣅⢀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⡂⠀⠀⠀⠀⢀⣆⣀⣀⣀⡀⢶
⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡾⣓⠶⣤⡀⠀⠀⣿⣿⣼⣿⠇⠀⠀⠀⠀⣾⢻⣿⢻⣿⣿⡘⡄
⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⡎⠀⠈⡂⠁⠀⠀⣿⣿⣹⣿⠀⠀⠀⠀⠀⢻⡿⣿⣿⢿⡽⢡⣷

⠋⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠰⠀⠀⠐⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠄⠀⠀⠢⠀⠀⠀⠂⠀⠠⠀⢈⠀⠀⠀⠂⠀⠁
⠒⠀⠀⠀⠀⠠⠀⣀⠀⠀⣀⣀⡰⠚⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣄⡀⠀⠀⠀⠀⢠⣤⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⣤⣴⣶⣶
⠉⠙⠻⣶⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⠟⠉
⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢿
⠀⠀⠀⢠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠿⠃⢀
⠀⠀⠀⠀⠙⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⢠⡄⠀⠈
⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠡⠤⡦⠀⠂
⠀⠀⠤⠀⣀⣀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⢀⣀⣤⠴⠟⠃⣄⣤⡀⠀⠀⠀⠀⠀⠀⣀⣌⠤⢄⠀⠀⠀⢀⠀⠀⠀⣠⢤⠆⠀⠐⠂
⠂⠀⠀⠀⠈⠉⠀⠀⠀⠁⠆⠀⠸⠢⠀⠀⠀⠀⠀⠃⠸⠀⠀⠴⠛⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠠⠈⠉⠀⡗⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠘⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠲⠐⠀⠁⠁⠀⠀⠀⠈⠀⠀⠰⠀⠀⡀⠐⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⢠⡀⠀⠘⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠄⠤⠠
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠠⠰⠲⠘⠊⠁⠀⠀⠀⠀⠲⠀⡀⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠬⡀
⠀⢀⠀⠘⠻⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠀⠀⠀⠀⠀⠂⣡⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠠⠀⠂⢈⠠⠄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⡒⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠙⠄⢀⡀⠀⠀⠀⠀⠀⠘⢳⣸⡁⠺⠂
⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣠⡄⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠢⡀⠉⠀⣤
⠀⠁⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢁⣤⠀⠈⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠠⠀⠀⢸⡿⠛⢷⣄⠀⠀⠀⠀⠁⠀⠀⣶⠆⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠀⠀⠀⠀⠰⠆⠀⢀⣰⠲⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⡄⠀⠀⠱⡄⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠃⠀⠀⠀⡰⠋
⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⢐⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⠀⢀
⠂⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⡊⠅⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⡀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠠⠏⡀⠀⠀⠂⠀⠀⠙

⢧⡆⠀⠀⠠⠤⠄⠠⠊⠀⠀⠀⠀⠀⢠⣤⡄⠴⠀⢿⠕⡂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠄⠂⠀⠀⠀⠀⠀⠀⠸
⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⡿⣻⠧⠘⠴⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⡀⠉⠛⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⡠⠀⢒⡦⢄⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠎⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠨
⠀⠆⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠘⠛⠡⢰⣆⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠐⠘⠓⠀⠀⠀⣀⡜⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀
⠀⠐⠆⠀⠀⠀⠀⠀⠀⡄⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⠀⢀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠁
⠀⢀⡾⠀⠀⠀⠈⠀⠀⠈⠖⠛⠿⣤⣤⢺⡧⠤⠒⢄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠶⢤⢀⠈
⠀⠸⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⣤⠾⠁⠉⠁⢂⠀⠀⠀⡀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡀⠞⠇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠀⡀⢤⠤⠄⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠄
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠠⠀⠀⠀⠀⠀⠈⠀⠀⠈⣄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠀⠘⠛
⠀⠐⠀⠀⠀⠀⠈⠒⠠⠤⢡⡀⢸⣈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋⢇⠜⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⢠⡖⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠑⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡄⠂⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⣀⣀
⠂⠐⠀⡀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠠⠈⢀
⣀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣐⠀⣒⣀⣤⣄⠀⣀⠀⠀⠀⠈⢂⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⡀⢁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢑⣞⣃⣄⣲⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠆⡴⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠄⠀⢶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣀⣄⣀⣠⡿⣿⣶⣤⡀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⠓⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⢾⠰⡀⠀⠐⣘⣿⣿⣿⣿⣿⣿⡏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡐⠶⡟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠀⢸⡄⢂⠀⠀⠈⠛⢿⣿⣿⡿⠋⠐⠃⠀⢀⣀⣴⣶⡿⣿⣷⡤⣥⠟⣀⡉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⠀⠀⠸⣾⣿⣷⠀⠂⠀⣠⣾⣿⡇⠀⣀⣤⣶⣿⣿⣿⣿⣟⣭⣭⣽⢿⣿⣿⠿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⣀⣀⡀⠙⣿⢿⣿⣾⡠⣿⣿⣿⠀⠀⠀⠉⠙⠋⡉⢉⣽⠏⠻⠿⠟⠛⠉⠉⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡬⢔⠑⢀⠰⣁⣾⠟⢩⣷⣿⣿⣧⣤⣤⣤⡴⠖⠛⠛⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣞⡒⣜⣉⣼⣻⢋⣰⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠠⠂⠀⠘⠀⠆⢰⠂⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣩⣴⡘⢛⣴⣯⣾⡿⡿⣿⣿⢿⣿⣿⣿⣿⣧⠀⡄⠀⠀⢀⡤⡴⣀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣅⡁⠠⠋⣿⣿⣼⣿⠿⣯⣿⣿⣥⣿⣿⣿⡄⠀⠀⠀⠈⠁⢀⣀⠴⠞⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠛⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⠄⠀⠀⠀⠊⢀⡀⠂⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠹⣿⣿⣏⣹⣿⣿⠻⣿⣿⣿⣿⣿⣧⠀⠀⢾⠀⢦⡦⠀⢀⠎⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⣛⣻⣿⡇⡀⠙⣿⣿⣿⣿⣿⣧⠀⢀⠐⡀⡐⢀⣣⢠⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⢢⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢚⠘⣿⣿⣿⣿⣿⣆⢂⣽⡟⢰⣿⣿⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢘⠁⠀⠀⠀⣿⣿⣿⣿⣿⣧⢀⡄⠤⢻⣿⣿⣿⣿⡟⢰⣿⠁⠿⢿⣿⣥⣓⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⣿⠿⠿⣿⣿⡟⢸⠂⡄⢻⣿⣿⣿⣿⡇⠸⠏⠀⣠⣸⣿⣞⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⠈⠀⠀⢠⣧⣿⣶⣿⣿⠁⣠⡴⠆⢾⡉⣽⣿⣿⠀⣤⢠⣿⣿⣿⣿⣧⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠾⠀⢄⠀⢘⣿⣿⣿⣿⣟⣴⡻⣧⡀⣿⠀⣿⠟⠛⢁⡿⢸⣿⢻⣿⡿⢈⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠠⢂⣄⠀⢷⢄⣈⣿⣿⣿⣅⣺⣅⣥⠀⠉⣠⡇⡸⠁⠘⠁⡆⣀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⣻⣦⣼⣷⣾⠁⣙⠿⡿⠶⢻⣿⣿⣿⠀⢠⢙⡽⠃⡄⠀⠰⡇⠛⣌⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡛⢫⡍⢋⣛⣛⡿⠈⡨⣀⠐⠀⠸⠃⣮⠂⣀⠋⢸⡄⠀⠀⠀⠀⡍⠀⠃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⡤⠼⠛⢀⡲⠧⠅⣿⢿⡾⣔⡾⡎⣠⣠⢄⠰⠀⠀⣄⠀⢀⡀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⣀⡤⠴⠿⢲⣭⠀⢘⣋⣀⢉⡀⠀⠙⠁⠛⠴⠴⢾⢀⠉⣀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠐⠂⠀⠀⠀⠀⠂⠒⠀⠃⠂⠃⠀⠀⠐⠀⠐⠀⠀⠀⠀⠈⠀⠀⠘⠈⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡄⠀⠀⠀⠀⣀⣀⣸⣜⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⠤⠗⠣⡀⠀⡞⠁⢘⠗⠒⠠⠟⠉⠙⡆⠀⣼⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣩⣶⢈⡷⠒⢄⡔⣿⣾⡁⠀⠀⠀⠀⠀⣀⡀⠀⢸⠀⢸⠋⠳⣤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣎⣠⣿⣾⠁⠀⠈⠁⢹⡇⡇⠀⠀⠀⠀⡜⢰⡋⢀⣮⠶⠋⠀⠀⠀⠉⠑⠌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣌⣨⡟⠁⠀⠀⠀⠀⣸⣇⡴⠖⢪⡉⠟⢓⡘⠙⠫⣽⡷⣤⣄⠀⠀⣠⠶⣢⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⣋⠏⠀⠀⠀⠀⠀⠀⣽⠏⢠⠊⠈⠹⠊⠀⠀⠙⡉⠈⠐⠈⠫⣉⠱⣿⠈⠈⠪⡡⡀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣼⣬⠟⢦⠀⠀⠀⠀⠀⣰⡿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣸⣖⡞⣆⡀⠑⢰⡜⠁⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⡟⠁⠀⡼⠒⢒⢶⡩⠍⢉⣷⡤⢄⠀⠀⠀⠀⢠⡺⢢⠔⠋⠩⠐⠐⠈⠉⠉⠳⣦⠀⣩⡅⠀⢢⣈⢣
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⠇⣠⠼⢂⠕⢉⠊⠁⠉⠀⠀⠀⠡⠉⡹⠖⢠⣶⣧⡷⠤⢤⡴⠂⠀⠈⠁⠐⢄⠘⠆⢤⣇⠀⢸⡀⠙
⠀⠀⠀⠀⠀⠀⠀⢹⢀⡖⢀⡾⠁⢠⠏⢀⠆⠀⠀⠀⠀⠢⡀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡀⠀⠀⠀⠀⣦⠄⠀⠙⣆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠹⣧⣾⡆⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⢳⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠉⢣⣤⠤⠖⢳⣄⣄⡀⣈⣣⣷
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⡼⢇⣄⠠⠀⠀⠀⠈⠢⣀⠀⠀⢸⡇⢹⣀⠀⠀⠀⠀⠀⠀⣴⠟⠂⠀⣮⠸⣠⠖⠉⣾⠉⠙⢄⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠁⢹⣆⣡⠤⠤⠄⠒⢘⡛⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠙⠒⠂⠒⠢⠶⠧⣀⣰⠓⢄⣀⠼⡖⠚⢢⡀
⠀⠀⠀⠀⢠⠖⠉⠉⠉⠉⢽⡖⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡁⠀⢸⣄⣸⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⢴⢹⡏⢰⡆⣴⢸⡏⢸⡇⣴⢰⡗⣶⢰⡄⣾⢰⡆⠀⠀⠀⠀⠀⠀⡗⠀⣎⠀⢘⡆
⠀⠀⠀⠀⠈⠣⣄⠀⢀⠀⡼⠀⠀⠀⠀⠀⢠⣠⠆⠘⠷⠸⠧⠻⠎⠙⠙⠗⠛⠚⠇⠛⠸⣇⠿⢸⡇⠀⠀⠀⠀⠀⠀⢣⡴⠋⠁⢞⠁
⠀⠀⠀⠀⠀⠀⢸⢀⣼⣿⠇⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣄⣉⣀⠀⠀⠀⠀⠀⠸⣌⣢⡤⠿⡀
⠀⠀⠀⠀⠀⣠⠶⠋⠑⠈⠀⠀⠠⠔⢺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⠢⠤⠀⠀⠁⠊⠓⠦⣷
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠣⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⠀⠜⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠉⠈⠩⠃⠀⠀⠀⠀⠀⢀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⡀⠀⠀⠀⠀⠀⠘⢍⠁⠉
⠀⠀⠀⠀⠰⢁⡀⠤⠄⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠠⠤⢀⡈⠆
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣲⣶⡶⢶⠶⢶⠒⢲⣶⡶⢶⣶⣶⣶⣶⣶⣶⣆⡆
⠀⣿⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢿⠥⢢⠤⢦⣌⡇⢉⡤⠴⠦⠟⣿⣿⣷⡉⠛⠻⡇
⠀⢿⡷⠀⠈⠀⠠⠀⢠⠂⠀⢀⠀⣀⣠⠆⠀⠀⠒⠄⠀⠀⠀⣀⠸⠿⠙⠒⠚⠓⣾⣌⣸⣿⣶⣦⣷⣶⣿⣿⣼⣶⣾⣷⡇
⠀⣿⡁⠀⡀⣀⣰⡶⠷⣶⣠⣷⣶⡿⠥⠀⠀⠀⠀⡀⣽⡇⣾⡁⠀⡀⠀⠀⠀⣤⣿⣯⣯⣭⣭⡿⢄⣽⣿⣿⠿⠿⠷⢿⡇
⠀⣿⣿⣿⡟⠁⠀⠀⠀⢠⣽⣿⠿⠶⡀⢠⠀⣀⣨⡟⠋⠙⠀⣠⣶⣷⣤⣤⣴⣿⣿⣿⢿⡷⣿⣿⣿⣟⠋⠀⢀⠠⠀⠀⠃
⠀⣿⣟⣿⠁⠀⠀⠀⠀⢸⠋⠀⠀⠘⠓⠃⢀⠞⠉⠀⠸⠶⠚⢿⢿⠉⠉⠀⠁⠀⠀⠈⠟⠉⠁⣠⣼⣏⡀⠸⢶⡄⡵⠂⡆
⠀⣿⣿⣿⣦⣤⠤⠄⠀⣯⡄⠀⠀⠀⠀⢶⣾⠀⠀⠀⠀⠀⠀⠈⡂⠀⠐⣶⣤⣤⣶⡶⣄⢀⠸⠟⣯⣟⠛⠳⢤⣠⢒⣟⡀
⠀⣿⣭⣿⣯⣟⠷⡴⣁⣉⡆⠀⠀⠀⣃⣼⣿⣷⡄⠂⠀⣀⣶⣾⣿⣾⣾⣇⡤⢉⣿⣿⣿⣹⣾⣿⣿⣿⣿⣿⣦⣽⣭⣼
⠠⠿⠿⠾⠿⠿⠯⠥⠿⠿⠿⠿⠶⠿⠿⠿⠯⠦⠦⠦⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠽⠿⠿⠿⠿⠽⠿⠿⠿⠿⠿⠿⠿⠿⠆