Bento Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣲⣽⣷⣶⣤⣤⣤⣄⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣐⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⣾⣿⡿⢿⣿⢛⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⣿⠏⢁⣤⣤⣤⡿⢋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⡿⢿⣿⢨⣿⠸⣿⠻⣿⡿⢿⣿⠟⠻⢿⡿⢿⡟⢿⣿⣿⠏⢀⣾⡄⠘⣿⡏⠀⣾⣿⠟⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢿⣿⣏⢸⣿⢐⣿⠀⣿⠀⢛⡟⢸⣯⣘⣛⢻⣷⠐⣿⣿⣿⠏⢀⣾⣿⣿⡄⠘⢧⡀⠛⢧⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⣯⣸⣷⣸⠿⠀⠙⠀⡀⣀⠸⢯⣍⣉⣼⣿⣄⣉⣽⣯⣱⣾⣉⠉⠀⣡⡄⠈⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠞⢁⡴⡫⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡿⠛⣡⠖⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⢋⣤⢞⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠹⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⡴⢋⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠙⠲⠶⢤⡤⠴⠶⢋⣡⠞⡫⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡓⠲⠶⠶⠒⠚⢉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⠤⠔⠚⠁

⠀⠀⠀⠀⠀⠀⣠⡶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤
⠀⠀⠀⠀⠀⢸⡏⣴⣟⡛⠛⠛⠛⢿⡾⢛⣛⣛⣛⠛⠛⠛⣛⣛⣛⠛⠛⠛⠛⠛⠛⢻⣦⢹⡇
⠀⠀⠀⠀⠀⢸⡇⣿⡏⣱⡶⠷⣦⣸⣿⠟⣋⣍⡛⢷⣴⡿⢋⣉⣙⢻⣦⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⡇⣿⡀⠀⣸⣿⣟⢸⣟⢉⣿⠈⣿⠰⣿⠉⣻⡇⣿⣧⣴⣶⣤⣸⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⣧⣽⣿⠾⣟⢹⣿⣮⣛⣛⣋⣼⠿⣧⣙⣛⣋⣴⡿⢡⣶⣶⣌⢻⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⡏⠉⢹⣷⠉⢸⡏⠉⠛⠛⠋⠁⠀⠈⠙⠛⠛⢻⣇⢻⣧⣼⡿⢸⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⣷⣤⡾⢏⡘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣬⣭⣶⢿⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⢹⣷⣶⣶⣮⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣾⡟⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⣷⢶⣶⡶⢶⣶⣶⣦⣄⠀⠀⢸⡇⢀⣴⣶⣶⡶⠗⠀⠶⣦⣄⢸⣿⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣿⣿⣆⠙⢿⡄⠙⣷⡈⠻⣷⡀⢸⣧⣌⣁⠻⠷⢾⣿⡛⣃⣠⣿⢸⣿⢸⡇
⠀⠀⠀⠀⠀⢸⣇⠻⣿⣿⣤⣼⣷⣤⣾⣷⣤⣾⣷⡾⢿⣽⣯⣤⣤⣤⣬⣤⣽⣯⣤⣾⠟⣸⡇
⠀⠀⠀⠀⠀⠀⠙⠷⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⡶⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄⢀⣰⣤⡤⣶⠋⠻⡄⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⠤⣤⡤⠘⡏⠁⢀⣷⡀⢺⡏⠉⣿⠀⢠⠟⠲⢾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠘⠉⢉⣯⠴⠚⠁⠀⠀⣧⠄⢸⠉⣧⢸⠃⠀⣿⠀⢺⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⡤
⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⠶⠖⣚⡿⢂⡇⠀⣸⠀⠸⣾⠀⠀⠿⠀⠀⡉⠀⢸⠀⠀⢠⡄⠀⠀⣴⢋⡴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠴⠛⠁⠀⠈⠓⠋⠙⣀⠀⠉⢰⢀⢀⣴⣀⣷⣫⣿⠞⢧⠞⠀⠀⡼⠵⠫⠞⠁
⠀⠀⠀⠀⠀⠀⣠⠶⠻⡇⠀⠀⠀⠀⠀⠀⣄⣤⣿⣰⡆⣸⠹⠿⠇⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧⢶⡴⡶⠻
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠆⣀⣤⣤⣧⡛⠗⣿⠯⠇⢿⠴⠂⠀⣀⡀⢀⣀⣤⣤⠶⢶⡋⣉⣉⡉⠉⠒⢬⡁⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣾⣏⠽⠋⢻⠹⠇⠘⠛⠀⠀⠀⣀⠔⠋⠈⠙⢯⣰⢯⣀⣱⠀⢹⠤⡀⠙⣦⠀⠀⠈⠳⢄⡀⠠⠀⠰
⠀⠀⠀⠀⠀⠀⡤⠄⡟⠉⢸⠁⠀⠀⠘⠀⠀⣀⣠⡴⠒⢋⠍⠀⠀⠀⠀⠂⠻⡷⢟⣳⣁⡼⣤⢹⠀⢸⢗⡓⢦⡀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠘⣇⡴⠃⠀⠀⠀⠀⣀⠤⠒⢛⡿⠿⢷⣀⡌⠀⢀⡠⠤⠤⠒⡄⢸⠎⠡⠈⠑⢄⡞⢠⣏⡀⢳⠀⡇⣠⠤⡄⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⢁⠀⠀⠐⠂⠀⠃⢈⠓⢤⣉⢀⣀⠀⠀⠸⠃⠀⠀⠀⠀⠈⢳⠿⣩⣏⡞⣰⠟⡡⣺⠎⣩⠂⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠀⢔⡈⠐⢄⠰⢈⠑⠌⠂⠂⣡⠀⠈⠛⢿⣷⢠⠃⠀⢠⠄⠒⠒⠦⢀⡶⠋⠁⠉⠳⣊⣴⠃⡰⢡⠗⢈⡸⢂⡈⢳
⠀⠀⠀⠀⠀⠀⢠⣏⠙⠛⢻⡄⠈⠢⠄⠓⢈⠠⠀⠒⡡⠚⡀⠃⠀⢀⠈⡛⢦⡀⠂⡀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠘⣧⣈⠔⡡⡴⢫⣟⡤⠟⢹⡆
⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⡗⠘⡂⣉⢉⡁⢤⣒⢇⡈⢢⡀⠂⢰⣾⠿⠿⣆⣈⣙⢿⣷⢀⠅⠀⡔⠂⠉⠉⠉⡆⠸⣉⣫⡶⠖⠋⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠲⣇⡀⠃⡉⠆⠈⣧⢹⣄⠁⣀⡤⠴⠚⢦⣀⡴⠉⠀⠈⠑⡌⠛⠦⣀⡇⣶⢰⣦⡤⠷⠚⠉⠠⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠙⢮⣅⢨⠳⡜⠛⠛⡿⠋⠀⠀⠀⠀⡝⢀⡔⠚⢲⡀⢸⣀⣀⡬⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠙⠧⣄⠀⢸⠃⢀⡖⠉⢢⠀⠇⣾⣀⡤⠴⠗⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠾⠶⠶⠞⠛⠋⠉⠀⠀⠤⠖⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⣀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢠⡄⠈⠙⠲⢤⣀⣀⣈⣤⠤⠖⠚⠉⠉⠀⠀⠀⠀⢠⣦⣠⢻⣴⢻⡾⠸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠋⠀⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀



⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠋⠉⠀⠉⠉⠉⠻⢦⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠋⠉⠙⠳⢦⣄⡀⠀⠀⣴⣾⣿⣿⡿⢻⣿⣿⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣤⣤⠀⠀⠉⠛⠓⠀⠈⠻⠟⢉⣴⣿⣿⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠀⠀⢀⡀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠘⢷⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠚⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⣠⡀⢸⡁⠀⠀⠀⠀⠀⠀⠰⣿⠀⠻⠃⣠⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠁⢸⣿⣶⣾⣿⣧⣀⣀⣠⣿⣿⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠈⠙⠛⠿⢿⣿⣿⣿⣭⠷⠟⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠒⠀⢀⢀⠠⢄⠀⠀⠀⠒⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠉⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠁⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⣀⠠⠄⠒⠒⠀⠀⠘⠒⢤⣀⡀⠀⠀⠔⠉⠀⠀⠉⠢⠀⣀⣀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⢠⠞⠻⢿⠿⠓⠲⠀⠀⠀⠀⢀⢔⠉⠤⢀⣇⠠⠠⡀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠠⠂⠈⠲⣇⠀⠀⠀⣠⠐⠀⠆⠒⢄⡠⢆⠺⠖⣡⢪⠔⡐⠀⡇⠀⠀⠀⢁
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⣤⣶⣦⣮⣙⠒⠒⠀⢀⡃⠆⣀⠀⣿⣿⡗⠒⠋⡀⠄⠀⠀⠀⠄⠘⡂⢩⡇⢌⣋⢰⣿⡇⠀⠀⠀⠈
⠀⠀⠀⡐⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠈⢅⠀⢀⡠⠃⠀⢀⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠸⡛⠋⡿⣇⠀⠀⠀⢰
⠀⠀⢠⠀⠀⠀⣰⠋⢉⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡄⠃⡅⠈⠈⡆⡰⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡄⠀⠀⠇
⠀⠀⢸⠀⠀⢀⠆⠒⠀⠛⠂⠀⢀⣀⡙⣿⣿⣿⣿⣿⣿⣀⣠⣀⠂⠁⠥⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠈
⠀⠀⢸⠀⠀⠈⠆⠀⠀⠀⣤⠀⠉⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⠀⣍⡄⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢸⠀⠀⠀⠀⠀⠂⢀⣀⡀⠀⠀⠀⣠⠞⠉⣉⠉⣛⠿⣿⣿⣿⣿⣿⣿⣿⡁⡐⠄⠀⠓⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⢀⠄⠀⠀⠟⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠰⠟⠀⠹⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⠄⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠠⠄⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⣶⣶⣶⡶⣄
⠀⠀⠀⠀⠀⡤⠶⠶⣶⣶⣾⠟⢻⣄⡘⣯⣭⣭⣿⣤⣰⣶⣶⣾⡿⠟⠛⢉⣉⣹⣿⣌⢦
⠀⠀⠀⠀⠀⣧⢸⣿⡟⢿⣜⠳⢬⡐⢤⠉⢿⣿⠿⣿⣇⢻⣿⣁⡤⠖⠛⠉⠁⠀⢀⣿⣯⢣⡀
⠀⠀⠀⠀⠀⣿⣆⢻⠁⠀⠈⢣⡀⠹⡄⢱⡌⢿⣿⣿⣿⣇⢻⣿⡀⢠⠤⠖⢂⣉⣐⣛⣛⣃⠳⡄
⠀⠀⠀⠀⠀⣿⣿⡌⢇⣀⠀⠀⠻⠄⢹⣀⣛⣋⣙⣯⣭⠥⠶⣶⣶⡔⡿⠻⠏⢻⣭⣭⣽⣿⣷⡹⣄
⠀⠀⠀⠀⠀⠸⣿⣷⡠⣶⡶⠞⡻⣍⠻⠛⠋⡡⠮⠉⠀⠚⠗⠀⠙⠻⣅⠐⣂⠈⢿⣤⣤⠴⠿⠿⣜⣦⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣧⢹⣷⣄⠘⠊⡀⠤⠀⠉⠀⢠⣶⣌⢡⡀⠛⠗⣠⡦⠉⠱⠦⣼⣗⣒⣲⣿⣯⣬⣶
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⣿⣿⣷⣤⠙⠂⣀⣰⣷⣀⣭⣼⣯⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢀⡀⠀⠀⠀⠐⠁⠀⠀⡔⠁⣀⣴⣁⣀⠀⠀⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⢻⡿⠛⠢⣤⣶⡀⠀⢀⡞⢠⠾⠛⠛⠛⠛⢿⣦⠀⢸⡇⡀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⣆⠀⠀⢀⡌⠀⠀⠀⠀⠀⠈⢿⠏⣀⣯⣤⣤⣤⠀⠀⠀⢿⡇⣞⠀⠈⠎⠉⠷⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠸⠻⢿⣿⣷⣦⣤⣦⣀⠀⣠⠏⠘⠉⠀⠀⠀⠙⢿⣆⢀⣼⠃⡘⡇⠀⠀⡀⠀⢀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠁⠀⠀⠀⠈⠁⠀⢈⠟⢿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠀⠈⣿⠟⣱⣟⠾⣟⠛⣶⡶⡎⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣨⠃⠁⠀⠀⠀⠀⠀⠀⠀⠠⠏⢠⣿⠏⢰⣧⠞⣹⣇⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠘⠋⠀⠙⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠄⠀⠀⠀⢄⢀⡀⡰⠁⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠚⠰⣼⠁⠀⠀⠀⠀⠀⠀⣰⠏⣈⡩⠷⣦⠀⠀⠀⠀⠂⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣼⣯⣰⣶⣿⠦⠌⠀⠀⠀⠀⠀⠠⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⢧⡀⠀⠀⠀⠄⠂⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠴⢶⣿⠁⣸⣅⣹⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⠶⠛⣉⡵⠋⠀⠀⠀⠀⠀⢠⡟⣠⡶⢠⠏⡿⢰⡇⣠⠏⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢻⡇⣀⣴⣞⣥⠤⠤⣄⠀⢠⣞⣧⢾⣷⢋⣧⠏⢸⡇⠈⠛⠋⠀⢠⡆⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣀⡴⢛⣡⠔⠀⢸⡟⠋⠉⠀⠀⢀⡴⠋⣠⣼⣋⠟⠸⠃⠀⠁⠀⠈⠀⠀⡆⣠⣄⣼⢃⡼⡿⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠾⠷⠞⠋⠀⠀⠀⢸⡇⠀⠀⣀⡴⠋⠀⠀⠀⠈⠉⠀⡆⠀⣠⢠⡆⣰⣇⢰⣷⡏⣸⣿⠋⢰⡇⠀⠀⠡⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠛⡷⢻⣿⣼⠉⠟⠁⣿⠀⠘⠃⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⢸⠇⢀⣠⠄⠀⣾⠈⠿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠋⠀⠀⠀⠀⠉⣭⣖⠀⠀⠀⢿⠶⠛⠁⠀⠀⠛⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡔⠒⢋⠛⠉⠉⠢⢌⡉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⢚⠿⠋⠁⢀⠀⡈⣾⠋⠈⠙⠂⡆⠈⢦⠀⠈⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠙⠁⠀⠀⠀⣀⡀⢠⠖⢶⠿⣍⡳⣄⣀⠋⢀⢀⣀⡤⠃⢀⡸⠗⠒⠒⠢⡇⠀⡤⠀⢠⣣⠔⠚⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⣀⠀⡴⢦⣸⠁⠳⠋⠀⡀⠀⠀⢣⠤⡍⠛⢬⣉⠀⢀⠔⠁⠀⢀⢠⡠⠘⣡⣰⣃⠞⠉⢀⠔⢺⠭⢱⠄⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠉⠓⠁⢀⠀⠀⠈⠀⠀⠀⠀⡖⡦⠀⢇⠀⣀⡈⡹⡿⣤⠐⠓⢊⡥⠒⢉⣠⠤⠬⣝⠢⡀⠓⠼⠒⠉⣀⡤⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⢸⠙⠁⠀⢠⠖⠚⠀⠉⠘⣦⠠⣝⠲⣯⡀⠰⣅⢸⠂⢀⡼⠀⢈⣧⡶⠖⠋⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠐⠀⠀⢀⣀⣼⣿⣟⠀⠀⠀⢸⠁⢀⣠⣤⣾⣳⠄⠈⠉⣴⠉⠳⢦⣍⣉⡥⠶⠚⠉⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠳⢦⣀⠀⢀⠞⠉⠀⠀⠀⠈⣳⣰⣦⣯⡴⠋⠀⠀⠀⠈⢧⠀⢀⣸⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠙⠷⣼⣀⠀⠀⢠⠞⠁⠀⠀⠉⢳⡄⠀⢀⣀⡤⠾⠚⠉⠁⠀⠀⠀⠔⠊⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⣄⣇⣀⣀⣤⡤⠟⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⠀⠀⠃⠀⠀⣀⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⢠⣄⣤⡴⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠛⠉



⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⠔⠀⠤⡀⠐⠤⠀⠂⠉⠔⠇⠒⠒⠀⠄⠠⡀
⠀⠀⠀⠀⡠⠊⣀⠐⠂⠂⠀⠁⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⡀⠀⠈⠳⣄
⠀⠀⢠⠞⢀⠼⠅⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠋⠀⠀⠀⠀⠁
⠀⠀⠈⠀⡞⡀⠀⠀⠄⠀⠀⠀⠀⠈⠐⠀⡘⠀⠀⠐⠁
⠀⠀⠀⡘⡄⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⡀⠀⠀⠇⠤⠀⠆⠀⠀⠀⣀⠀⡘⠒⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠇⡄⠀⠀⠀⠀⠐⠚⠀⠀⠀⠄⠂⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀
⠇⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢⣿⠆⠁
⠀⠀⡀⢹⠄⠀⠀⠀⠈⠠⠤⠐⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠝⠉⢳⣬⣦⢀⠀⢀
⠀⠀⠐⠀⠗⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠢⢄⠠⣾⠗⠋⣠⢞⡩⢔⡿⠟⠓⣄⡈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⠶⢋⢔⡩⢚⠏⡀⠀⠀⠀⣸⡱⠄⠁
⠀⠀⠐⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠑⠚⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⢰⠛⡀⢔⠵⢷⣆⡠⡴⠈⠀⠀⠀⠓⣤⠀⢄
⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⠉⠉⠙⠂⡀⠀⠈⠠⠛⡷⣞⠄⢀⠀⡈⣁⠀⣄⠠
⠀⠀⠀⠀⠀⠠⡀⠈⢀⠄⡀⠀⠐⠀⠈⠀⠀⠀⠀⠺⠶⠀⠀⠐⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣀⢶⠃⠉⠛⠲⢘⠁⠀⠁⠨⢄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡈⢡⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠶⠦⠀⠀⠰⢶⡃⡀⠀⠀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠂⠙⢆⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⡖⠀⠂⢰⠊⠉⠛⢺⠽⠆⠃⠒⣖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⢄⠑⢤⠀⠀⠀⡠⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⢀⡴⠀⠒⢀⡀⠬⣀⡁⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠄⠰⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠲⠈⠙⢦⡂⠉⠀⠀⠈⠱⡞⠂⠀⠲⣀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⠢⣄⠀⠀⣰⠂⠀⠀⠀⠨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠬⢳⣤⡆⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠠⠈⠛⠍⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡉⠉⠛⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣤⡁⠀⠀⠀⠀⠀⠀⠀⢀⠝⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⢔⣀⡄⢩⣶⣴⣀⠍⠤⠀⠀⢀⠀⠂⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣤⡤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣈⣳⣄⣀⣀⣀
⣿⣿⣛⣙⣛⣉⣛⣻⣛⣹⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⡀⠠⠔⠀⠁⠀⠀⠁⠢⡀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠈⠐⠠⡀
⠀⠀⠀⢀⠠⠒⠁⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠄⠠⠤⠋⠠⣄
⢀⠄⠊⠀⠀⢀⠤⠊⠀⠀⠀⠀⠠⠀⠀⢐⠁⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠔⠂⠀⠂⣂⠶⠨⠐⣄⡀
⠐⠠⡀⠐⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⡀⠴⠚⠁⠀⠸⠀⡠⠔⠊⠀⠀⢀⡠⠘⠉⠳⡠⢀
⠀⠀⠀⠃⠢⢈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⢮⣀⠀⡀⠀⣙⣀⡀⢀⠠⠊⠡⠄⠈⡁⠄⠋⠢⠈⠂⠄⡀
⠀⠀⠀⠢⠀⠀⠈⠐⠄⡑⠠⢀⠀⠀⠀⠀⠀⢀⠤⠖⠁⡔⣤⣕⣤⡢⠀⠐⠤⡘⢋⣥⣤⣣⡀⠂⠠⠒⠁⠀⠀⠘⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠂⢄⠀⠀⠁⠠⢈⠂⠀⠐⠈⠠⠦⢵⡺⠤⠬⣋⣀⡗⠋⠋⠒⢄⠈⢡⡆⠀⠈⡒⠉⠁⢢⣀⣀⣀⣀⣀⠤⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠈⠂⠄⡀⠀⠢⢾⡀⠀⠀⠀⠈⠙⠆⠀⠀⣄⣄⡤⣠⠰⢾⣕⠄⡈⠜⢃⣨⠖⠋⠁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠑⠠⢀⠁⠀⠀⠀⠄⢐⠅⠀⠒⠲⠖⢲⠂⠆⠒⠀⢀⠤⠚⠉⠀⡠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠁⠂⠄⡀⠀⠸⠀⠀⠀⠀⠸⠀⠀⡀⠔⠈⠀⢀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠈⠐⠠⠀⠀⠀⢀⠠⠂⠁⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠤⠤⠄⠐⠒⠒⠒⠒⠒⠀⠤⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣂⠈⠀⠀⠀⠀⠉⠓⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠉⢙⣦⣤⣀⠀⢠⠜⠁⠀⠀⠀⠙⠄⠀⣀⡤⣄⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⡰⠊⠡⠒⠈⠁⠁⠐⠠⡀⠀⢠⣾⣿⣿⡿⠟⠛⠺⡀⠀⠀⠀⠀⠀⢸⡫⠥⠄⢸⣧⠴⠶⡄⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠨⡀⠀⠀⠀⠀⣠⠤⠶⣤⠃⠀⠙⠋⠀⠤⢠⠀⢁⢀⣀⠀⠀⢀⠾⠧⢊⣴⢫⠐⡰⠀⣿⠀⠀⢱
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣻⡦⣈⠐⠀⠀⢰⢃⡀⠀⠈⣦⣀⠀⢀⡆⠠⠤⠎⠙⣁⣈⣉⠉⠷⠦⣾⣿⠃⠛⢚⢠⣿⣿⠀⠀⢸⠄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⣠⠔⠚⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠦⣄⢸⠈⠁⠃⠀⣿⣿⠢⢼⠩⠑⠀⠤⣁⡀⠠⠐⠉⠆⠀⠉⠉⢿⣼⣿⠼⣿⣿⠀⠀⢸⠄
⠀⠀⠀⢀⠁⠀⠀⢠⠎⠀⠀⣰⡿⠉⠒⠆⡉⠉⡀⠄⠀⠄⠀⠈⠻⡄⠀⠀⠘⡍⠉⠀⠆⠀⣀⣀⠷⠸⠗⠂⠈⠉⠘⠓⠒⠒⠈⠉⠀⠀⠀⠁⠀⠀⢸⠄
⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠻⣧⣀⡠⠖⠋⠉⠉⠨⡄⠀⠀⠀⠀⡀⠀⠔⠘⠃⠠⠤⢦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⢸⠀⠀⠀⢿⣄⠀⠀⠀⠈⠉⠐⢄⠀⢀⣀⠠⠌⠁⠀⢀⣠⠿⠦⠖⣲⠦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠹⣷⣦⣄⣀⠀⠀⠀⠉⠁⠀⠀⣀⡠⠚⠉⠀⡠⠒⠹⠀⠀⣀⣄⣊⣦⡄⣀⣀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡜⠀⢀⡀⠁⢥⣞⠉⠀⠘⣿⡀⠀⠘⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣇⠀⠀⠀⠈⢱⠁⠀⠀⠀⠀⢑⠦⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠠⠤⢀⣀⣀⣀⠀⢀⠀⣀⠀⣀⡀⠠⠤⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠀⠉⠍⠢⣄⣀
⠀⢀⣀⡤⠤⠴⢞⣡⠔⠂⠀⣄⠀⡀⠈⠡⣠⠆⠀⡀⢀⡠⣀⠈⡇
⠀⣏⠀⠀⣠⡔⠋⠑⣤⠀⠀⢈⠿⣅⠠⠀⠀⠀⠠⠈⠁⣀⣠⢴⠇
⠀⠘⡶⠦⢤⣌⣳⣉⡀⢈⣂⣀⣀⡠⠴⠒⠛⣋⣉⣉⣉⡡⠴⠋⢀⣀⣤⣔⣪⣿⣯⣵⣖⡒⣒⢤⡀
⠀⠀⠈⠷⣤⣀⣀⣈⢉⣉⠉⣉⣁⡤⠴⠊⠉⠁⠀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⡿⣛⣁⠛⣿⣎⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠤⣒⣯⣵⣶⢶⢟⣳⣦⣼⣷⣿⣾⣿⣿⡕⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠟⣷⠫⣝⣾⠿⢯⣭⡭⠿⠭⢿⣿⣿⣿⣟⣸⡿⢥⡾
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣞⢠⣿⡇⠀⣿⣿⡇⠀⠀⠀⢹⣿⡦⢀⣀⡠⠟⠁
⠀⢀⡴⣫⣶⣦⢰⣍⠒⠤⢤⣄⣀⣀⣀⣀⣈⣉⠁⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠋⠉⠉
⠀⣾⣴⣿⣿⣿⠸⣿⣿⣿⠿⢃⣶⣶⣶⣶⣤⣍⣙⠢⣄
⠀⡇⣿⣿⣿⣿⣆⠠⣭⣀⠒⠛⠛⠛⠛⢛⣉⣭⣭⣶⢘⡆
⠀⣇⠹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣥⣾⡇
⠀⢹⣦⣝⡛⠟⠃⣸⣿⣿⣿⣿⣿⠟⣫⠴⠋⠁⣠⠴⠛⠀⣀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢿⡄⠉⠛⠒⠬⢭⣭⣭⣭⣶⣿⣿⣤⠔⠋⠀⢀⡔⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠊⠁⠀⠈⠓⠤⡀
⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠓⠤⣀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠀⣀⣠⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⠀⣶⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠁⣐⡂⠀⠀⠐⢒⢖⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣈⢣⠒⡟⠘⣇⡖⡄⠀⠀⠀⠀⠀⠀⡜⠠⣀⠔⢂⠀⢈⣦⠴⠓⡄⠀⠳⣄⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⢱⣠⡄⡂⢀⡸⢹⣠⡆⠀⠀⠀⠀⢰⡧⠀⠙⣦⡴⠚⡍⠀⢱⣤⠞⠣⡀⢈⠦⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠾⠞⣹⡻⡁⣄⠙⢉⠘⡿⡄⠀⠀⠀⠸⢈⠀⠈⠉⢶⣀⠝⢿⡁⢈⣧⡔⠉⠣⡀⡨⠶⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣧⣿⣿⣿⣯⠾⡍⢐⡀⢸⣦⠀⠀⠈⠃⣱⣀⠀⠋⠱⣄⡠⠓⣏⠀⢙⣦⠐⠉⠂⣠⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠿⠛⠋⠃⡀⠀⢻⠚⠓⠊⠘⠂⠀⠈⢿⢁⡃⢄⣀⣉⠃⠀⠬⠓⠉⢀⣠⠴⠋⠀⠈
⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁⠀⠀⠀⣶⢉⡓⣚⣹⠃⠀⠀⢐⠀⠀⠀⠁⠀⠀⢈⡉⢋⠉⠉⠉⠉⡉
⠀⠀⠀⠸⠉⠉⠉⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣦⡃⠀⠀⠘⠀⢱⣦⡦⠘⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀
⠀⠀⠀⠀⣤⣤⣤⣴⠷⠤⣤⣀⣠⣤⣤⡄⢀⣀⠀⠀⠘⠝⠙⠀⠀⠀⠀⣪⡙⣷⡴⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣡⠶⠺⣕⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣟⣦⢄⡒⣛⣸⠑⢦⣄⡐⢝⣀⡠⣄⡀⡈⠓⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣧⠈⡀⠈⠹⣿⠘⣇⡀
⠀⠀⠀⠀⠀⠀⢀⡙⠏⠞⠃⠢⠀⡁⠰⡵⣸⡏⠀⣷⢟⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢋⠴⣊⣬⢿⡮⡅⠀⠀⠉⠀⢇⠄
⠀⠀⠀⠀⠀⠀⠠⠙⠲⠽⣟⡳⢀⣺⣡⣎⠉⠀⠀⢡⡼⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠷⣾⢛⣼⡿⠉⠈⠱⡄⠀⠀⠀⠾⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢻⡿⠺⢖⣤⡀⣠⣬⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢁⣴⠾⣓⡯⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠙⠮⣭⢱⣎⡀⠄⠚⠁⠀⠀⠀⠀⠀⣀⣤⠔⠋⣉⠠⢚⣩⠔⠛⢉⡴⠀⠀⠌⠀⠀⠀⠈⠀⠀⢀⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢀⣀⣤⣶⡷⠷⠒⢒⣩⡴⠞⠉⠀⠀⠀⢸⣿⣄⠀⠀⢶⣀⠂⠈⠐⠀⠁⠀⠎⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣧⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⠓⠀⠀⠀⢹⣇⠀⠀⠀⣨⢀⣴⠇
⠀⠀⠀⠀⠀⣠⠖⠀⠂⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀⣀⣀⣰⣿⣯⣻⣿⡶⠦⣦⡄⠀⠄⠠⣀⣺⣟⣾⡿⢷⡄⠀⣀⣼⣟⢃⣠⠜⣡⠞⡟
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠭⠿⣾⠿⠿⣭⣉⣉⣙⣙⠿⢿⣦⣭⣠⣡⡤⠶⣊⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠿⢶⣭⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢦⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⣬⣿⣦⣧⠀⠀⠀⠀⠋⠀⠈⠐⠓⠒⠒⠉⠉⠁⠀⠀⢱⣄⡀
⠀⢲⡻⣷⣿⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⢸⣾⣇⣿⣼⣅⣿⡾⠀⠀⠴⢄⣀⣀⡀⠀⢀⣀⣀⣠⣴⡆⠀⣾⠇⠁
⠀⢻⣭⣻⣢⡦⢰⡲⣯⡳⣽⡏⠀⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠈⠙⢿⣇⢸⡿⠿⠿⣿⣦⠸⡟
⠀⠀⠙⠻⣿⣷⣶⣿⣮⣽⠟⠀⠀⠀⠈⢢⡻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢺⠹⣸⠀⠀⠀⢌⡏⢠⠇
⠀⠀⠀⠀⠈⠻⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣩⡭⡯⠍⣹⡄⠀⠀⠀⠀⠀⠈⠈⠢⠋⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⡘⠀⢤⠀⠀⠀⠀⢰⠋⠛⠤⡷⠞⠋⢳⠀⠀⠀⢀⢾⢀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣧⠀⠀⠸⡧⠀⢠⡿⡟⣿⡄⠀⢠⡴⣻⣭⣵⡽⢿⣷⡆
⠀⠀⠀⠀⣀⡄⡰⠁⢀⢂⣤⣀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠘⠷⣷⠷⠃⠀⣵⡞⣿⣿⡟⣿⣯⠻⣿
⠀⠐⣿⣶⣌⣿⡇⠀⠀⣹⣏⣠⣶⡷⠀⠀⢀⠀⠀⠀⢆⡀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢠⣁⣾⣿⣧⣿⣻⢄⡿
⠀⠀⠈⠉⠋⢻⣿⠀⢠⣿⠏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠾⣼⣿⣷⣠⡀⠀⢸⡿⣽⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠘⣿⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⡀⠀⠀⠤⢤⣴⡏⠀⠀⢠⡷⣱⡿⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠱⣥⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⣭⠄⠀⠀⠀⠀⢸⡇⠀⠀⠸⣟⣫⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠚⠉⠓⠢⣄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠔⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣧⡀
⠀⠀⠀⠀⢀⡴⠋⡠⠒⠀⠐⠈⠍⣻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣷
⠀⠀⠀⠀⣼⠁⡎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡶⠦⣤⣤⣀⣠⣤⣤⣖⡯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⢠⡿⠀⢧⠀⠀⠀⠀⢀⡴⠖⢒⢶⡄⠙⢢⡀⢀⡤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⢸⣇⠡⠘⢆⠀⠀⠀⡞⠀⠊⠉⢳⣿⠀⠀⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⣿⡀⢁⠘⢆⠀⠸⡇⡆⠀⢀⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼
⠀⠀⠀⠀⠸⣧⠀⠣⡈⢣⡀⠳⣝⣒⣋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⣿
⠀⠀⠀⠀⠀⠙⣧⠀⠈⠢⡱⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎⢰⡟
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠪⣳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠚⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠈⠓⢌⡉⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢚⡡⠔⠉⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠑⠒⠨⠵⣲⡶⠶⠶⠶⠶⠖⠖⠒⠒⠚⣉⡥⠔⠚⠁⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⠁⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⠟⠛⠛⠛⠛⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠶⠖⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠏⠉⠙⡥⠀⠀⠀⣛⠛⠛⠛⠷⢤⠦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⠃⡀⠰⠀⠀⠀⠈⠉⠀⠀⠀⢀⡈⠀⠂⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠛⠉⠀⠠⠀⠈⠀⠀⠀⢀⡄⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⠂⠀⢰⠂⠀⠀⠰⠂⠈⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠈⠀⠍⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠚⠀⠀⠞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⠀⠀⡀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⢀⣤⢿⠄⣴⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠷⣄
⠀⠀⠀⠀⠀⣴⠋⢠⡟⠀⠰⡂⠀⠀⡉⠁⠀⠀⣀⡀⠀⠀⠀⠈⠃⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠰⠄⣿⠀⢸⣧
⠀⠀⠀⠀⠀⣿⡄⠘⢧⣉⠀⠀⠀⠘⠒⠀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⡼⢻
⠀⠀⠀⠀⠀⣇⠙⠶⣄⡉⠳⢦⣀⡁⠀⠘⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠂⠀⠀⠔⡆⠀⠀⣀⣠⡾⠋⣠⠞⠁⣼
⠀⠀⠀⠀⠀⢻⡀⠀⠈⠙⠲⢤⣈⡙⢦⡴⢶⣦⣤⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠾⢉⣠⡴⠚⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠤⣤⣉⣉⣉⡉⠙⠛⠛⠛⠛⢋⣉⣉⣠⠤⠶⠚⠋⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⡈⠉⠙⠛⠓⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠛⣉⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠦⠤⠤⠤⠤⠤⠴⠶⠖⠛⠋⠉

⠀⡴⠟⠻⣦⣤⣤⡀
⣼⠀⠀⠀⠁⠀⠈⢻⣄⣀
⠻⣤⣤⣄⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠈⠻⠦⢦⣤⡀⠀⠀⠀⠀⠈⢙⡷⠶⠾⠿⠷⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠶⠾⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⣉⣤⠤⠶⠶⠶⠒⠒⠲⠦⢄⣉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣤⢾⡄⡀⠀⠀⠀⢀⡴⠋⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠙⢦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢿⡀⠀⠉⠀⠀⠀⣠⢏⡴⠉⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠟⠁⠀⠀⠸⡇⠀⠀⠀⠀⣴⢣⠏⠀⠀⠀⣠⡤⠶⠶⢤⣀⠀⠀⠀⡴⠊⠉⠀⠀⠈⠉⠙⠢⡀⠀⠀⢸⡆⢿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⢣⠆⠀⠀⣴⠟⠁⠀⠀⠀⣠⠈⢳⠀⢸⡁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡇⢸⡀⠐⢯⣄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡆⠀⢠⢇⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠴⠃⠈⠧⣄⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⢸⠁⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣿⠃⠀⠀⢸⣇⠀⡟⣸⠀⠀⡼⠁⠀⠀⠀⠁⠀⢠⠎⢁⡤⠶⢤⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠃⠀⠀⠀⠀⣿⢰⠇⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⡏⠀⢸⠁⠀⠀⡿⠀⢹⠀⠀⠀⠀⠀⠀⢀⡟⠀⡼⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢰⡇⠀⢸⡀⠀⠀⠀⠂⠀⠀⢧⠀⠘⠦⠤⠞⠁⢠⡆⠀⠀⠀⠀⠀⢀⡞⠀⡼⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⠋⢀⡼⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⣧⠀⠀⠘⢦⣀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⠞⠁⣠⠎⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠁⢀⡴⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣉⣙⠒⠒⠶⠶⠶⠒⣒⣊⣩⣥⠴⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠖⠐⠢⠄⣠⠔⡲⠂⠟⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠀⠀⠀⠿⠈⠀⠀⠀⠀⠀⠀⠙⢆⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠼⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠁⣂⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⢀⡴⠚⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣀⣄⡢⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⠎⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠢⣀⢀⡠⠠⠠⣀⣀⡴⠞⠧⡀
⠀⢸⠂⡐⠤⠀⠁⠀⠀⠀⣝⡠⠤⣤⣦⡴⠴⣤⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡃⠀⠀⠙
⡰⠋⠁⢀⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡎
⡯⠀⠀⠈⡀⠀⠀⡀⠤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⡆⠀⠀⠀⣠⣜⣡⠋⠀⠀⠀⠉⠉⠛⠀⠀⠃⣴
⠑⣢⠔⠒⠉⡐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠠⢀⡽⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠑⢤⠵⠊⠈
⠸⡄⠀⡀⠀⣄⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⣀⢈⢂⡤⠞⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡎⣠⠏
⠀⠸⢤⣀⣨⣇⠀⠀⠀⠀⠀⢀⣏⠀⢀⣤⣩⠟⠉⣷⣄⣤⣂⣀⣴⣦⣀⡀⠀⣀⣀⣂⡡⠎⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠈⠓⠦⣤⠤⠟⠙⣪⡹⠯⠁⠙⣧⠀⢹⡇⠙⣇⠀⠘⡟⠈⢙⡷⠖⡶⠏⠀⠀⣀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠦⡤⠾⡆⠘⡄⠈⡇⠀⠸⠀⠀⡇⡾⢭⠴⠞⠁⠈⠓⠦⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠠⢀⣧⠀⠀⡄⠀⠁⠀⣎⡴⠔⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⠇⠈⠀⠈⠁⠘⠀⠀⠁⠀⠀⢠⠟⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⣨⠻⡀⢱⠀⠀⠀⠀⠀⠀⠀⠠⣠⠆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣨⠁⢸⠁⠘⡀⠀⠀⠀⠀⠟⠁⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡔⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⡄⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣫⣽⣶⣶⠒⡠⣔⣫⠽⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣭⣾⡿⠛⠛⠛⢁⣦⡉⣓⠾⣭⣿⣓⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⠏⠁⡰⣜⢮⡿⣷⣽⣾⣧⠈⠻⢿⣓⣶⠾⢤⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣉⡁⣴⣿⣿⣮⣳⣝⡮⣷⣿⣿⡬⣧⣄⠺⣭⣽⣛⡂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⣮⣳⡜⢿⡯⣟⢮⣗⢿⣚⠩⣿⣣⢿⣾⣦⠙⢳⢯⣟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠻⣿⣧⠈⢿⣮⣟⡮⣝⡾⢈⣓⠾⣽⣲⠏⠀⠈⣓⢏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠻⠃⠄⣶⣝⡲⣝⡛⣭⣐⠮⣝⡆⣬⣛⠂⣐⢎⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃⣼⠀⢿⣿⣝⡲⣽⡷⢮⣙⠾⣱⢰⣝⡷⠌⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⣿⠀⣷⣽⡻⣽⣻⢏⡳⣭⣳⣇⡻⣮⠃⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⡿⢠⡹⣿⣿⡳⢍⡳⣝⢮⡻⣯⡻⠀⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⢃⣺⣷⣝⢟⢿⡳⣝⢮⣳⡽⠎⢁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡾⠏⡰⣝⢮⣿⡇⠠⠅⠈⠀⠁⢀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣶⠁⣰⣿⣾⣯⠗⠀⠀⠀⠀⣀⣴⢸⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠟⡃⣾⣯⣿⡿⠃⠊⠀⣠⣴⡇⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⡙⠙⠛⢋⣀⣠⡆⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣇⣷⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢶⡴⠒⠛⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⠀⠀⢸⡀⢀⡀⠀⣸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⢀⠀⠈⠀⠀⠀⠈⠉⠉⠀⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⡠⠜⠡⣾⠑⣶⡦⢆⠀⣤⠞⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠏⠸⢋⣠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠋⠀⠀⡤⠀⠀⠀⠀⢀⠴⠊⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠔⠀⠰⠈⠀⠀⣐⠐⠀⠋⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⡀⠐⣀⠀⠀⠈⢧⠰⡌⠳⣖⠉⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠧⠂⠈⠙⠁⣆⣀⣉⣉⠁⠀⠀⠛⠀⠀⠇⠀⣿⡟⠉⠀⡊⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠘⣦⣴⣄⠀⠀⠨⠿⡏⣡⡞⠠⠁⠀⠀⢀⣠⠉⠁⠀⠀⡘⠉⢲⡴⠏
⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠹⠀⣀⠀⠙⠉⡄⠠⢄⠀⠀⠄⢻⠀⠀⣠⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⠋⠈⠑⠀⠀⠀⠀⠱⡀⠐⠬⠧⣀⡿⠶⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⢀⡠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⢀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠂
⠐⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠄
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⣄⣤⠛⠁⢠⡴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⢄⠀⠀⣁⠔⠀⠀⠀⠀⠀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠅⠀⠄⠈⠈
⠀⠀⠀⠀⠅⠀⠸⠒⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠁⠀⠀⡀⠀⢀⣼⠉⡪⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⡀⠀⠀⢄
⠀⠀⠉⠀⠀⠄⠀⠠⠀⠀⠁⠀⡰⠋⠑⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠘⠀⢠⡀⠊⠀⠀⠀⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠒⡂⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⡔⠁⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋⠉⢰⠁⠀⠀⠀⠘⠲⣀⠀⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠒⠉⠀⠁⠐⠉⠑⠢⠀⠈⣄⣀⣠⣿⠀⡀⠘⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠀⠒⠀⠀⠀⠀⠀⢘⠦⣔⢈⡇⡼⣿⠉⠑⢠⠀⠀⠀⠊⠑⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⡈⠀⠀⠀⠀⠀⠀⣤⠶⡍⢷⡀⠱⡝⠃⠉⡁⠀⢰⠃⠀⣠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠇⡐⠀⠱⢄⠀⠐⠀⠀⠀⡈⢠⠙⡌⢿⡄⢡⠀⢰⠁⢀⠜⣠⠖⡽⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢹⡀⠀⢀⠜⠫⡝⠂⢆⠐⠈⢇⢈⠀⢋⡿⠃⡔⠁⠀⠉⠈⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⢁⡤⠀⠈⢦⠘⡄⠀⠘⠸⠀⠘⢀⠎⢀⠔⠀⢄⠀⠀⠀⠀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠒⠒⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠁⠁⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠀⠀⠖⠋⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡸⠶⠲⡶⠶⠒⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠠⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⢼⡗⢠⡀⠀⠀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠁⡤⢇⠀⠀⠀⠀⠈⠂⠀⡀
⠀⠀⡰⢠⠐⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠨⠒⠀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠞⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠓⠀⠀⡶⠦⠀⠀⠉⠡⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⣀⠳⠀⠠⠀⠀⠀⠀⠀⠀⢾⠀⠀⠔⠈⠀⠂⠀⠀⣶⠋⠙⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠠⠄⠉⢠⡀⠀⠀⠀⢀⡤⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⠤⠒⠂⠀⠨⣆⠈⠀⡆⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠞⠁⠀⠀⠀⠀⠘⠢⠐⢆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡀⡀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠠⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⢶⣳⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠠⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⡞⠉⣩⣆⠈⠛⣿⣄⠀⠀⠀⠀⠀⠀⠓⢄⠀⣑⡈⣳⣤⣶⡛⠋⠁⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣨⠇⠀⠎⠛⠁⠀⠀⠀⠛⡆⢀⠀⡀⠀⠉⠻⣅⢠⣶⠟⣉⠙⡛⠛⠉⠈⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣶⣄⣀⠀⠀⠉⠲⣄⠀⠀⢲⣄⣼⠦⠶⠃⠄⠀⣈⠀⠀⡀⠈⢉⡟⠉⠛⠉⠙⠋⠀⠐⠋
⠀⠀⠀⠰⠂⠀⠀⠀⠆⠀⢾⣿⢁⠹⣜⢦⠀⠀⠙⠶⣽⡮⠹⣿⣍⣷⠶⠶⠟⠿⠿⢷⣬⡤⠀⠁
⠀⠀⠀⠀⣨⠥⠀⠀⡤⠀⠈⢿⣟⣷⡜⢿⡇⠀⢀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠐
⠀⠀⠐⡤⠿⠔⠀⠀⢅⠀⠀⠸⣿⣿⣿⣛⣣⡄⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡦⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠡⣀⠀⠄⠀⠀⠀⢄⡀⠈⠻⠿⣿⠟⠁⠀⠁⠀⣀⠤⠀⠀⠀⣠⠠⢲⠇⢰⡆⢀⠀⠀⠀⠀⠀⠈⢶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⢠⠊⠀⠀⠀⠄⢀⠘⣠⣷⣤⣼⣿⣿⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⣀⠀⣈⡄⢦⣤⠀⢄⡀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣷⡦
⠀⢀⠀⣀⡿⠟⣹⢧⣭⣶⣛⣳⠛⡆⠀⠀⠀⠋⢒⠘⠃⡀⣿⣿⣷⣿⡿⣟⠙⠙⠏⠙⠢⣅⣾⠁⠀⠀⠀⢀⠔
⠀⠘⣿⢿⠳⢞⢧⢺⣿⣟⠻⡿⣷⢤⣀⠀⠀⠐⠚⠒⠶⠚⠛⠛⣁⣈⠉⠻⡗⢲⠖⣢⣴⣯⣿⣦⠒⠆⠀⠁⠐⠶
⠀⠀⢰⣾⡖⣸⢋⡧⠌⠹⠇⢰⡜⣧⣌⣧⣄⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⠓⠴⠼⠿⠟⠁⠀⠀⠀⠂
⠀⠀⠈⢛⣿⣽⡿⢶⠐⣆⡀⢈⡷⣼⠟⣿⣟⣆⠀⠀⢀⣄⣴⠰⣾⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡤
⠀⠀⠀⠨⠙⢛⣛⣛⠁⣬⣿⣟⣿⣯⣯⣿⣿⠷⠂⠀⠀⠙⢿⠂⢩⠃⠈⠉⠉⠀⢧⣤⣡⣶⣿⣿⣧⣄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠈⠁⢲⣍⢡⠀⡀⠀⠀⠿⢻⣧⣽⣷⢾⣤⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⡓⢸⠂⠀⠀⠀⠼⡦⠀⠁⠀⢀⡄⠈⣿⣿⣿⣸⣯⡐⠀⠀⠀⢠
⠀⠀⣀⠀⢀⡤⠴⠶⠚⠓⣒⠈⢉⠀⠀⠀⠀⠀⠸⣿⣷⠲⡤⣤⡤⠀⠁⠲⠂⠀⠀⠐⢃⡟⣿⣯⣿⣷⣷⡖⠀⡐⠀⡀
⠀⢠⣏⢳⣛⡅⠶⠾⠿⣷⡎⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠤⠂⢉⡭⣿⣇⠀⠀⠀⠩⡰⠛⣿⣿⣿⣿⣷⣵⣤⡟
⠀⠀⣿⣿⢽⣷⣿⣾⣿⡟⠑⠁⠀⠀⡠⠞⠀⠀⠂⠘⠂⠀⡰⣯⣿⠿⠷⠛⠁⢀⠀⠀⠀⠠⠾⣛⠛⠿⢿⣛⠷⠚⠁
⠀⠀⠘⣿⣵⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠈⠐⠀⠒⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢷⠀⠀⠀⠀⠾⢥⣶⣴⠟⢿⣦⡀⠀⢀⠀⠀⠀⠀⢀⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡒⢉⣡⢤⡾⠀⠀⣴⣤⣀⠂⢤⡀⠀⢾⠿⣿⠟⠻⣷⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⢰⣏⢱⠍⠐⠋⠀⠀⢶⡶⢶⣿⢿⣦⣈⠿⠛⠳⢤⡀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⢤⣉⠂⠠⠊⠀⣠⠶⣯⣵⡿⠟⠋⠀⣀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣳⣦⡀⠙⠧⠀⠈⠀⠤⡉⠻⣿⣶⡆
⠀⠀⠀⠀⠠⢌⠲⢠⣰⡾⣱⣾⡽⠋⠀⠀⠀⢀⠀⠈⢰⣶⣾⣿⡷⠤⡀⠀⠀⠀⠀⠈⠙⠛⠦⠘⢦⠀⠀⣀⣀⡁⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠒⠿⠾⠛⠁⠀⠀⠒⠂⢀⣷⣮⣓⣞⣟⣛⣻⣥⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠈⠻⠲⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣯⣒⠚⠛⠛⠛⠻⣿⣿⣿⣿⠟⠎⢀⠀⠀⠀⠀⡄⡠⠀⠀⠈⠓⠠⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⣾⣿⣷⣷⡶⣞⣾⣶⣾⠗⡶⠁⠀⠀⢀⣻⣴⡌⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠛⠿⠇⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡤⠖⢚⣋⣉⣉⣉⣉⣀⣠⣤⣤⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⣷⣶⣤⣀
⠀⠐⣏⠛⢛⣻⣿⣿⡿⠿⠿⠿⠿⠿⢯⣭⣭⣭⣭⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⠥⠤⠤⠤⠤⣤⣬⡉⢧
⠀⠀⠙⣆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠟
⠀⠀⠀⠈⠲⠿⠶⠒⠒⠒⠶⠞⣶⣄⠒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣶⣶⢄⡠⠶⢶⠻⠋
⠀⠀⠀⠀⢀⠀⣨⠿⢟⣿⠿⠿⢿⡿⠯⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢭⣭⣭⣭⣭⠝⠋⠀⠂⢸
⠀⠀⠀⠀⡾⡜⢡⠖⠉⠀⠀⠀⢸⣷⠃⣀⡬⠓⢦⠀⠀⠀⠀⠀⣠⠔⢋⣩⠽⠋⠁⢠⣤⢀⠀⢸⡷⣄⡀
⠀⠀⠀⢰⢇⣷⠃⠀⠠⠴⠶⣦⢼⠿⠋⠀⠀⠀⠈⢳⡀⠀⠀⣴⣧⠴⠋⠁⠀⠀⠀⠈⠁⠘⠃⠘⡇⠀⠙⢆
⠀⠀⠀⣸⢸⡇⠀⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⠴⠚⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠃
⠀⠀⠀⡏⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⢸⣠⠾⠃
⠀⠀⠀⡇⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢥⡤⣴⡄⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡦⢾⣿⡆
⠀⠀⢰⡇⡏⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣹⣍⡉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣠⣿⣤⣼⢸⠁
⠀⠀⠈⢧⢧⡀⠀⠱⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⣿⢯⣙⠓⠒⠚⠛⠛⣉⣭⣿⣟⣛⠻⢧⣤⣄⣸⣺
⠀⠀⠀⠈⢳⠬⣝⣛⣛⣓⣒⣒⣒⣒⡿⣺⣥⣄⡏⠈⠳⠈⠙⠓⣖⣚⠉⢁⡾⣍⣛⣿⢻⡽⢯⣉⡏⡧
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠉⠉⠉⢹⣿⠁⠘⢾⣶⣠⣶⣤⣴⣚⣁⣘⣞⣉⣀⣉⣩⣯⠬⠤⠚⡽
⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣄⣀⣀⣘⣋⣀⣀⣀⣀⣉⣀⣀⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣒⠋⠭⠒⢂⣈⡠⢤⠄⣀⣀⣀⡤⣤⢤⠄⣀⡀⠉⠉⠛⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢞⣫⡴⠞⠋⠁⣀⠔⣩⣤⠆⣹⢭⣋⡿⢶⣻⣷⣶⣧⣏⠉⠛⠏⡏⠛⡿⡖⣶⣄⠉⢷⣦⣀
⠀⠀⠀⠀⠀⣠⣟⠵⠛⢛⣇⣤⡦⣚⣕⣺⢏⣖⡺⠗⠻⣞⣫⠯⣗⣻⡖⢮⡿⣦⣤⣀⣄⣀⣠⣆⣋⠟⢻⡗⣜⢿⡷⡄
⠀⠀⠀⠀⢠⣿⡏⢀⡰⢯⣿⣤⢙⣖⣩⣿⠿⣿⡾⠿⣷⣿⣻⠿⣟⡼⠿⢏⣸⠯⠘⣿⣿⣿⣶⣒⣻⣍⡽⢫⢸⠘⢉⣧
⠀⠀⠀⠀⢸⡿⣷⢬⡳⣯⣽⡯⣟⠛⢷⡾⣷⠿⣶⡏⡼⢿⣭⡿⢭⣿⣳⣿⣤⠞⠋⠒⣿⡔⣫⠿⠭⣯⣵⣾⣗⡷⣺⣿
⠀⠀⠀⠀⠀⣿⠘⠳⢿⣗⡺⠭⠟⡕⣲⣶⠒⣫⣝⣺⣳⣿⣿⣿⣷⣿⣽⣿⣯⣀⠶⣎⡹⣟⣓⣶⢿⣿⣯⣽⣿⡟⢱⡇
⠀⠀⠀⠀⠀⢸⡆⠀⡈⠀⡏⢛⡲⠤⣝⣚⣣⣏⣸⣟⣿⣙⣍⡁⠻⡩⢟⣿⣞⣯⣶⣾⣼⣷⣾⣿⡿⠿⡟⠋⣧⠇⣾⠃
⠀⠀⠀⠀⠀⠀⢿⠀⢇⠀⠀⠈⠭⣓⣒⠢⠭⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⢋⠩⠭⠁⠀⠀⠈⠁⢸⠋⣸⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⢚⣩⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣤⣤⣤⡤⠤⠴⠒⠊⠉

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸⣿⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⠀⠸⣿⠀⠀⣧⡈⠳⣄
⠀⠀⠀⠐⡄⢀⡤⠖⠉⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⢞⡥⣸⡷⠀⠀⠀⢿⠀⣄⣿⣧⡄⠈⣳⡄
⠀⠀⠀⠀⠘⠾⡀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣤⡴⠋⢠⢸⡇⣿⡇⠀⠀⣠⠀⢰⣯⣿⡟⢃⢞⠝⠁
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⡑⠈⢿⣧⠹⡄⢸⢸⡇⣿⡇⠀⠀⣿⠀⢸⠛⣃⢔⠕⠁
⠀⠀⠀⠀⠀⠀⣈⡆⠀⢐⠆⠰⡁⠘⣆⠈⡿⠛⠛⣆⢼⡇⢹⠀⠀⠀⡟⢀⣠⡾⠗⠁⠀⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢳⡀⢹⣄⣸⠖⠃⠀⠀⠈⢆⠁⢸⠀⢀⣠⡶⢟⣋⠴⢒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡾⠛⠉⠀⢘⠇⠀⠏⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡎⠀⢀⣸⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⢤⣤⣄⣀⣠⡤⠶⠒⠚⢛⣒⣚⠛⢧⠀⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣥⣤⣍⡉⠉⣤⣤⣄⠲⣶⣶⣶⣶⣶⣿⢃⣾⣿⡿⣋⣴⣿⢀⡟⣷⠇
⠀⠀⠀⠀⠀⠀⣼⠁⠾⣿⣶⣯⣽⣿⣦⡘⢿⣿⣷⣮⣿⣿⣿⡿⠃⣚⣻⣻⣿⣿⣿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠶⣿⠗⠲⠶⠤⣭⣛⠿⣿⣿⣌⡛⢋⣭⣭⣭⣍⠐⢋⣭⣭⣭⣭⡭⠀⢀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠆⡖⢩⣛⠶⣌⡙⠻⠶⣦⣭⣭⣭⡴⠿⠟⣋⣉⣥⠴⠞⡻⢟⣼⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡲⠶⣾⣿⣑⠈⠉⠛⠒⠶⠶⠶⠖⠚⠋⠉⠉⠀⠰⠖⣋⡵⢛⡁⠦⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠁⢀⠍⠙⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠛⠋⠇⠀⠢⠀⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠙⠛⠉⠉⣉⠁⠁⠀⢀⠠⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠉⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⡹⠛⠉⠉⠁⠉⠝⠋⠀⠀⠀⠈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡌⠀⠀⠀⠀⡠⠊⠁⠀⠀⠉⠐⢄⠀⠀⠙⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠒⠚⠓⠐⢠⠔⠂⠉⠁⠲⡀⣀⡀⡀⣀⠇⠀⡰⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣤⡇⠀⠀⠀⢀⡤⠋⠝⠋⠟⢩⣉⢯⠀⠀⠀⡸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡴⠡⢐⠑⠰⡖⠺⡻⠐⡀⠀⠀⠀⠋⣀⣫⣤⡄⠒⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢾⠀⠀⠄⣀⠀⠈⠀⡘⠄⠐⠆⠀⠀⠀⠁⠈⠰⠹⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⡟⠙⢄⡤⠐⠚⢦⣉⠁⠀⣀⠀⠀⠈⠚⠄⠈⠢⡀⠀⢱⠁⠀⢾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠸⡇⢀⠊⠀⠀⠀⠀⣱⠠⠤⠤⠀⠘⠒⠠⢀⠀⠀⠈⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡷⠘⠀⠀⠀⠀⢀⠇⣉⠀⠒⠀⠀⠀⠐⠂⠁⠂⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠡⣄⡠⠠⢯⠁⠀⡀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡁⠀⠀⢹⡀⠀⠖⠒⠀⣀⠠⠀⢤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠱⣀⠀⠀⠳⠤⠯⠴⣁⠀⣠⡴⠏⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣅⣼⣥⣀⣀⣴⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠉⠉⠉⠈⠉⠉⠐⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠉⢉⣙⠛⠷⢶⣤⣀⠀⠀⠈⠑⢄
⠀⠀⣤⢠⣄⣤⣤⡄⠀⠀⠀⠀⡠⠊⠀⠀⣠⣴⣿⠕⠊⠉⠉⡉⠉⣒⢄⡰⠁⠀⠉⢦⡀⠈⠙⠳⣦⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡴⢄
⠀⠀⢽⣿⣿⣿⢹⡇⠀⠀⠀⡜⠀⠀⢀⣴⢟⠟⠀⠀⠀⠀⠘⠜⠈⠊⠈⢟⠀⠀⠀⢠⠊⠙⢷⡖⢁⠙⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⡇⠀⠱⡀
⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⡞⠀⠀⢀⡾⢃⠎⠀⠀⠀⠀⠀⠓⠀⠚⠐⠗⡟⠀⠀⠀⠀⠑⡬⠷⢵⡦⠼⠚⠿⡄⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⢱
⠀⠀⠈⢿⠻⢛⡟⠀⠀⡸⠀⠀⢀⣾⠁⡎⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⣇⣀⠤⠄⠠⢄⣥⠒⠀⣷⡛⡤⠔⢻⣆⠀⠀⢱⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⢹⡇⠀⠀⢀⠃⠀⠀⣸⠇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⢤⠀⡯⠇⡒⡌⢉⠛⣿⡟⠃⠀⠀⢻⡄⠀⠀⡇⠀⠀⡇⠀⡠⠃
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡿⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⢌⢉⡸⠝⠀⡬⡠⠚⠓⠖⠓⠒⠒⢄⠘⣧⠀⠀⢰⠀⠀⢧⡔⠁
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⡀⣨⢇⣰⡎⡤⡔⠋⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⣯⠜⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⣘⠚⠉⢉⢕⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⠀⠀⢸⠀⠀⡘⡇
⠀⠀⠀⠀⢸⢰⠀⠀⠈⡄⠀⠰⣁⣄⠀⠀⠀⢠⠊⢀⠤⣄⠸⡡⠀⠉⢢⡈⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡟⠀⠀⡆⠀⠀⡇⡇
⠀⠀⠀⠀⠸⢸⠀⠀⠀⢱⠀⢀⣸⡟⢢⠖⠤⠃⢀⠓⠀⣈⠀⡱⣮⢄⣀⠗⠀⣘⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣾⠃⠀⢰⠁⠀⠀⡇⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢣⢇⣀⡀⠘⡄⠀⠀⢸⠀⠀⣼⢸⠄⠉⡆⠀⢰⡩⢃⠵⠈⣉⣢⣀⠀⠀⢀⠔⢁⣾⠃⠀⢠⠃⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠣⡀⠑⠚⢷⣄⠀⠘⠮⠔⠁⠸⡠⠈⡇⠀⠘⢾⡴⠞⠋⠑⣬⢧⠉⠉⠀⣴⡟⠁⠀⡠⠃⠀⠀⠀⢸⠀⠁
⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⢷⣄⡀⠀⠀⠀⠑⠜⠁⢠⠻⡄⢙⡆⠛⠭⠿⠃⣀⣴⠟⠉⠀⢀⠔⠁⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠈⠺⣬⡖⣁⣠⣤⡶⠟⠋⠁⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠉⠉⠛⠛⠛⠓⠚⠛⠉⠉⠀⠀⢀⡠⠔⠊
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡠⠋⡞
⠀⠀⠀⠀⠀⢠⠞⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣠⠞⣡⡾⡇
⠀⠀⠀⠀⢰⣃⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⣠⠞⢁⠜⠁⣿⠃
⠀⠀⠀⠀⢸⣌⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⡛⠛⠛⠓⠒⠒⠒⠒⣒⣒⣒⣒⣒⣒⣉⣉⣉⣡⠔⠁⠀⢠⢿
⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⠀⠈⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⢸⠀⠀⠀⢸⢺
⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⢸⠀⢀⣀⡼⣸
⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣀⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⢸⠀⠀⡴⣣⠃
⠀⠀⠀⠀⠀⢸⣸⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡠⢞⠞⠁
⠀⠀⠀⠀⠀⠈⢧⡳⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⢋⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠖⠒⠒⠒⠒⠒⠛⠋⠙⠛⡒⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠀⠀⠉⢀⠉⠓⠲⣄
⢀⡤⠴⠖⠚⠛⠉⣥⡴⠞⠉⠀⠀⠳⣄⢀⡔⠀⠀⠢⡴⠋⠀⠢⡀⢀⠴⠃⢄⠀⣼
⢸⠀⠀⠀⣡⣴⠛⠁⠈⢢⣤⠀⠀⠀⡨⠻⣄⠠⠖⠁⠀⠀⠀⠤⠈⠁⢀⣀⡤⢾⡇
⠈⣷⢤⣤⣀⡈⠙⢦⡚⠁⠈⠑⠄⠀⠀⠀⢈⣡⡤⠖⠒⠒⠒⠒⠚⠛⠉⣁⡴⠏⠀⠀⢀⣀⣠⠔⣫⣽⣭⣓⣒⠤⠤⠤⢄⡀
⠀⠈⢳⣄⣈⠉⠉⠛⠓⠶⠖⠲⠖⠒⠚⠛⠉⢀⣠⠴⠖⠒⠚⠛⠋⠉⠉⠁⠀⢀⡴⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠆⣿⣶⣌⠳⣄
⠀⠀⠀⠙⠛⠷⠴⠤⣴⣤⣤⣤⣀⡴⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣘⣻⣿⣛⠿⠿⣛⣛⣿⣛⣡⣶⣶⡆⣹⣿⣷⣜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⣫⣽⡶⢿⡿⠿⣟⣩⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣿⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠿⡗⠮⣍⣲⣟⣿⣯⣭⣭⠭⠽⣯⣼⣟⣛⣛⣛⣿⡿⣃⣿⣋⣥⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡄⠀⡿⠀⣾⣿⠁⠀⢸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣧⡉⠉⠉⠁⢠⡿⠃
⠀⠀⢀⡴⢒⣛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠚⠳⠶⣿⣿⣥⣤⣼⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠧⠶⠒⠚⠉
⠀⣴⢋⣾⣿⣿⣇⢸⣧⣄⣉⠓⠲⢶⠶⠶⠶⠶⠶⠶⠦⣤⣀⡀
⢸⢃⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⠿⠋⣰⣿⣿⣿⣿⣶⣶⣤⣉⣙⠶⣄
⣿⢸⣿⣿⣿⣿⣿⡄⠈⣉⣉⠁⠴⠾⠿⠿⠿⠿⠟⠛⠋⣉⣉⣩⣤⠘⣆
⣯⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠋⣠⣿
⢹⣆⠹⣿⣿⣿⣿⡟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⠤⠶⠞⠻⣿⡏
⠀⣿⣷⣬⣉⡛⠋⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣡⡖⠋⠁⠀⣠⡴⠞⠋⠀⣀⡤⠔⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠸⣿⡀⠈⠙⠓⠲⠬⣭⣉⣉⣉⣭⣴⣾⣿⣿⣧⣠⠖⠋⠁⠀⢀⡴⠊⠁⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠛⠉⠁⠀⠀⠉⠓⢄⡀
⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⠞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣤⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⠉⠓⠒⠚⠛⠉⠉⠀⠀⢀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⣠⡤⠴⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⢛⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⣄⡀⠀⠀⢀⣠⠴⢚⣋⣭⠤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⢭⢼⠖⠗⢋⢻⡶⠞⣫⡵⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠾⡖⠂⣍⣨⠷⢊⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣞⣉⣭⣥⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠶⠶⠦⠤⠤⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠫⢅⡶⠬⠖⡀⠵⢠⡤⢈⡓⠦⠄⣉⣙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⢀⣠⢞⠚⠣⡼⢑⣩⣄⢘⡀⠱⡶⠀⠆⡈⢁⡤⠤⡄⠨⢙⠊⢂⡉⡳⣆⡀
⠀⠀⢰⡶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠓⠒⠒⠶⠶⠶⠶⠾⠿⢶⡆
⠀⠀⠀⠻⣔⠂⠒⠀⠒⠀⠂⠐⠂⠒⠂⠒⠀⠐⠀⠒⠀⠒⠂⠒⠀⠒⠂⠒⠀⠒⠐⠂⢒⡾⠁
⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠭⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠼⠯⠭⠭⠽⠦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢆⠀⠀⠀⠀⠸⣛⣛⡫⠭⢍⣉⡓⠒⠠⠤⢀⣀⡔⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠤⠤⢤⣤⠤⢤⡤⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⡆⠀⠀⠀⣇⡃⠀⠈⡟⡐⠂⠠⠭⢅⣒⡢⠤⠭⢖⣋⠒⠢⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠘⠃⠒⠂⠀⠆⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠇⠀⠀⢰⢰⠀⠀⢀⠳⠆⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠬⠭⢒⣒⠢⠤⢌⣉⡒⠒⠢⢤⣄⠀⡧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⡄⡌⠀⠀⣸⠠⠀⠀⠀⠀⡠⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠪⡍⡏⠁⢸⠀⠑⣆⠒⢒⡶⡶⠒⠒⡟⠒⡴⠋
⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⢸⠀⢀⣧⣄⣀⣠⠳⠆⠀⠀⡠⡖⠃⢤⠀⠀⢨⡤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⢃⠃⠀⡌⠀⣠⠾⠄⠀⠀⠀⠀⠀⡆⠀⢣⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⡶⠋⡠⠤⠤⠬⡑⢄⠀⠰⠁⠱⡀⠀⢧⠀⢸⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠸⠘⠀⢀⠃⢰⠁⠉⣩⢉⠍⠉⠉⠉⠹⡉⠁⠸⡀
⠀⠀⠀⠀⠀⠀⢘⠀⠆⠀⠀⠀⠀⠷⠉⢀⠴⠒⠏⠑⠺⢦⠃⠐⠀⢃⠀⠈⡆⠂⠑⡄⠀⡌⡜⠀⠀⠀⠀⠀⡆⡆⠀⢸⠀⡞⠒⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢇
⠀⠀⡠⠔⡊⠥⢨⡄⠒⠉⠁⠈⠑⠛⢤⡃⢰⠚⢳⠀⢀⣎⣐⣀⡐⠘⡄⠀⠸⡈⡆⠘⠘⡼⠙⡀⠀⠀⠀⢠⢁⠃⠀⡇⢠⠓⠂⠀⠀⠀⠀⠀⠀⠀⢂⡋⡇⠀⢸
⢀⠜⠐⡡⡲⢶⠋⠀⠀⠀⡠⠒⢍⢁⣀⠑⣬⠀⡽⠒⠉⠠⠀⢀⡈⠉⠓⢤⡀⢣⠁⠙⢴⣣⠀⠱⡀⠀⠀⠸⠸⠀⠀⠂⢸⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠸
⠘⢀⢊⠎⠀⠇⠈⠀⠀⢰⡡⠒⡉⠀⢀⠉⠻⣸⣓⠓⠈⠉⠙⠌⢀⣠⠴⠊⠀⠸⡄⠠⠀⡏⠉⠲⢧⡀⠀⡈⠇⠀⢸⠀⡿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⡇⡄⡄⠀⢸⠀⠂⠀⢀⠎⠀⠚⠂⠀⠀⠑⠲⠧⠤⠉⠛⢖⠒⢊⠉⠂⠀⡇⠀⠀⢂⠠⢰⡁⠀⠂⢄⡙⠲⣿⠀⠀⡆⠀⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⡆
⡇⡘⠀⠀⠈⡄⠐⠀⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡀⠃⢰⠀⠀⢸⠀⠑⠙⡄⠀⡠⢀⡴⠻⠀⢠⠁⠀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⡇
⠰⠁⢀⡠⣪⠷⡀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⠀⡸⠀⠐⢨⠀⢀⠔⢃⡠⢚⠝⣢⡧⠒⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢰
⠀⠀⡟⠬⢷⣦⠌⣾⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡄⢀⠀⢱⠃⠀⠀⡜⡐⢰⢔⡯⢒⡥⠊⠀⡇⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣⠆⢸
⠀⠀⡇⠀⠀⠀⠉⠑⠚⠯⢖⣢⠤⣀⡀⠀⠀⠀⠀⣘⠜⠀⡜⠐⠂⢠⠇⠀⠀⡸⠡⢰⠗⡫⠖⠉⡇⠀⠀⡇⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠙⠺⡭⢖⣲⡤⣁⣠⠞⠤⠀⣠⠃⠀⠀⣼⡡⢛⠕⠊⠀⠀⠃⡇⠀⠀⡇⠀⠀⠀⠀⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣀⡠
⠀⠀⡀⠀⡈⣉⡉⠲⡀⠀⠈⠑⠶⡤⢤⡇⠀⠀⠉⠙⠚⠩⢖⣶⡧⣀⣠⢞⡩⠂⠉⠀⠀⠀⠀⣀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢀⡇⠀⡜⠁⡹⠞⠁⠀⠀⠀⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⠉⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⡠⠃
⠀⠀⠉⠐⣧⠄⣇⣢⠰⠄⠀⠀⡖⡆⠀⠀⠀⠀⣠⠤⣄⡀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠋
⠀⠀⠀⠀⡅⡈⡆⠀⠉⠐⠲⠤⢍⣁⠀⠀⠀⠰⣁⣀⡀⢸⡆⠀⠀⠁⢸⠀⠀⠀⠠⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠱⡱⠘⢦⡀⠀⠀⠀⠀⠀⠉⠑⢒⡤⠋⢠⡟⠋⠀⠀⠀⢠⢸⠀⠀⠀⣰⠔⠉
⠀⠀⠀⠀⠀⠙⢦⣀⠉⠓⠲⠤⠤⠤⠤⠒⠉⣠⠔⠉⠉⠑⠒⠤⢄⣁⣸⣀⠴⠊
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣒⣦⣤⣤⣤⣶⣒⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⡤⠤⠄⠀⢤⣤⡤⠀⠤⢤⡶⠚⠉⣁⣴⣶⣿⠟⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣠⣶⣯⣴⠶⠞⣿⠟⠁⠀⠀⣰⣿⣡⣴⡾⠿⣽⡿⠁⠊⠀⣀⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠶⣶⠟⠛⠉⠁⠀⣠⡾⠁⠀⣀⣤⣶⠿⠟⠋⠁⠀⣰⠋⢀⣠⣶⣿⡿⠋⢀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡾⠃⠀⠀⠀⣠⣾⣿⡴⠾⠛⢻⡟⢁⡤⠀⠈⣠⣾⣧⡶⠿⠛⣡⡟⠁⠈⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡋⣀⣠⠤⣶⠾⠋⡁⠀⠀⢠⣼⠏⢐⣁⣴⣶⠟⠛⠛⠁⠀⠀⣼⣿⣥⡶⠶⠶⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⣠⠞⠁⠀⠀⠀⣠⣞⣩⣴⠞⠉⣼⠟⠁⠈⠀⢀⣨⣤⠞⠉⠡⠀⠀⢀⡾⠃⣀⣷⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠻⣄⠀⠀⣀⣠⠞⠛⢩⠄⠂⣠⡜⢁⡠⠔⠒⠋⢉⡼⠃⠠⠄⠂⠈⣠⠎⢀⣠⣾⣿⠀⠈⠲⠦⠞⠀⠴⠺⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣪⡟⠁⠀⠀⠀⣠⣾⣿⣾⣿⣗⣶⣶⣶⣿⣤⣤⣄⣐⣦⣾⣧⣶⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⣿⣧⣠⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢫⣑⣟⣹⠟⣿⣷⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⣿⣧⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣿⠆⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣸⣻⡿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣐⣚⣍⠴⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠚⠋⠉⠉⠀⠈⠉⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁





⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠹⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠁⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⢀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠄⠐⢲⠒⠉⢹⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡭⣽⣿⣆⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠀⣠⡄⠤⢼⠒⠂⠛⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⡿⣻⣛⡃⣿⣽⣥⣿⣿⣿⡿⢟⡅
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⠀⢸⣀⣀⣤⠤⠀⠂⢀⠴⠊⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⡿⠿⠿⠇⣿⣿⣿⣿⢟⣭⣾⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡴⠃⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⢟⣵⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠑⠦⢄⣀⣀⣀⣀⡤⠔⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣻⠿⣿⣿⣿⣿⠿⣛⣵⣿⠟⠁
⠀⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠙⠾⣏⣉⡙⠲⣤⡤⠖⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⣁⣀⣀⣤⣤⡀⠀⠀⠀⠙⢦⠀⠀⠔⠲⠤⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡾⠉⠉⠋⠀⠀⠹⢤⡀⠀⠀⢸⣀⠀⠀⠀⠀⠈⠀⠘⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⣀⣤⣤⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣹⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠉⠳⢤⠴⠶⢧⡀
⠀⠀⠀⠀⢠⠞⠉⡼⠃⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠴⢤⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⢀⡴⠾⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠃⠀⠈⠉⢳⡄⠀⠘⣧⡀
⠀⠀⠀⠀⠀⡷⠈⠳⣄⣀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣼⠁⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢧⡀⠀⢀⣀⡴⠒⠲⡦⠤⢶⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁
⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⡀⠀⠉⠉⢉⣥⣤⡤⣾⡇⠀⠀⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣤⠞⠙⢦⡀⠈⠃⠀⠀⠘⠃⠉⠉⡟⠙⢦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠾⠛⢛⣋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢟⡛⢛⡯⡽⣧⣄⣀⣤⣴⠶⢟⣛⣋⣭⣥⡷⠾⠟⠛⢛⣉⣉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠋⣧⠅⠺⣥⢙⡈⢿⣿⠷⠾⣛⣛⣩⣭⣤⡶⠶⣾⣿⣛⣫⣭⣭⡽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠊⣥⠤⠅⣲⣀⣩⡥⠾⢿⣛⣛⣯⣭⣽⠶⠶⠟⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣴⣯⣭⡿⠷⠞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣼⡟⠛⠿⠛⠉⢁⠙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠾⠛⣋⡭⢀⠈⠋⣤⡤⠘⠃⠉⣠⡙⠷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⡶⠿⢋⣀⡴⠎⡉⢀⡘⠁⠐⠒⠢⣈⣋⡀⠐⠷⣤⡜⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣿⠆⢉⡤⠿⢉⠀⠛⣀⣥⠀⠻⠿⠋⢙⣉⠉⠷⢤⡃⠈⢛⣀⠈⠻⠶⣦⡀
⠀⠀⠀⠀⣀⣀⣾⣏⣁⣊⣁⣀⣈⣉⣥⣤⣬⣥⣤⣈⣳⣦⣬⣥⣤⣤⣤⣤⣄⣀⣀⣀⣈⣃⣹⣷⣀⣀
⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣀⣤⠀⢀⣀⠀⣀⡀⢀⣀⠀⣀⡀⢀⣀⡀⢀⣀⠀⢀⠀⠀⢀⡀⠀⢀⣀⠀⢀⣀⢀⣀⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠀⠈⠉⠀⠈⠉⠀⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠁
⠀⠄

⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠦⠀⠀⠀⢀⠀⠀⠀⠐⠂⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⡄⢢⠀⠀⠀⠀⠀⠈⠀⠅
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢋⠀⢱⢸⡆⠀⠀⢀⡆
⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠤⠬⠼⠥⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠄⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡄
⠀⠀⠀⠠⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢁⢠⡀⠀⠀⠀⠀⢀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠠⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⡀⠐⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠁⠒⠒⠉⠀⠀⠀⠀⠀⠄⡄
⠑⠄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠠⣮⠡⠠⣀⣀⠤⡄
⢀⣰⣲⡺⢐⡦⢧⣊⣀⣶⣉⠆⡙⣙⡘⣋⢍⣁⡠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⡀⣀⣀⣀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠉⠉⣿⠋⡉⡉⣿⡏⡩⠍⢹⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣒⣀⠿⣄⣒⣃⠿⢇⣁⣋⡼⠟⠀⡠⢀⡋⣫⠩⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡤⠔⠒⠊⠉⠀⣀⣀⣀⠤⠤⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡠⢐⡈⣉⣥⠤⠤⠖⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣔⣺⢿⣿⣿⢻⢗⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠻⣿⣿⡽⣷⣫⣿⡟⡟⣿⡿⣯⢾⣟⣷⢿⢶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣭⣿⣸⢿⣿⣯⢛⣾⣧⣽⣏⡿⣛⣿⣻⣷⣷⡇
⠀⠀⠀⠀⣾⣿⣿⠃⠀⣴⣶⣶⣶⣶⣦⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢀⠀⢠⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⠿⠿⠷⠄⢸⣿⣿⣿⣿⣿⣿⡇⠴⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠛⠛⠋⣁⣠⠤⠔⠒⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠖⠊⣉⣀⡤⠤⠤⠒⠒⠀⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣓⣚⣊⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⡀⣤⠀⢀⣤⠠⢆⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠔⠀⣀⠠⣤⣤⢝⣠⣮⠐⣣⣰⣆⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣠⣤⠾⠀⠐⠒⠃⠉⠁⣀⡀⣠⣤⡤⡶⣎⣩⡴⣀⠀⠀⠀⠐⠲⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠠⠖⠋⠉⣀⡤⡤⣴⣶⣶⢿⠿⠟⠻⠍⠃⠴⢲⣄⠁⣉⡉⢂⠲⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠂⠀⣀⣤⠔⠚⠋⠅⠒⠂⠉⠁⠈⠨⡷⡤⡄⠀⠐⠂⡔⢈⠭⠀⠈⣯⠀⠁⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠐⠞⢱⡆⠀⠀⠀⠂⠈⢿⣷⣀⣤⣤⢠⠀⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠐⢉⣠⡖⢕⡊⢎⡑⠎⠰⡌⢛⠒⠋⢀⡀⠀⠀⠀⠀⠐⠀⠂⠠⠀⠀⢁⠤⠀⠈⠅⠄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠖⠁⠀⠒⠉⠃⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠛⠏⠿⠉⢿⠛⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠯⡁⠀⠁⠀⠃⠔⠄⠜⠡⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠋⠰⠠⠋⠔⠂⡰⢣⠠⣿⣿
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣧⡨⢀⠐⠃⢠⡚⡉⠻⠔⠠⢈⡖⣤⣿
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠈⡈⠠⠂⣀⠢⡤⠃⠀⠺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣦⡀⢀⠀⠌⠨⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣿⣶⣷⣾⣿⡿⠟⠁⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡧⡃⡆⣴⠂⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠉⠁⠉⠂⢤⡠⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠙⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠑⠂⠒⠊⠉⠙⠂⠀⠐⣄⠀⠀⠀⠀⠘⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⢬⣀
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠰⣀⠀⠀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠋⠑⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠞⠁⠈⠉⠉⠑⠒⠀⠢⠄⢄⢀⡅
⠀⠀⡠⠄⠀⠀⠀⠀⠀⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⡈⠁⠀⠀⠀⠀⠠⠜⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⠛⠤⣄⣀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⡄⠀⠀⠀⠀⠀⠀⠀⡸⠘⠑⠀⠀⠀⠀⠀⠀⠾⡌⠲⡒⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢄
⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⠀⠘⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠸
⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠒⠒⠁⠈⢦⠀⠀⠙⡇⠀⠀⠤⠀⠀⠀⠀⠀⣀⠔⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠉⠲⠤⡀⠀⠀⠀⠀⡤⠃⠀⠑⣄⠀⠀⠈⢣⡀⠀⢷⠀⠀⠀⠙⠖⠒⠴⠒⣁⡤⢲⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⡔⠚
⠀⠀⠀⠀⠀⠈⠣⠦⠜⠊⠀⠀⠀⠀⠈⢦⠀⠀⠀⠱⡀⢸⠀⠀⠀⠀⠅⡠⠛⠉⣠⡰⠃⠀⡔⡹⠓⣤⠶⠖⠉⠒⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠹⣼⠀⠐⠀⠀⢰⠁⠀⣰⠃⠁⠀⢨⠞⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡀⢹⡆⠀⠇⠀⢨⠀⠀⠈⢀⠀⠀⠏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠸⡌⡇⠀⠀⠀⠘⣀⠀⠀⠌⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢣⡇⠀⠀⠀⡀⡷⠄⠊⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇⠀⠀⡈⠉⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢻⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣵⢂⣀⢀⣶⣀⣶⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠈⠀⠻⡿⠛⠉⠉⠉⠛⠛⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠠⢒⡒⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣴⠾⠋⠀⠀⠀⠀⠀⠀⠠⠀⣠⢀⡼⠄⢁⢀⡈⠀⡀⠀⠀⠀⠀⠠⠀⠀⢫⡴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣷⠟⠀⠀⠀⠀⠀⠀⠀⠲⠀⢥⣼⣻⣷⡼⢨⣜⠷⡞⠧⣠⠀⢀⣤⠀⠀⠀⠈⠷⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡙⠉⠠⠀⠀⡀⠳⡤⢶⣄⣆⣩⣴⣾⣻⣾⣿⣾⣿⣧⢹⣏⣿⣬⣻⣯⢿⣁⣄⣳⣄⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠶⠀⣴⠆⠀⡀⡉⣁⢶⣶⣿⣯⠿⣷⣿⣿⣿⡰⢹⠋⠋⣽⡟⣾⣷⣿⣬⣿⣹⣧⢾⣿⣛⠈⢃⣴⡀⣰⠄⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠀⢾⣫⡀⠠⣽⣩⣏⣸⣷⡟⢾⣏⣯⡕⠛⠃⠉⠀⢠⡏⠈⣞⢻⠛⣾⡟⣷⣶⣦⣼⠟⣧⣾⣯⣿⣥⠖⢡⡄⢥⢲⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣖⣤⣶⢿⡿⣧⠐⡾⢧⡾⠯⣞⣹⡿⠇⠹⣷⠐⠀⠀⠀⠸⠁⢠⠛⠲⢶⣿⣷⣿⣿⣹⣿⣏⣿⣶⡟⢳⣿⣻⣾⡝⠶⣦⠘⣦⠠⠾⠃
⠀⠀⠀⠃⠀⣀⡄⡤⠞⣥⣻⠞⣿⡿⣄⣿⣯⠻⢻⣿⣷⣄⠀⠀⢻⣇⠀⠀⠈⠁⠀⡿⠀⠀⢸⣿⢠⡿⣾⠇⣽⣷⣿⣿⡟⢻⣿⣷⣤⡶⣶⡛⣲⣯⣗⡎
⠀⠀⠀⡇⠀⠀⣀⡧⣺⣾⡽⣏⡀⠻⣟⠛⠻⢿⣇⠀⠹⣿⣇⠀⠈⠁⠀⠀⠀⠀⢰⡇⠀⠀⠈⣿⡿⠸⢟⡴⢳⠟⠟⣹⣿⣿⣯⣿⡟⣶⣾⣻⡟⠙⠋
⠀⠀⠀⠙⠀⡀⠰⣤⠇⢿⣵⡏⠀⠀⠙⠀⠀⠀⠙⢆⠀⠘⡟⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠔⠉⠀⠀⠀⠀⠽⡷⣿⣏⣼⡿⠷⠋⠉
⠀⠀⠀⠀⠀⠈⠓⠛⠃⢘⣧⡀⠾⠿⠶⣄⠀⠀⠀⠀⠣⡀⠙⠻⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠣⠉⢡⢦⣾⡿⠁⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡾⠁⠀⠀⠀⠀⠀⠀⢠⣿⣴⠶⠿⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣷⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⣠⣶⣯⣤⡀⠈⠻⣿⣦⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠟⠉⠁⠀⠈⠢⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡟⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⠄⠈⠳⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠿⠷⠖⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣦⡀⠀⠀⣈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⢈⢿⣿⣿⣷⣄⠀⠀⠀⠂⠈⠑⢄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠈⢢⡈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡒⠲⡄
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠐⠐⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⣹
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠐⠘⢦⣀⠀⠀⠀⠀⢀⣠⠏⠀⢰⣏
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢀⡤⣄⠀⠀⠀⢀⣿⣿⠀⡀⠀⠀⡠⠀⠀⠀⡀⠈⠈⠉⠓⠒⠚⡿⠀⠀⠀⠘⠈⠳⡄
⠀⠀⠀⠀⠈⣿⣿⡄⠀⢠⡏⡞⢢⢳⠀⠀⣸⣿⡏⢀⠇⠀⠀⣇⠀⣠⠀⣇⡤⠂⠀⠀⠀⣀⣽⠤⠤⣄⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠘⣿⣷⡀⠘⣇⢧⡼⡸⠀⣠⣿⡟⠀⡼⡠⠊⠀⣿⠞⣁⡴⠿⠒⠚⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠉⠉⣁⣴⣿⠟⢀⣠⠏⢁⡠⢚⣧⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⣟⠥⠒⢁⣮⣔⡫⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠶⠴⠾⠏⢈⡍⠁⠈⣭⢁⣗⠺⠦⢆⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠮⠟⠀⢀⠀⢴⠀⣘⣋⡾⠐⠀⠀⠉⣀⣀⢀⣌⠓⠲⠦⢤⡀
⠀⠀⠀⠀⡤⢚⣡⡟⠋⠛⢠⠀⠀⠑⠛⠀⡠⠁⠀⢠⢤⡠⠞⠃⢀⣌⠈⠋⠈⢆⣀⡀⠙⢷⡢⡀
⠀⠀⢀⡎⣰⠟⠋⠁⠀⢈⡼⠃⡀⠘⠂⢂⣺⢆⢤⠦⠀⠀⢀⣤⠀⠉⠀⢠⣄⠀⣈⠂⠘⠈⢻⣎⣦
⠀⠀⠸⡇⣿⣄⠺⠤⣀⠬⠀⢈⣉⣀⡥⠈⠉⠛⠀⢆⣴⣀⠨⠈⠀⠀⠒⠋⠀⠀⠀⣬⠀⠀⢰⡟⢸
⠀⠀⠀⣇⠬⡻⢦⣤⠸⠍⠀⠈⣀⠐⠆⠀⠀⠁⢒⠙⣦⡴⠐⢒⠀⡤⠀⠀⠀⢰⠤⢤⣤⡴⢋⡠⣿
⠀⠀⠀⢹⡀⠈⠲⢌⡛⠶⣦⣬⣑⣀⡂⠐⠶⠟⢆⠟⠏⡛⠮⠙⢃⣄⣚⣹⡦⢶⣚⣯⠵⠚⠁⢠⡟
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠀⠒⠺⠿⠭⠽⠽⣿⣿⣿⣿⣿⣿⠭⠭⠿⠿⠒⠛⠉⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⣄⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⠤⣶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠉⠉⠉⠉⠉⠉⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠚⠋⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⡑⠚⠳⠶⣤⣄⣀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣨⠛⠙⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠈⠁⠻⡳⠶⢤⡴⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢄⠀⠀⠀⢈⠦⠀⡅⠠⢄⠀⡞⠣⠤⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄⡀⠃⠀⠀⠄⠐⠜⠀⡧⠤⣀⠀⠈⠉⠒⠻⠶⣆⡤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣻⡓⣉⡢⠼⠛⠲⣎⡀⠀⠀⠀⠉⠒⠂⠤⠀⡀⠀⠉⠚⠉⠖⣢⣄⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡟⠻⣿⡈⢤⣿⣸⢀⣏⡼⢚⣩⣟⣰⣓⡤⢄⣠⠄⢀⠀⠀⠀⠀⠈⠁⠀⠂⠤⢄⣑⣔⢀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⡚⠍⡗⠁⣸⣧⣀⡬⢙⠂⡆⠙⣭⡷⣿⠟⣡⢄⡹⠚⣉⠉⣷⠫⡵⠾⣥⣖⣢⡖⠒⠠⢄⡀⠀⠀⠈⠑⣦⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢀⡴⠞⡋⠁⣈⠑⠐⡚⠓⠤⢉⣀⡈⣆⡩⠥⣿⠫⠒⡡⢮⠰⣁⢾⣠⠊⢠⢃⡼⠁⡤⠄⢨⡇⣁⠿⠗⠶⠾⣞⡀⠤⣀⡀⠙⡑⡀⠀⢀⡴⠃
⠀⠀⠀⠀⢸⠃⠒⠂⠀⣛⠒⠀⢉⡉⠐⡀⣸⡦⠻⡀⠀⡆⢠⠊⠀⠰⡆⠁⠀⠛⠖⢉⠞⣁⣌⡠⢡⡾⠥⠆⠈⣀⠠⠈⠉⠙⠻⠖⠫⣵⠋⣡⡴⠋
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠒⠠⢍⡙⠢⠄⣠⣁⢀⡴⣁⠀⣤⢁⠂⠀⢸⢺⠀⢸⡟⢁⣸⠦⣭⢘⣁⠍⠠⠀⠅⠢⡌⣠⡦⠞⡂⠕⠊⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠬⢈⢛⠰⠶⣸⣁⡀⠲⠈⣏⡬⠷⠓⠦⠀⢄⠈⠀⠘⠈⠰⣤⠤⠞⡃⠅⠂⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠈⠉⠀⠉⠧⢜⣰⠯⢄⣁⠈⢁⠀⠂⠈⣳⠰⠖⡊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⡀⠀⠀⠀⠀⢀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠨⠭⠁⠉⠥⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⠤⠴⠶⠚⠋⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠈⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠄⠀⠀⠄⠀⠃⠘⠃⠘⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⢛⠛⣛⡿⠖⠛⢋⣉⡤⠄⢖⣊⣳⡂⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠘⠷⠶⠖⠛⠉⠁⠀⣀⣀⣤⣬⣽⣦⠘⣄⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠛⠛⠻⠷⢖⡤⡒⠋⠉⢉⣒⣂⣠⣬⣧⠘⣦⣤⣄⣬⡍⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣈⣛⣛⣛⠻⠿⠿⠿⠿⣛⣛⣛⣫⣭⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠘⠲⠤⣤⣤⣀⣤⡔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⣧⠈⣉⡉⢁⠀⢀⡀⣀⣀⣀⣀⠤⠴⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⢿⡀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣤⣄⣀⠀⢀⣠⣤⠤⠀⠀⠤⠤⠤⣤⣤⣤⣤⣴⣾⣍⣀⣀⣻⡀⠉⠉⠉⠉⠉⡼⠋⠉⠈⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡿⠛⠁⠀⢠⡰⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⡍⠉⠛⠛⠛⠲⡾⠷⠶⢤⣤⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠋⠁⠀⠀⠀⠀⠀⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣇⣤⡶⠶⠟⣾⠓⠚⠓⠲⢦⡀⠀⠈⠉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⣄⠀⠀⢀⣤⠶⠚⣩⣶⡾⠛⠁⠀⠀⠁⠶⠞⠃⠀⠀⠀⢹⣦⣤⠞⠁⢸
⠀⠀⠀⠀⠀⢠⣶⡛⠋⠙⣇⠀⠉⠉⠛⠛⠛⠷⠶⢶⣤⣤⣤⣤⠼⡧⡙⡂⠜⣋⡤⠖⢿⣿⡟⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠾⠿⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⣷⣽⣿⠞⢉⣤⣴⠋⣹⡇⠼⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠾⣷⣶⣾⣍⣷⡀⣀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠂⣰⢂⡿⠂⠀⠀⠀⠀⠀⡔⠒⠲⠦⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡷⠟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⡜⢀⠀⠈⠣⣄⣀⣀⣀⣀⡀⢀⣀⣴⠏⠀⣴⠃⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣒⣒⣂⠀⠀⠀⠀⠈⠉⠉⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠶⠶⠞⠛⠉⠀⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠛⠉

⣷⠀⠀⠀⣤⠶⢤⡁⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠁⠀⠀⠠⠘⢷⡀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿
⠀⠀⠀⠀⠀⠐⠃⠀⠐⠀⠀⢀⣤⣶⣠⣀⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⣶⣮⣽⣿⣿⣿⣿⡀⠀⢀⡀⢶⡄⢨⣍⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠓
⠀⠀⠀⠀⢰⠶⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠷⠀⢸⣿⣷⣦⡐⠶⠄⣬⣵⡆⠀⠀⠀⣀⡄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠
⠀⠀⣤⠀⠔⠀⠀⠀⢀⠀⠀⠀⠀⢀⠴⡖⡲⣲⢦⡈⠛⠿⣿⣿⣷⣿⣿⡿⠁⠀⡀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠀⠠⡀⠀⠀⠂
⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠉⠛⠟⠋⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⠁
⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢴⠆⠀⠠⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⣾⣿⣿⣆
⠀⢰⣿⣿⣿⠟⢠⣄⠻⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣤⠀⠀⠀⠀⠈⠢⠀⠀⠸⠛⠋⠁
⠀⠀⠻⠋⠁⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡬⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠁⠈⠆⠀⡄⠀⠀⠀⠀⠈⠻⠟⠁⠀⠖⠀⠀⠼⠁⢀⠄⠀⠠
⣑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⢸⣷⣦⣤⣀
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠉⢡⢀⡌⠻⢿⣿⣿
⠉⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣷⣄⠀⠀⠐⠂⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⣀⠄⠉
⠄⠄⠁⠁⠀⠀⠀⠀⠀⠴⠋⠀⠀⢀⣘⣛⣽⣿⣿⣿⣿⣿⣿⡷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡈⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠻⠿⠿⢿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢒⡀⠆⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⡀⢀⡀⢒⠂
⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⡆⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⣤⡶⠶⠶⠶⣤⣴⣦⡾⢿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⠞⠋⣠⡙⠒⣠⣄⠐⣃⠀⢀⠀⠰⢦⣀⣉⡁⠙⠛⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⢈⡄⠉⣥⠏⠉⣉⠁⠤⠀⠉⠁⠛⠙⠠⢶⠀⠈⠃⠴⠰⠶⣤⣀⢭⡛⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⡙⡫⠶⡞⢃⣁⣴⢲⡀⢉⡀⠀⣛⡛⠂⠘⢂⡀⢀⡤⠤⠴⢦⡀⠤⠌⣉⠠⠅⣤⠨⡝⣿⣄
⠀⠀⠀⣤⣤⣤⣤⣿⣯⣥⣭⣤⣥⣬⣥⣤⣤⣤⣬⣦⣾⡦⠶⠾⠷⣶⣴⣾⠶⢶⠶⠶⠶⣾⣶⣶⣦⣥⣤⣤⣤⣤⣤⣤⣽⣷⣤⣤⡄
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡠⠤⢾⣛⣒⣊⠩⠭⠭⠒⠒⠒⠀⠈⠒⠲⡵⡄
⠀⠀⠀⠀⠀⢀⡠⠴⣒⡪⠭⠝⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵
⠀⠀⠀⢀⢔⠝⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⡜⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⢸⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠈⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⢧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠸⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢒⡔⠒⠚⠛⠒⠒⠤⣀
⠀⠀⠀⠀⠀⢳⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠒⠒⠉⠉⠀⠈⠉⠀⢀⣀⡀⡄⢀⡀⠤⣑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢇⢇⠀⠀⣀⣀⣔⢐⡖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⠛⠃⠀⠀⠀⠱⡀⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠘⢌⣲⣏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⢤⡀⠀⠀⢀⡤⠄⠒⠒⠊⠁⠀⠀⠀⠉⠛⢭⡙⠢⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠤⠔⠒⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠒⢴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⡓⢆⡀⠀⢀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡩⠶⠛⠉⠁⠀⠀⠀⠀⠀⣀⠤⢤⠤⢤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠤⠔⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢊⣣⣠⢼⡃⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⡄⢳⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠒⠙⣍⡽⠂⠀⠀⠀⠀⢀⡠⠤⠒⠋⠉⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢲⠙⡁⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⣀⠴⠋⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⣀⠠⠤⠤⠾⡄⠹⢍⡁⠀⠀⢀⣀⡠⠤⠒⠋⠁⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠉⠉⠁⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣷⣷⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⠿⡿⢿⢿⡿⠿⢿⢿⠿⣦
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠚⢀⠀⢰⣄⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣾⣶⣧⣶⣶⣶⣶⣾⣷⣾⣿⡇
⠀⠀⠀⠀⢀⠀⠛⠻⣧⣯⡄⠀⠾⢃⣤⡙⠟⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠐⠶⣆⠸⠿⣝⠓⠂⢈⣿⠂⢀⠘⠿⣤⣩⣴⣠⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠒⠻⠓⠀⠀⠚⠳⠘⠛⠃⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⠀⠀⠀⢀⡠⠐⠉
⠀⠀⢀⡀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠠⣀⠀⠀⠀⠚⡿⣟⣯⣶⣤⣶⣧⡀
⠀⠀⢀⡭⢃⣠⠀⢦⡋⠰⠿⣦⡀⠀⠄⠀⠉⣀⠀⣶⣾⣿⡏⢨⡭⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠳⣄
⠀⠸⣿⠘⢳⡟⠩⠡⡏⣣⣶⡿⠛⠢⡄⠀⠉⠀⠔⣿⡟⣿⠇⠀⢰⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡛
⠀⠀⠉⠲⢿⡉⠀⣽⠋⠁⠀⠀⢿⠌⠀⠀⠀⠀⠀⠋⢴⢿⠀⠀⠾⠿⢿⠀⠀⠀⢀⠀⠀⠀⠠⠤⠤⢶⣾⡿⢧
⠀⠀⠀⠀⠀⠀⠲⠛⠀⢤⣿⣮⣿⠉⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠻⠝⠊⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠁⠢⢀⠀⠀⠀⠀⠀⢠⣤⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣠⣶⡾⣛⠻⠟⠛⠻⢿⢶⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠃⠀⠀⠀⠀⠠⠀⠀⠉⠁
⠀⢠⣴⡟⣧⡬⠂⠙⠂⠒⢀⡠⠈⠮⠿⠿⢿⡆⠀⠀⠀⠀⠉⠁
⠀⣾⡿⠏⠉⠈⠙⠂⢠⡀⠘⢷⡀⠀⠂⢐⣘⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣀⡴⠋⠀⠀⡀⠀⡀
⠀⣿⣱⠖⠆⠀⠀⣀⠀⢱⣄⡔⠑⠀⢀⠖⢹⣿⠀⠀⠰⢶⡄⣤⣄⡀⠀⠀⠈⣿⣧⡄⠀⠐⣽⢛⡋
⠀⠹⣤⣰⣄⢄⠾⡾⠛⠛⠸⢾⢎⡡⠰⣄⣼⠋⠀⠀⢀⣐⢒⣿⣿⣿⠀⠀⢀⠻⣿⣇⣀⣠⣿⣷⡶⠄
⠀⠀⠈⠻⢿⣶⣿⣿⣶⣤⣶⣾⣷⣶⡿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠓⠛⠉⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⣠⡆⠀⢀⠆⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠒⠒⠀⠁⣹
⠀⠨⢰⣤⢠⠀⠀⠒⠐⡭⠛⠀⠀⠘⠃⠒⠈⠀⠀⠠⠀⠀⠀⢠⡾⠛⠛⠚⠀⠀⠊⠀⠀⠲⠆⠀⠀⠀⠊⠉⣀⡁⠼
⠀⠀⠙⠁⠘⠀⠐⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠴⡮⠁⠁⠀⠀⠀⢀⡀⠀⢀⢠⠔⠆⠀⠀⠀⠀⠀⠤⠄⢒
⠀⡤⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣷⠸⠁⠀⠀⠰⠀⠐⠀⠀⠐⣂⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⢤⣤⣀⣀⠀⠀⠀⠀⠔⠸⠂⢸⠀⣆⠀⠀⠙⠳⠤⠗⠀⠀⠀⠀⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠉⠈⠻⠛⠀⠀⡒⠂⡃⠘⠂⢸⣴⣿⠀⠀⠀⠀⠀⠀⢠⢋⠔⠡⠈⡠⠊⡠⠂
⠀⠀⢰⣄⠀⠀⣀⣀⣀⣀⡄⠀⠁⠠⡀⠀⠀⠀⠉⠉⠉⣋⠈⣣⣞⡧⠁⠀⠀⠒⠷⣶⡄⠈⠟⠶⣣⢆⣀⠞⢠⠊⢠
⠀⠀⠈⢿⣯⠁⣯⣹⠁⠣⠃⠀⠀⠀⠈⠁⠀⠀⠈⠻⢷⣾⣮⠿⠈⠀⣤⡄⠀⠀⠐⠁⠙⠃⠀⠀⠈⠈⠛⠛⢷⡶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⣤⣶⣏⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⣿⣿⢿⣄⠀⠀⠀⣠⡿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⡟⣧⡆⣴⡏⡷⣿⡿⣿⡏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡽⢿⣿⣿⡟⣷⢿⣸⣿⣿⣿⢟⡴⣿⠁⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣙⡾⠿⠿⡇⢹⣷⣿⣿⡭⣿⡟⢰⣟⣠⡴⠞⠋⠉⠀⠀⠉⠛⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣛⣷⣦⣙⡌⢿⡇⠀⣸⣿⠶⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠉⠳⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣙⣻⣿⣿⣿⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣀⣌⣩⠿⠛⠁⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠂⣉⡿⠿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⡴⠞⠁⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢀⡀⠀⠠⠀⠀⣀⡴⠖⠛⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⢀⠐⠂⠀⠀⠐⠂⠀⠁⠀⠀⣠⣴⣛⠁⠀⠀⠀⠀⣀⡴⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⣄⣀⣀⣀⠀⢀⣀⣠⡤⠴⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⢀⣠⠶⢋⡉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠛⠋⠐⠚⠉⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠛⠶⠦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠶⠶⠦⠤⠤⡤⣄⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠾⠿⠴⠶⠒⠒⠒⠶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⢤⣤⣤⡤⠴⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠾⠛⠛⠛⠛⠛⠛⠛⠶⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣋⡭⠶⠒⠚⠋⠉⠉⠉⠉⠙⠛⠓⠲⠶⠤⣤⣌⠉⣛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠉⠁⣀⣤⡴⠶⠶⠶⠟⠛⠛⠛⠛⠳⠶⠶⢶⣤⡀⠰⣯⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣖⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣯⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣧⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣿⣼⣧⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣴⠞⠋⣡⠔⢂⡤⠔⢀⣠⠤⠆⣀⡠⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠉⠛⢶⣄
⠀⠀⠀⢀⡴⠋⠀⡴⠋⣠⠞⠉⣠⠔⠋⠀⠐⠋⠁⠀⠘⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠀⠀⠀⠙⣧
⠀⠀⢠⡟⠁⣠⠎⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢠⡟⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣖⣒⣶⠦⠤⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡉⠉⠉⠉⠙⠛⠒⢲⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠉⠉⠛⠒⠲⢶⡄⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⢸⢸⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣼⠛⠒⠒⠲⠶⠤⠤⣤⣄⣀⣸⣇⣇⠀⠀⠀⠀⠀⢸⡇⢸⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠸⠈⠀⠁⠁⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠉⣟⠛⠛⠒⢲⡾⠧⢼⣷⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣀⣀⣤⠤⠶⠚⠛⠉⠉⠀⢀⢠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⠍⠙⠛⠓⠚⢁⡄⢸⣿⡇⠀⠉⠉⠉⠙⠛⠛⠒⠒⠒⠶⠶⠶⠶⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⢸⢸⢸
⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠶⠦⠤⠤⣭⣥⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⡇
⣿⠀⣐⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⣚⣒⡾⠭⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠻⠶⠶⣤⣤⣭⣍⣐⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⠶⢦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠶⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⢦⣤⣀⣀⡀⢸⡇⣀⣠⣤⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣶⣶⣾⡿⠟⠛⠿⠿⠟⠻⡿⡿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⣠⠊⠉⠟⢋⣿⠿⡿⠿⠿⠻⢻⣿⠉⠀⠀⠀⠀⠀⠀⣈⠥⠀⠒⠛⠉⠁⠀⡀⢀
⠀⠀⢸⣷⣿⣿⣳⣿⠋⡞⠁⣠⠆⣴⠎⢠⠆⣠⣂⠀⠤⠒⠈⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠉⠛⢿⣿⣿⣶⣄⣼⣇⣪⣼⣶⣿⣿⣿⠟⠁⢀⡀⢰⢋⣄⠄⠀⠀⠀⠀⠀⠀⡰⠁⠀⣃⣆⡃⢂
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠀⠼⣏⠁⡄⠀⠀⠀⠀⠀⠀⠰⢃⣄⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⠀⠠⠀⡀⣰⠆⠁⠀⠑⠀⡴⠆⢉⡀⣤⣤⣀⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⢿⣀⠀⣨⡴⢷⡀⠁⢀⡤⠀⠀⠛⡛⠷⠾⣿⣿⣉⣀⣀⣠⣄⡀⠤⢶⣤⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣫⡍⢙⢻⡄⠀⠷⢡⣷⡟⢩⠧⢴⡖⢈⢁⠠⠔⠀⠂⢉⣫⣙⣷⣾⣿⣟⡋⣴⣴⠦⠓⢒⠼⠀⢠⡟⠿⢶⡄⠀⢦⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠙⣿⣷⣄⡈⠺⠿⠿⣿⠻⣜⠖⣬⡾⣿⣛⡯⣝⠻⣤⣅⠀⠒⠂⠂⣁⣠⣶⣏⡄⡈⠎⢀⣰⣿⡿⡾⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠀⠙⠫⢿⣓⣀⣁⢀⣀⣴⡙⠯⠾⠾⠾⠛⠋⠉⠉⣀⣠⣴⣶⣿⠏⠹⠚⠋⢁⣠⣴⡿⠧⠒⠋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣉⣁⣀⣀⣤⢤⣴⢶⠾⠿⠿⠻⠛⠛⣉⣁⣠⣤⣤⣶⣶⠿⠟⠛⣉⣡⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠘⠶⠤⠴⠶⠖⠒⠚⠛⠋⠙⣯⣉⣉⣡⣬⡤⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⢀⠤⠔⠒⠒⠢⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⡀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠒⠢⠤⠋⠙⣦⣀
⠀⡠⠔⠋⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠁⠑⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠜⡠⠔⠒⠒⠠⠄⣶⠤⣑⠂⣄
⠸⣀⠀⠀⢠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠃⠀⠨⠀⠀⠀⡠⡔⠋⠀⠀⠂⠈⡹⠯⠶⡄⡀
⠀⠈⠑⢢⢄⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠂⢡⠁⠀⡄⠀⠂⢇⡔⠉⠀⠀⠀⢋⠤⠒⠉⠠⠄⠀⢹⣌⡑⠢⣄
⠀⠀⠀⢸⠀⠉⠒⠤⡈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⠤⠀⠀⠘⠢⡀⠀⠄⢀⣠⣦⡲⠀⡀⠂⠁⠀⠈⢀⡀⠄⠊⠁⣠⢹⠀⠀⠉⠂⢄
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠑⠢⢌⠑⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⡋⠀⣰⠥⠴⢦⣤⣌⡂⢁⠈⠢⢄⢩⣴⡶⢶⠵⣄⠑⢀⣞⡉⠀⠂⠀⠀⠁⠀⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠉⠒⠄⡉⠒⠀⠒⠊⠀⡰⠧⢭⣚⡥⢤⣥⣇⣀⣼⠚⠉⠉⠂⠆⠀⠀⢰⠁⠀⠀⠙⠉⠁⠙⢢⣀⣀⠀⠀⣀⢇⡠⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠈⠑⠠⢀⠀⠀⠑⢤⢾⡁⠀⠀⠀⠀⠉⠛⢦⠀⢀⠀⢠⣄⠠⡀⢀⠠⠴⡁⠀⠀⠀⠈⠂⠈⡉⠄⠊⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠉⠒⢄⡀⠉⠃⠀⠀⠀⠀⢀⡀⠜⣀⣀⢠⣌⡨⠏⣘⠁⡀⢠⠈⠁⠀⢀⡠⠒⠉⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠁⠀⡎⠀⢀⠀⠀⢙⡄⠃⠀⠓⠁⣀⠤⠊⠁⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠁⠢⢄⡀⠀⠃⠐⠀⠀⠀⠈⠃⢀⡠⠔⠈⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠈⠐⠤⣀⠀⠀⣀⠤⠂⠁⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⣀⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢦⣤⠀⠀⠀⠀⠀⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡏⢙⠿⠉⠀⠀⢀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠠⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠉⠁⠀⠀⠈⠀⠀⠘⢀⡀⠀⠀⣀⣁⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠈⣩⣭⣷⣶⠄⠀⠀⠀⠀⢀⠘⠋⠀⡠⠂⡛
⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠤⠤⠀⢘⡀⠀⠀⠀⣀⢸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⡀⠀⠀⠀⡠⠀⢀⠜⠁
⠀⠀⢻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠄⠁
⠀⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢰⠀⣰⠊
⠀⠀⠀⠀⠀⠐⢧⣄⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢒⠒⠀⠤⠤⠠⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠼⠖⠁
⠀⠀⠀⠐⠒⣀⣀⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠒⠒⠂⢀⠌⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣴⣾⣿⣿⣿⣿⣷⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠒⠂⠀⠀⠘⢦⡙⠻⠿⠿⠿⠿⠛⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠛⠉

⠀⠀⠀⠀⣴⣿⣿⡿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⢸⡟⠛⠛⠃⠈⢿⡇⠀⠀⠀⠀⠀⠀⡠⢸⠁⠀⠀⠀⠀⠀⡍⢰⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⣿⣿⡆
⠀⠀⠀⠘⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠘⠀⠀⠀⠀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠋⠀⠙⢿⠇
⠀⠀⠀⠠⠠⠙⠋⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠆⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠀⣀⣀⡄
⠀⠀⠀⠠⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣅⠎⠀⠀⡀⠂
⠀⠀⠀⠀⠚⠀⠀⠀⠒⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠀⣀⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠠⠜
⠀⠀⠀⠠⠈⠉⠑⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡁⣠⠤⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠐⠐⠒⠠
⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⣶⣄⠀⠀⠀⢀⣠⠖⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠛⠁⠘⣿⠀⠀⢀⢸⠡⠤⠀⠀⠀⠀⡉⢲⠀⠀⢰⣿⣿⣿⡿⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠀⠀⠸⠘⠀⠀⠀⠀⠀⠈⠃⠸⠀⠀⠻⠟⠙⠛⠁⠘⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠒⠒⠒⢦⠀⠀⠀⠀⠀⢀⠶⡆⠄⠰⡀⠀⠀⠀⠀⠀⢂⣀⢀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⠀⢃⠀⠀⠀⠀⠮⠄⠀⠀⠀⠑⡀⠀⠀⠀⠠⣨⡰⠁⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠢⡭⠀⠀⠀⠀⠂⠀⠀⠀⢀⠄⠃⠀⠀⠀⠐⠀⠁⠀⠀⠃⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠑⠒⠠⠤⡆⠀⠀⠀⡄⣈⡁⣀⠤⠠⠁⠀⠀⠀⠀⢈⠄⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠶⠤⠢⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠁⠀⠀⠀⠀⠀⠀⠐⢳⣀⣠⠖⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠉⠋⢟⡀⠀⠀⠀⠀⠀⠀⠈⢠⡯⠁⠁⠐⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠁⠀⠈⠄⠀⢸⣄⡄⡐⠀⠀⢀⣀⣀⣿⠃⠀⠀⠀⠀⠈⠀⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⠀⠀⠀⠘⠴⣖⣶⠲⠋⠁⠀⡀⠛⣶⣠⠀⠀⠀⠀⠀⣰⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠁⠀⠀⠀⠀⣻⠀⠀⠀⡠⠀⠀⠄⠀⠈⠳⢄⢀⡀⡼⠃⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣁⡥⠦⣄⣼⣋⣰⡧⡄⠀⠀⢀⠀⠀⠀⠀⡀⠀⢺⡉⠁⠀⠀⠀⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠀⠈⣧⣦⣄⠀⠄⠀⠀⠀⠀⠀⢰⣟⣀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢠⠫⠀⢻⣤⡾⠄⠀⠀⣁⣀⠞⠉⠙⠒⢮⡡⢤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡼⠀⠀⠀⠀⡿⠋⠙⠶⣦⢿⣞⣉⠀⠀⠐⠂⠀⠁⠀⠋⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣼⠷⢀⠇⠀⠈⠀⠀⠰⠺⠧⢾⣨⠀⠀⠀⠀⠀⠀⠈⢀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠟⣄⠀⠀⠀⠀⠀⠀⣀⣠⣅⣠⣬⣿⠀⢀⡀⠀⠀⠀⠀⠂⣈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⠁⠀⠀⠁⠀⠀⣀⣀⣴⣿⠉⠁⠀⠀⠀⠈⢻⡙⠖⠀⠀⠂⢈⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⠞⠀⠀⢀⡠⣴⢂⢾⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠼⠬⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢻⡀⡴⠋⠉⠳⡥⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⠚⠇⠀⠀⢰⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⡆⠀⢀⣀⣄⣁⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡎⠐⠋⠀⢲⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⠠⡀⢰⢠⢀⣠⠀⡄⠀⡄⣄⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠈⠈⠈⠉⠀⠁⠈⠀⠈⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡗⢺⣆⠧⠔⠀⠀⠀⢀⡜⡏⣿⠋⢀⡴⢾⣟⣭⣿⣿⣿⣧⠀⠀⠀⢹⣧⣄⠀⠉⢳⡄⠀⠀⡇⠀⡃⠀⣇⠀⡃
⠟⠊⠁⠀⠀⠀⠀⠀⠈⢷⣿⣯⣤⢻⠽⣴⣻⣮⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢿⣿⡇⠀⠀⢧⣄⢰⡀⠱⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠓⠒⠚⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⣴⣶⣾⣭⣴⣟⠙⢫⡿⠀⠀⠈⠂
⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⣴⣿⣥⠙⢦⣭⣏⡘⣆⠀⠀⠉⠻⠏⠿⠯⠽⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣠⣾⣧⣿⣷⠀⠀⠀⠀⠀⢰⣿⣟⢿⣧⡄⢸⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡀⠀⠀⢀
⢠⡞⢹⣿⡯⢞⠛⠀⠀⠁⠀⠀⢸⣏⠛⠊⠉⠸⠿⠁⠀⠀⠀⢀⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⡿
⣇⢨⡴⠋⠂⠀⠀⠠⠁⠀⠀⢠⣟⢁⡀⣠⡼⠃⠀⠄⠀⣠⣬⣶⣤⡾⢳⡖⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢮⣾⠃⠀⠀⣾⡜⢻⡿⠉⠢⠀⠀⠀⢰⡟⠀⠿⠋⣼⣷⣶⣏⠽⣷⠄⠀⠀⠀⠀⢠⠏
⣠⣤⠖⣦⠠⣾⠇⡏⠀⠀⠐⢯⢕⡈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⢻⣿⡏⠷⠴⣯⠘⢦⣀⠀⣰⠏⢀⣀⣤⣤
⢏⠁⠀⣀⣠⣡⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢢⡀⠀⠉⢯⣀⣘⣃⠛⢻⣯⣄⣘⠿⣷⡒⣨⣿⠋⢠⣾⡟⠛⠻
⡄⢀⢈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠈⠛⠯⣽⣏⣚⣷⣶⣿⡿⠟⠁⢠⣿⡅⣳⠆⢂
⣶⡿⣫⣿⠏⠀⠀⢆⠀⠘⡄⠀⢢⠀⢃⠘⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣿⣱⡀⣠⣼
⣸⣿⠟⠁⠀⠀⠀⢠⣡⠀⣇⡀⣸⡆⢨⡄⣱⠀⠀⠀⠰⡈⠿⣷⠶⣦⣄⣀⣀⣀⣀⣤⣤⡀⠀⠀⢿⣿⣆⣩⡌
⠋⠁⠀⣤⡀⠀⣶⡛⢿⣶⡉⡙⡋⠙⣋⣻⣿⠿⠇⠀⠀⠈⢷⣍⠓⢮⣭⣭⣭⠷⣶⣶⣈⣿⣦⠀⠈⣙⣛⣩⣵
⠀⠀⣴⣹⡿⠀⣻⣧⠀⠛⠿⠷⠲⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠙⠳⣔⣏⠉⠈⠒⠈⠛⠻⣿⢿⣶⡄⡀⠈⠉⠉
⡼⠋⢉⣽⠁⣰⠋⠋⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⠀⠀⠀⠀⠛⠀⣰⡏⣿⡄
⣤⡶⣼⡇⠀⣿⡒⠠⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠈⢳⡀⠀⢀⠐⣊⣼⣶⡿⠁⠀⠀⣴
⣸⢿⣿⠁⠀⠘⢿⣄⣉⣈⠻⢀⣄⣠⣠⡭⡴⠾⠋⠀⠀⢠⣶⡜⠺⢿⣷⡦⠀⠹⣗⣧⣌⣤⠾⠟⠀⠀⠰⠘⣿
⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢉⡀⠀⠀⠀⠀⠀⢀⣇⠁⠀⠈⠁⠁⣝⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙
⠄⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣖⣴⣾⡿⢻⣿⣿⣷⡶⣄⠈⠋⠙⢹⣄⡀⠔⢦⡾⠇⠀⠀⠀⡠⠂⡠⠀⡀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠠⢂⣴⢿⣟⠉⢻
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣈⠀⠀⠀⠀⠀⠀⢰⡏⠠⢻⠈⠟⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⡃⠀⠀⢠⡆⣴⠀⠀⠀⠀⠀⠄⣀⣀⣠⣤⣤⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⣷⡆⠀⠀⡀⣰⣿⠻⠛⠻⣿⡿⣯⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⣷⡻⣧⡁⢁⣴⣿⡏⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠘⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣾⣿⣻⣮⣗⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢇⠀⠙⠛⠥⣿⣿⣿⡷⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠶⠄⠋⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⣤⡜⠇⢾⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢩⡧⡶⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⠟⠶⣧⠁⠐⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡏⠀⠈⠻⠦⠁⡤⠌⢹⣿⣆⠀⠀⠀⠂⡀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣯⡐⠤⠂⠠⢢⡆⠐⢀⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣶⣦⣾⣿⣿⣷⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠛⠡⣶⡿⢠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣶⡶⣿⠛⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠈⠁⠀⢰⠃⢠⠊⠁⠈⠑⠦⡈⠑⢄⡀
⢠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠈⡆⠀⠙⢆
⡏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠂⠀⠀⠀⢀⠞⢀⠞⠓⣄⠑⡄
⢻⣄⠀⠀⠾⠷⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠙⠲⠤⣤⠏⣠⠋⠀⠀⠈⢦⠘⣆
⢀⡟⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠉⠒⠢⠤⢍⣉⡐⠒⠒⠚⠀⠘⡄
⣾⠀⠀⠀⣼⠛⠛⠻⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⡀⢳
⠘⠷⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠱⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡦⢄⣀⠀⠀⠀⠀⠙⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠀⠀⠀⠈⢣⡘⢦⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠙⢦⡙⠦⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⣦⣤⣀⣀⠙⢦⡈⠓⠦⣄⡜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢿⣷⣤⣀⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠤⠤⠤⠶⠐⠒⠂
⠀⠀⠀⠀⢀⣤⡶⢞⣻⣟⣻⣿⠛⠙⣷⣶⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣶⡆⠐⠂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⠒⠂
⠀⠀⠀⢰⠿⣿⣿⣿⣻⣿⠿⣿⣿⠗⠑⠻⢛⣽⠀⠐⠀⡀⠀⠀⠠⠀⠀⠀⢸⣿⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⣨⢩⠂⠀⢈⡇⠉
⠀⠀⠀⠙⢶⣇⠀⠀⠀⠀⠀⠀⣏⠀⠀⢀⡿⠃⠀⠀⠀⠈⠀⡀⠀⢶⣿⣿⣿⣿⣷⣿⡗⠀⠀⠀⠀⠀⠀⡀⢿⣧⢺⣿⣾⣧⡄⣀⠰⡇
⠀⠀⠀⠀⢀⠉⠙⠒⠶⠴⠶⠯⠝⠒⠒⠉⠀⠀⠀⠀⠀⠀⠂⣾⡆⣴⣿⣟⡿⠿⣼⠿⣜⢲⣷⠀⠄⠀⠀⠑⠾⣿⣷⣭⣿⣿⣮⣿⣚⡁⠂
⠀⠀⠀⠀⠀⠁⠀⣄⣀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⣽⠃⠀⣀⢎⢧⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⢀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣄⠴⣝⣂⣤⣀⣀⡀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠓⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⢰⡆⣿⢾⢵⣾⣵⣿⠏⢳⡔⣽⠆⡀⡀⠀⠀⠀⠀⠀⣀⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣿⡗⢈⣶⡾⠟⢀⠠⣤⠋⢀⠀⠀⠀⢎⣼⣧⠾⣝⢡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠙⢡⡲⠶⠊⠁⠐⠀⠀⢀⡆⣼⣿⡿⢠⢏⢾⡄⠀⠰⠀⠀⠀⠸⠀⢀⣀⣠⣤⣤⣄⠀⠀⠀⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣿⣇⣷⡿⠗⣡⢀⡾⠀⠀⠀⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠄⠀⡀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢼⣧⠞⠁⢈⠀⠀⠀⠀⠀⠔⠀⠀⠀⣀⣽⣿⣿⣿⣿⣀⡀⠀⠀⠒⢦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡿⠒⠁⠀⠁⠁⠀⠀⠀⠀⠘⠠⠿⡏⠤⠖⠀⠀⠀⠀⢠⠋⢀⣠⣾⣿⡿⣯⣿⣿⣿⣟⣿⣿⣷⣦⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡀⢸⣿⢷⣴⡜⠉⠉⠉⠙⢿⠛⢙⣿⣿⣷⠀⣶⢠
⠀⠀⠀⢀⡠⠀⠀⠀⠁⠀⠀⠀⠀⡼⠿⢟⠷⠎⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣟⣷⣏⠀⠀⠀⠴⠂⢈⡇⠈⢈⣿⣏⡜⠉⠃
⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠄⡒⠀⠉⠡⠀⠀⠀⠀⠀⠸⢿⣭⡙⠛⠲⠶⠶⠶⠿⠛⢛⣿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠠⠷⢶⠾⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠀⢀⠔⣨⣬⢼⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⣠⣴⢶⠶⠛⠛⣿⣷⣶⣦⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⢨⣿⡛⠉⠈⠙⡻⣿⣾⣿⣎⠀⠀⠀⠠⣴⣿⡿⠀⠋⢐⡔⠚⢹⣿⣿⡿⣟⢹⣦⠀⠀⠀⢀⡔⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⣿⠃⢶⠶⠃⠓⠻⣇⠀⢨⣿⠀⠀⠀⠀⢻⣿⡀⠀⡴⠋⠀⠆⢀⡛⢯⣶⣿⢛⡿⠁⠀⠁⢸⡃⢀⡼⠁⠀⡴⠂⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠁⣿⣦⡏⠀⠀⠀⠀⠈⣿⣟⣿⡈⠀⠀⠈⠀⠈⠛⠿⢷⣤⣤⣤⣴⠿⣾⡧⠛⠋⠀⠀⠀⠀⠘⢷⣠⣿⠀⢸⡇⠀⠀⠐⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠸⢿⣷⣀⢀⢀⣀⣴⡿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠷⢤⣤⠈⠄⠐
⠀⠀⠀⠀⠀⠈⠑⠛⠻⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠔⠍⢏⠕⠉⡰⠐⠠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣿⣣⣥⣎⡤⣆⣏⠙⠧⣠⣌⢻⣯⣍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣛⠟⢿⣿⣿⣿⡿⣬⣧⣼⣷⡾⢶⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢻⣾⣶⣷⣿⡾⢙⣿⣿⣮⣻⣛⣿⣾⣿⣿⣯⣿⣿⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡟⠊⡍⣝⣿⢿⣿⣽⣿⣧⣽⣿⣿⣷⣯⡟⢿⣿⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡮⡑⠎⣾⣿⣿⣿⡿⣿⠋⢹⢿⡹⠉⢫⠄⠀⠛⢿⣿⣿⡿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣢⣿⣿⣿⣿⡛⠀⠀⠈⠀⠁⢠⠿⣼⡆⠀⢣⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠧⢛⣿⣿⣿⡏⠂⠀⠹⢦⠀⠀⠀⠀⠈⡰⠿⠃⡠⢾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣴⡚⣻⣿⣿⠉⠀⠀⠀⠀⢣⠀⠀⠀⠀⠃⠀⢸⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣴⣿⣿⡿⠃⠐⠘⢿⣧⢀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡄⠀⠀⠀⠀⠀⠈⡆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⢁⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⡀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⠉⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⢤⡴⠶⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⣤⢶⣫⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⠀⠁⠀⠈⠀⡀⠈⠈⠷⠶⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⢀⣀⡤⠶⣒⣫⠽⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡞⡛⠠⠂⠠⠆⠐⠀⠈⠀⠀⠀⠈⠃⠈⠉⠳⢦⣀⣤⠶⠚⠉⠀⠀⠀⢀⣠⠴⠖⣋⣭⠴⠒⠋⠁
⠀⠀⠀⠀⠀⢀⡼⠁⠀⡤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠉⠀⢈⢷⠀⠀⠀⠀⣀⡴⢚⣩⠴⠚⠋⠁
⠀⠀⠀⠀⡶⠋⠀⠀⠀⠈⠀⡀⢀⡀⠲⠀⣀⠀⠀⠀⠀⣀⠀⠀⠘⣿⠀⢀⡤⠞⣡⠖⠋
⠀⠀⠀⠀⣷⠰⠀⠲⠂⠀⠀⠀⠉⠋⠀⠀⠁⠀⠀⠀⠘⠁⣀⢀⡼⢃⡴⠋⣠⠞⠁
⠀⠀⢀⣴⣿⠂⢤⠀⠀⢠⠄⠀⠀⠀⠀⠠⡖⠀⠘⠁⢀⡤⠞⣩⠞⠋⢀⡾⠁
⠀⠀⢸⣿⣇⠡⡀⠀⠠⣄⢀⣀⡘⠂⠴⠂⢀⣠⠴⢚⣩⠴⠋⠁⠀⣰⠋
⠀⠀⢸⠙⣮⡛⠶⣤⣄⣀⣤⣬⡤⠴⠒⢋⣩⡤⠖⠋⠁⠀⠀⣠⠞⠁
⠀⠀⠘⢧⡀⠙⠓⠶⠬⠭⠤⠤⠴⠖⠛⠉⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠒⠚⠋⠉⠁

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠠⠀⠂⢄⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⠠⠂⠁⠀⢀⡠⠖⠃⠂⢄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⡀⡀⣤⣦⣀⠀⡤⠒⠁⠀⠀⢀⠠⠚⠁⠂⠄⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⡄⣤⣤⢤⣀⠈⢁⡬⡝⣦⣤⣤⡀⠂⠁⠀⠀⢀⠠⠊⠉⠑⠀⡀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⢠⠔⠋⠁⠀⠀⢀⣤⣤⣤⣀⠈⠁⡬⡜⢶⣶⢧⣅⠈⠁⡀⡥⡤⢄⡀⠊⠀⠀⠀⢀⣠⡞⠉⣹⡤⠠⡀⠀⠀⠉⠓⢤
⠀⠀⠀⢸⠀⠀⠀⠀⠰⠋⠉⠛⢉⣽⣧⣄⣡⡄⠀⠁⠀⢈⢀⣺⠉⠀⠀⠀⠈⡆⠀⣠⡞⠅⣹⠭⢾⠿⢀⣴⠷⠉⠁⠀⠀⠸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠋⠁⡌⠗⠚⠲⢤⠋⠀⠈⢱⠒⠀⠨⠤⣕⢤⣌⣩⣞⣧⢀⣼⠗⠋⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠂⠀⠀⢀⡀⠇⣀⡄⠘⠠⢀⠀⠀⢢⠤⠙⢩⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠈⠉⠁⡠⢒⣂⠳⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠠⠒⠉