Sun and moon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⣄⠀⠀⠀⠀⢀⠻⣄⠀⠀⠀⠀⠀⣿⠀⣀⠀⢀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠨⡳⣤⡀⠀⠈⣧⢙⢦⡀⠀⠀⠀⢻⠀⢸⡆⠈⠉⠉⠀⠀⠀⢠⣤⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⠹⡌⢿⡄⠐⠸⣇⠠⢻⣄⠀⢠⠇⣧⣿⠇⠀⠀⢦⡀⠀⠀⠉⠋⠏⠁⣀⡤⣴⠇
⠀⠀⠀⠀⢰⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⢄⡀⠀⠘⣇⢹⡈⣧⠘⠀⢻⡆⡏⣿⣴⠏⡰⣿⡏⠀⠀⢀⡟⣷⠀⠀⠀⠀⣰⠛⣡⡶⠋⣀⣠
⠀⠀⠀⠀⠀⠻⣌⡓⣤⢄⡀⠀⠀⠀⠀⠀⠑⣄⣝⢶⡀⢿⠈⡇⢹⡄⠀⣾⡇⡇⣿⡟⡜⠁⢹⣧⠀⣰⡟⢡⣟⠀⠀⠀⣰⢇⡾⠋⠀⠠⢬⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢯⣙⠳⣒⢤⡀⠀⠀⠈⢾⣦⢻⣾⣇⢻⡀⢿⣎⣿⢰⡇⣿⣿⣷⠀⡆⢿⣿⠋⣠⣿⣯⣤⠴⢚⠝⣸⠃⠀⠀⠀⠈⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡑⢮⢢⡀⠀⠀⣿⣆⢻⣿⣦⡓⣤⣹⣿⣿⣾⣾⣿⣿⣶⣷⡿⣷⣤⣿⡿⣫⠴⠒⡁⣲⡟⣀⣀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠹⣦⡑⣽⣶⣤⣿⡽⢦⣌⣽⣿⣿⠿⣿⣿⡿⠿⢿⣿⣿⣛⠿⣯⣞⠫⢟⣿⣞⣁⡴⠟⠛⠋⢉⣴⢇⠀⣀⣤⣤⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⡉⢛⣷⣤⣎⠻⣮⡻⢿⣿⣻⡿⠋⠈⠁⠀⠉⠁⠄⠒⠂⠀⠈⠙⠻⢿⣮⡻⢝⠲⣭⠺⣟⣶⡉⣀⣴⠟⢛⣿⠟⠉⣠⠞⠉
⠀⠀⠤⣤⣤⣤⣀⠀⠀⠀⠘⢦⣈⠓⢯⣓⠾⠿⢷⣶⠏⣼⠁⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣠⠀⠈⠻⡛⠦⣍⠒⠃⢈⢻⣻⣟⣁⣴⢟⡅⢁⡾⠁⠀⣄⡆⣠
⠀⠀⠀⠀⠉⠳⣌⠉⠂⠄⢀⡀⠈⠳⢦⣭⣽⣿⣿⢃⣴⠟⠠⠶⠶⠖⠳⠶⣤⡀⠘⠀⠘⣡⣶⠖⣛⣛⠑⠀⠁⠀⠬⣄⠁⢻⡭⠴⣋⣴⠏⠀⠀⠐⢿⢿⡷
⠀⠀⠀⠀⠀⠀⠘⠷⣄⠢⣌⠙⠳⠶⠶⢾⣛⣿⠇⠈⠁⠀⣠⠄⣤⡖⣿⣦⡈⠻⠀⠀⠀⠛⠀⣮⡍⢹⣦⠦⢤⣌⣓⠬⠷⢶⣿⣿⣿⣏⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣑⠦⢤⡬⠭⢾⣿⠀⠀⠀⠈⠙⢧⣙⠓⣡⡾⠀⢠⡇⠀⠀⡆⠐⣬⡓⢛⡩⢀⢰⣤⠈⠂⠀⡏⣿⠦⠾⠍⠓⠶⢤⣤
⠀⠀⠀⠀⠀⢀⣤⣾⡟⠛⠛⢿⡿⠷⠶⠟⣻⡇⠀⠀⠀⠀⠀⠒⠤⠄⠒⠀⠀⠈⡇⠀⠀⠇⠀⠈⠒⡾⠁⠨⠟⠒⠃⠀⠰⠇⢹⣿⣿⠿⢟⠛⠛⠁⢀⣶⣤⡂
⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠷⣶⣬⣍⣒⣋⣽⣷⢀⡄⠀⢠⡆⠀⣖⠒⢦⠀⢀⡀⠃⠀⠀⢀⠀⠠⠚⣃⡀⡄⠢⠧⠀⠀⠁⠀⣸⣍⣛⠿⣶⣤⣀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠒⠒⠛⠛⣋⣼⣿⡄⠳⣄⠀⠻⠦⣝⡡⠞⠀⠳⠤⢤⣀⠤⠤⠗⢀⠢⠭⢿⢷⡼⠂⣀⢔⢢⡀⣯⣤⣤⣤⣀⠉⣙⣛⢛⡛⠒⠲⣄
⠀⠀⠀⠀⣠⠴⠋⣑⣮⣿⣿⣯⣯⣭⣭⣭⣴⣿⣷⡀⠀⠉⠐⠲⢤⣴⠖⠀⠀⢀⡤⠤⠤⣄⠀⠀⠑⠶⢿⡀⣅⡠⡰⣡⢗⣽⣟⢿⣧⡏⠙⠻⠶⠤⠤⠶⠚⠉⠉
⠐⠓⠾⠯⠴⠾⠛⠉⠀⣠⡴⠶⠿⠿⠿⠟⠿⢚⣻⣷⡌⢦⡀⠀⠀⠀⠀⠀⠚⣓⢀⣀⣀⡘⠋⠀⠀⢀⣾⠗⢉⠚⡶⣏⣼⣟⠌⠳⢌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⣴⣶⣶⣶⣾⣿⡿⢋⣿⣿⣦⣝⣦⣄⡀⠀⠀⠀⠓⠶⠴⠖⢃⣀⣠⠶⠋⠀⣈⠄⡱⢘⣼⣟⠻⣿⠷⠶⣶⣼⣿⡶⠶
⠀⡀⠀⠀⢀⣠⠞⣡⡴⠟⠉⠁⢀⣴⡿⠟⢉⣴⣿⡟⢸⡿⣮⣝⡻⠿⣷⣤⣼⣧⣤⡴⠶⠞⠛⠁⡠⣠⣞⣅⣠⣵⠟⠃⠈⠛⢮⢷⡀⠀⠀⠀⢠⣀⣀⡀
⠀⠈⠐⠲⠤⠖⠛⠉⠀⠀⠀⣰⡟⠁⣠⠜⠋⣽⣿⢃⡿⣠⣿⣿⠷⣦⣄⣀⠀⣤⡤⣤⣤⣤⠤⠥⣞⣋⣿⠿⡟⣿⡟⠛⠛⠛⢦⡳⡝⢦⠀⠀⠻⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠞⠁⢀⣴⣿⡿⣻⡿⢫⣿⠏⣰⢇⣿⣿⡟⣿⠛⣿⢿⢿⣿⡻⡹⡝⣿⣆⠃⢻⣇⠀⠀⠀⠀⠹⣾⣦⡙⠢⢤⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢠⣾⡯⢃⡴⠋⣠⡿⣣⢞⣣⣾⡟⢹⣿⢸⢇⣿⠹⠸⣾⣷⣿⢸⣿⣿⢷⣄⡙⢦⡀⠀⠀⠀⠀⢉⠛⠓⠒⠚⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⣼⠁⢀⡟⢀⡴⠟⠋⠁⠀⣼⢇⢮⡾⣿⠀⠀⣿⣿⣿⣼⡟⠁⠀⠈⠙⠻⠿⠦⠀⠀⢴⣾⠧⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⢰⡇⠀⠀⢡⡏⠀⠀⠀⠀⣼⢫⢦⡿⠃⢻⡇⠸⡁⢹⣿⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⠀⠈⠁⠀⠀⠀⢰⡇⣞⢾⡇⠀⠈⢻⣦⠀⠈⠻⣿⣆⠑⢄⡀⠀⠀⣴⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢳⢸⡇⠀⠀⠀⠙⠃⠀⠀⠀⠉⠛⠦⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠇⢿⡀⠀⠀⣐⣤⣆⠄⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⢸⡇⠀⠀⠠⠿⠿⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇⠙⢦⡀⠠⣯⡀⣸⡇⠀⣿⡀⢀⣷⠀⢠⡴⠃⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡓⠶⣦⡀⠸⣷⣤⣼⡷⢀⠻⣿⡟⠁⢀⠘⣿⡿⠃⠀⣿⣄⣠⡿⠁⢀⣤⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢈⣿⠀⢈⡙⢻⡇⢿⣀⣸⣧⣤⣾⣤⣟⣰⡏⠀⣿⠟⠋⠁⢰⡟⠁⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢤⣤⣀⠈⠻⠿⣿⣄⠀⣿⣶⣿⣿⣭⣭⣭⣤⣤⣉⡉⠉⠛⠿⣿⣀⣴⠇⣼⣿⣶⠟⠀⠀⠀⡀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⣹⣷⠀⣆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠙⠳⣾⣩⡤⠄⢠⣾⠋⠉⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠙⠛⠛⠛⢷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢻⣅⣤⡿⠿⠶⠾⠛
⠀⠀⠀⠀⠀⠒⢚⡛⠙⠻⣷⡄⠈⠹⣷⣿⣿⣏⣽⣿⣿⣿⣿⣿⡿⣿⣿⡟⣩⣭⣽⣿⣿⣿⣷⡀⠀⠀⠹⣧⣀⣠⠀⣠⡶⠶⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⣿⠿⠶⣾⣿⣿⣿⣿⡿⣟⣫⣭⣤⣤⡘⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣯⣥⣾⣿⣄⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⢦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡎⣿⣭⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣿⡴⠤⠉⠉⠉
⠀⠀⠀⠀⠲⢦⣉⠁⠈⣿⣿⠶⢴⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⠳⣄⠀⠀⠀⠀⣿⣤⣤⣶⡿⠛⠓⠦⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠖⠾⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⢻⣏⡈⠁⠀⠀⠀⣿⡁⠈⠙⠿⣶⣶⠾⠋
⠀⠀⠀⠀⠀⠀⢠⣴⠶⢶⣦⣤⣤⣿⡄⢿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣄⠀⠀⠈⠀⠀⠀⠀⢰⣿⣛⣋⣠⣤⣤⡀
⠀⠀⠀⠀⢀⡴⢏⣤⣀⣤⣿⠏⣀⣸⣷⡀⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡽⢍⣒⣿⣿⡋⠀⠀⠀⠀⠀⠀⢀⣾⣤⡙⢿⣿⠁⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣬⣥⡼⢷⡄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⢠⣾⣇⣀⣁⣀⠙⠛⠋⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⣿⠏⠰⠛⠻⣦⡀⠀⠈⠙⠛⠛⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⢀⣴⣿⠀⠉⣿⡿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠶⠿⠋⣀⣤⣤⣾⠋⢹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢷⣌⣉⠀⠘⢷⣤⣄⣙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⣻⡿⠀⢚⣡⡾⢹⡿⠳⣶⡶⣦⡶⢶⡶⣾⠛⢻⣇⠈⠓⢸⣿⠛⠻⣦⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠰⠖⠛⠁⣴⠿⢿⣧⠘⠀⣠⣿⡀⠸⠇⣼⣆⠛⠀⢰⣿⢿⣦⠈⠻⠦⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣿⠀⣸⡟⠀⣾⠟⠻⣿⠀⣼⡟⠻⣷⡀⢸⣇⠀⢹⠀⠀⠀⠈⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠀⠀⣿⠀⣰⠋⠀⠘⢧⠀⣿⠃⠀⠙⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣧⠁⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢅⢀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠰⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡈⠁⠀⠀⠈⣡⠀⠰⡔⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠈⠍⠆⠀⠀⠆⠂⠀⠀⡀⡏⠀⠀⠇⠒⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⡀⠆⠀⢰⡌⡀⠀⠀⣀⣀⠀⡇⠾⡄⠙⠂⠠⢋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠈⠑⢤⣀⠘⠉⠉⠁⠘⠀⢩⢄⣀⡗⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⠘⠀⠃⠰⠁⠄⢄⢁⠂⠀⠰⠀⠄⡄⠀⢈⠃⠃⡖⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⡀⢀⡀⠀⠢⠈⠒⠤⡀⠀⠀⠰⡈⠂⢱⣁⠸⡀⡁⠊⢁⢊⠈⡄⠀⠀⠝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠂⠀⠀⢠⡐⣜⠀⠤⡑⠀⠀⣐⠄⠃⠈⠀⠀⠀⠀⠀⠁⠙⠦⣀⠀⠀⠈⢈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠒⠛⢀⠨⢮⠑⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠐⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠠⡉⠫⠄⠁⠄⠀⠑⢐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣀⠠⠄⠀⠈⠉⠉⠀⠲⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠈⠈⠀⣠⠀⡀⠐⠁⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠨⢉⣤⡠⠮⠅⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠊⠄⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠙⠦⠠⢂⣀⢊⡀⣀⠸⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⢂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠃⢀⠴⠒⢀⣀⡽⠊⠀⡔⣀⠀⡈⡻⣟⠒⠶⠤⠤⠤⠤⠖⠋⠁⠀⠀⠀⣀⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠊⠁⠀⠰⡀⠄⠌⢸⢀⠄⡴⠑⠈⠙⠲⣬⣤⣀⣤⣀⣄⣐⣤⠼⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠖⡴⠂⡁⡡⠊⠀⠜⡆⠀⠀⠗⠱⡨⠀⡇⣤⡘⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢒⠈⠁⡀⢁⠬⠊⠖⢦⡰⢨⠀⠀⠀⣀⢢⢆⡀⢈⡭⠒⠄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡴⠃⠀⠐⡢⠀⢈⢁⢈⠀⠂⠁⢋⡌⠀⢙⢛⠁⢀⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠗⠀⠡⠠⠂⠀⠀⡡⠸⡆⠀⠀⠎⡀⠈⢇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⠀⢲⢀⠃⠀⠀⢃⠔⠀⢳⠀⢀⡒⠁⠀⠀⠁⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢃⠂⠀⠈⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠐⠠⠀⠀⠊⠀⠀⠀⠀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠈⢄⢄⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⢀⠤⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠀⠠⠀⠀⠈⠀⠀⠐⠀⠘⠃⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠖⠁⠐⠀⠀⠀⠀⠀⠁⢀⣠⣠⠀⠤⠤⠤⠄⠔⠠⠄⠤⡀⠀⠀⠀⠀⠐⠘⠲⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠀⠀⠀⠀⣀⠤⠔⠒⠁⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠠⠀⠀⠀⢤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⣀⠀⠀⡙⢄⣠⠀⡂⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠰⢍⠈⣹⠤⠿⠠⣏⣉⢕⡁⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇⠀⠀⠠⣀⣐⡐⠠⠟⣀⡀⠀⠀⣀⣘⣧⣂⠐⠁⠀⠀⠀⡀⠀⠀⠀⣤⣶
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡆⠀⠀⢀⡀⣀⣀⠀⠘⠛⣽⠀⠀⠀⠤⠠⠘⠞⠀⠙⠃⠀⠀⠙⠁⢸⡅⠌⡊⠙⠂⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠃⠀⠀⠈⡀⠁⢉⠓⠀⠈⠹⠀⠀⠀⣀⠔⣁⠛⣄⠀⠀⢀⠀⠀⢀⣼⣑⠂⡤⡄⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢃⠀⠈⠆⠀⠐⢼⠁⠀⠀⠁⠀⡼⣉⣉⣱⠦⣤⠤⢶⡋⠂⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠀⠢⠄⣀⡆⠀⠀⠀⠀⠚⠂⠀⠀⢈⢆⠁⢂⠼⠉⠉⠻⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠾⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠄⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⡀⠀⠀⠀⠈⠓⠢⠤⠤⣀⣀⣀⣀⣀⣀⣀⡀⠤⠄⠀⠋⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠈⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠐⠂⠩⠎⠉⠀⡶⠂⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⠦⡀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⣩⣄⠤⣤⣄⡀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢑⡶⠞⠋⠀⠀⠀⠀⠈⠉⠛⢾⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠐⠀⠐⠀⠀⠀⠀⠲⠀⣰⠎⣀⣤⣠⣀⠀⠀⠀⣀⣤⣠⣄⠙⢧⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢠⡇⠈⠁⠀⠀⠉⢣⠀⠞⠉⠀⠀⠈⠁⠘⡆⠀⠀⠀⠀⠤⣤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⠀⠘⠯⠻⠟⠒⠀⠀⠀⠐⠻⠟⠭⠃⠀⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢀⠏⡀⠀⠀⠀⠛⠃⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢳⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⡼⠫⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠟⡁⠀⢘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠳⠲⣤⠤⠤⠶⠖⠉⠀⠀⠁⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠣⡤⣀⡀⠀⠀⢀⠴⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠉⠂⠀⠀⣤⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢺⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠀⡤⠀⣤⠄⠀⡔⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠
⠀⠀⠀⠀⢀⢀⠀⠀⡆⠨⣢⠀⢊⠀⡃⠀⠀⣀⡀
⠀⠀⠀⠀⠈⡄⡉⢶⡿⠆⠛⠛⠓⠾⣧⡞⢁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣊⣉⣉⢉⠑⠲⢄
⠀⠀⣀⣀⠤⣑⡟⡠⠊⠁⠀⠀⠀⠀⠈⠳⣗⡡⢄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⣆⠀⠀⠱⡄
⠀⠀⠐⢤⣈⣽⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢹
⠀⠀⠀⡠⠶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣸
⠀⠀⠞⠠⠄⠺⣦⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⠖⠤⠄⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣼⠏
⠀⠀⠀⠀⠀⡎⠋⣵⣦⣄⣠⣼⣾⣿⣿⡏⠓⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣒⠒⠒⠋⢁⢠⣴⡿⠋
⠀⠀⠀⠀⠚⠐⠊⠁⡏⠁⣫⠹⡳⠈⡇⠉⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠜⠁⠀⠈⠢⠃

⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡹⣦⡀⠀⠀⠀⠀⠀⠀⡿⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⣿⣾⣧⠘⢻⣆⣀⣠⣤⣴⡞⢱⣿⡁⠀⠀⠀⠀⠀⣠⣶⣿⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠷⣶⣄⡀⠀⢀⣿⠉⣹⣴⣿⣿⣿⣿⢏⡞⣰⢸⡟⣷⡀⠀⢀⣠⣾⣻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣷⡈⢸⣿⠶⣿⠟⣛⣿⡭⠽⠶⠿⠿⣾⣿⣿⣼⡇⢻⣿⣟⡛⠙⡻⠋⢼⡟
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡹⣿⡘⠟⢤⣶⣿⣯⣤⣄⡀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢮⣿⡿⢿⣦⣦⣾⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣿⡛⢦⣄⣀⣀⣠⣴⣿⡇⢸⡷⣠⡴⠊⠈⠉⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡏⣻⣿⣶⣤⣀⣀⣀⣀⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡙⠯⠭⢭⣭⣿⠃⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣛⣭⠿⠛⠛⣋⣩⣥⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡦⣝⣶⡾⠿⣱⠏⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⢿⡆⠀⠀⢀⣀⣀⣤⣀⣀⠀⠘⣿⣿⡴⢊⣡⢎⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣾⡏⠀⢰⡟⠀⢀⣴⣾⣛⣻⣻⣛⡻⣷⣄⠀⢸⣿⣿⣿⣿⣿⣯⣭⣉⣛⢷⣦⠙⣿⣿⠟⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣏⣐⢀⣿⠁⣼⢋⡽⣿⣋⣉⣹⣿⣿⣿⣿⡆⣼⣿⡿⠿⣿⣿⣿⣟⣛⣿⣾⣿⣷⣿⣿⣇⣿⣇
⠀⠀⠐⢦⣄⣠⡴⠶⢟⣫⣶⣿⣟⣽⣏⢸⣿⠀⠀⠀⠀⠈⢉⣛⣉⣙⣥⣤⣿⠃⣿⣿⠶⠦⢬⣭⣉⡉⠉⠁⠉⠀⠈⠽⣿⣿⣿⣿⢷⣄⣀⡀
⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣉⡙⢻⣿⡄⠀⠀⠀⠀⠉⠉⠉⠉⢁⣼⡿⠀⢻⣯⣤⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠐⣿⣿⢹⣿⢤⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣽⣿⡟⠿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣀⣘⡻⣿⣿⠷⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣆⣀⣤⡶⠖⠛⠛⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣷⣄⢻⣿⣆⠀⠀⠀⣠⣾⠟⢠⠿⠿⠿⣿⣿⣿⣿⠍⠂⠈⠻⣦⡀⠀⠀⠀⠀⣾⣿⣿⣾⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⡼⢻⣧⣿⣿⣦⠀⠈⠋⠀⢀⣀⣨⣿⣿⣿⣽⣿⣦⣄⣀⠀⠀⠉⠃⠀⠀⠀⣽⣿⣿⢦⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠵⠋⣒⣫⡽⣯⠻⣿⣷⡄⠀⡼⠋⠉⠻⣯⣉⣉⣉⣀⣩⠿⠉⠉⠙⠀⠀⠀⣤⣿⣿⣯⣉⡓⠍⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⠶⠛⠛⠛⠿⠷⣾⣿⣷⣍⠻⣿⣦⣄⡀⠀⠀⢈⣻⣿⣿⠟⠁⣤⣶⣈⣤⣠⣾⣿⣟⣡⣶⣦⣬⣭⣽⣦⣙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣴⡌⠙⠻⢿⣿⣿⣿⠿⠟⠉⣀⣀⣠⣼⣿⣿⣿⢛⣽⡿⠟⣿⠇⠀⠀⠀⠈⠙⠿⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣫⣼⣿⣿⣷⣾⣟⣛⣿⣷⠶⠶⣿⡿⣿⢿⡛⣿⣷⣴⣿⡏⢳⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡿⣿⡿⠋⣿⢽⢩⡟⣽⣿⣿⣷⡘⣧⢹⢨⣇⣿⣿⠋⠻⣷⣄⠻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⠟⠉⠀⠀⢿⣸⢈⡾⣿⠏⠀⠙⠿⣌⡆⢸⡿⠛⠁⠀⠀⠀⠉⠻⢦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⠉⠀⠀⠀⠀⠀⠘⣯⣿⣼⡟⠀⠀⠀⠀⢻⡇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⢀⠤⠐⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠐⢲⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠴⣁⠠⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⠁⠀⠯⣴⠜⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⡄⠀⠀⣅⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⢠⠉⡀⡀⠉⠀⠀⠀⠀⠀⠀⠀⢶⣜⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡞⠀⢆⠀⠁⢀⡼⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢲⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⢡⠀⠀⣦⠀⢀⣸⣠⠠⠔⠓⠒⠒⠚⠛⠂⠠⠭⢈⡉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢠⡄⠘⡈⠀⢂⠀⣿⣶⣈⣥⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢄⠀⠈⠱⣄⡠⠤⠤⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢄⠀⠹⡦⡐⢌⠠⠙⡏⠘⡆⢸⠀⡆⠈⡠⠁⡏⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡏⢀⡀⠀⠈⢣
⠀⠀⠀⠀⢢⣜⣤⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣈⠂⡺⠀⡄⢇⢂⡆⢸⠀⣰⠋⡠⢈⡴⠃⢈⠀⢙⠦⡀⠀⠀⠀⠀⠀⠀⠙⢌⠒⠁⠀⠀⣰
⠀⠀⠀⠈⠱⢟⠷⡍⠀⠀⠀⡀⠀⠀⠀⠈⠛⢶⣄⠀⣀⠐⢌⠁⢱⣄⢡⠀⠘⠃⠘⠀⠛⠠⢀⠸⣴⠕⢉⠔⢁⡀⢈⣦⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠛⠅⠀⠂⠤⠄⠵⣄⠨⠁⡀⠁⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡔⠁⣐⣡⣈⣔⠡⢳⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠉⠀⠪⡑⠀⢛⠋⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⢛⢁⠀⠀⠀⠐⠡⢳⠀⠀⠀⠀⠀⠀⠀⡦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢖⡂⠹⢄⣈⣐⠃⠀⢈⣩⣭⡉⠛⠂⠀⠀⠛⠋⣩⣭⡉⠀⠈⢁⣀⠊⠈⠉⣓⠾⡇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠀⠀⠀⠀⠘⠁⠈⠉⣉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡉⡁⠀⡙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⡰⠒⠀⠀⠀⠤⠄⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣀⠀⠤⠄⠀⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠲⠀⠤⠶⠶⠍⣠⠤⠤⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⡉⠣⡄⠩⢿⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠀⠀⢀⠠⢂⠔⠀⣀⠀⢁⣼⢆⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⡠⢦⡔⠢⣌⠢⠀⢡⠇⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠓⠄⣴⣴⠗⠂⠀⠡⢂⡠⡁⢈⠕⢀⠔⢁⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠑⢄⠀⣅⠈⡓⣰⠃⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣨⠄⠀⠀⠀⠉⠁⠀⠀⢀⡴⠟⠉⡠⢁⠔⢁⠔⡌⡱⠀⠛⢰⡆⢰⠀⣶⠀⠉⡄⠹⡀⣄⠑⢌⣡⠞⠁⠀⠀⠀⠀⠀⠀⢠⠚
⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⠔⠡⠀⡉⢊⡜⣡⠊⡠⠎⡅⢸⠀⠁⠈⡆⡇⢸⢄⣨⠵⠊⠀⠀⠀⠀⠀⠀⠀⢀⡴⠣⣜
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⠀⡀⠀⠹⡀⠀⣠⡶⠁⠀⠀⣼⠟⠀⠀⡍⠿⣓⠒⠣⠼⠴⠷⠶⠗⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡋⡠⠀⢸
⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠉⠁⠀⡰⠁⠘⠉⠀⠀⠀⠘⠁⠀⡐⠠⢀⠀⣾⠛⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠁⠀⠀⢠⠤⠊
⠀⠀⠀⠀⠀⠀⠈⣳⠤⠤⠤⠔⠊⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣦⠂⠁⠀⠏⠀⠈⢸⠈⠈⠙⠖⠖⠒⢶⣖⠂⠪⡉⠀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⣠⣠⠎⠁⠀⠉⠳⡄⠀⠀⠸⠿⠒⢢⡀⠀⠀⢀⣿⠖⠒⠢⡤⠃⠀⠀⠻⠀⠀⠀⠁⠈⠁⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢈⠀⢰⠛⠀⠀⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⢴⠋⠀⠈⠓⠒⠊⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣄⡀⠤⠊⠀⠀⠀⠀⠀⠒⣯⠛⣽⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠞⣄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠉⠀⠈⠉⠀⠀⠀⠈⠙⠐⠋⠀⠀⠀⠀⠀⠀⠐
⢀⣀⣀⢀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⢠⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠠⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣰⣿⣿⢀⠇⠁⠀⡸⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠲⠀⠈⠣⠀⢦⡄⠀⣼⣿⣿⡇⠈⠠⠃⠀⠁⢠⡀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⡄⠳⠈⣆⠀⢀⣼⡇⠀⣿⣿⣿⡇⠄⣀⣤⣤⣶⡿⠁⢀⣠⣤⣴⣴⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡀⡀⢘⣿⣿⣦⠀⠈⢂⣾⣿⣇⣤⠽⠿⠿⠷⠶⠾⢿⣟⡉⢠⣾⣿⣿⣿⡿⠋⣠⠔⣐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⣷⣤⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠟⠁⠀⣁⠤⠀⠀⣀⠀⠀⠈⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡈⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣴⣈⡀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠐⠒⠀⠂⢹⣿⣆⣰⠋⠀⠀⠐⠒⠲⢤⣄⠀⠀⠀⠀⣠⡴⠖⠒⠂⠀⠀⠙⣿⠿⣿⣶⡶⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⡀⠐⠢⣄⢀⡻⢿⡏⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣆⣤⣤⣄⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠁⠀⣠⣈⣁⣀⡀⠀⠀⣺⠁⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣿⣿⣿⣿⠀⢀⡄⠀⠉⠉⠉⠁⢀⠀⠀⠀⠀⠀⠈⠉⢭⣭⠆⠀⠀⠀⣟⠉⡉⠉⢙⠛⠛⠛⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠨⠉⠙⠻⠿⠟⢻⡇⠄⠁⠀⠀⠀⠀⠀⠈⠑⠦⡀⣀⠀⠀⠀⠀⠿⠀⠀⠀⢸⣷⣦⠀⠐⠤⠈⠁⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⢠⡴⢶⣶⣶⣿⡄⠛⠃⠀⠀⠀⠀⠀⠀⠰⡛⣉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣿⡆⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠛⡿⠹⣄⠀⠄⠀⠀⠀⠀⠀⠒⠛⠲⠟⠁⠀⠀⠀⠀⣠⣿⣶⣄⠙⠻⠶⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠊⠁⠀⠔⠒⠁⠀⣠⣿⣷⣤⡀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⠞⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⡠⠒⣉⣴⣿⣿⣿⣿⠏⢉⣷⣶⣤⣤⣤⣤⣤⣤⠶⢺⣿⣷⠂⠀⠈⢻⣿⣿⡣⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⣺⡿⠿⡻⠟⠋⠁⣴⡿⠿⠿⠑⠀⢸⣿⣿⣿⠀⢸⡿⠁⠀⠳⠀⢆⠙⣿⣧⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠁⠀⠈⠏⠄⠀⢀⠆⠀⢸⣿⣿⡿⠀⠘⠧⠀⢀⠀⠁⢌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⡜⠀⠨⢠⠃⣾⣿⡟⠃⠄⠀⠀⠀⠀⠣⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠊⠈⠀⠻⡏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠠⠐⠊⠀⠀⠁⠄⠀⠈⠀⠀⠀⠂⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣴⣄⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⢤⠄
⠀⠀⠀⢀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠛⠉⠀⠀⠀⠈⠙⠲⣶⠀⠀⠀⠀⠀⠀⢤⠓⡄⠀⠀⠀⠰⠒⠢
⠀⠀⠀⠆⠀⢁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠂⠀⠀⠀⠀⠈⠉⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇⠀⠀⠙⠁⠀⠀⠙⠁⠀⠀⣿⡤⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠔⠂
⠀⠀⠀⡀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠲⠆⢠⠴⡄
⠀⠀⠀⠐⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠈⠃⠋⠀⠀⣠⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠋⠃
⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡶⠶⣤⡴⠶⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠐⠢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⠔⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠊⠉⠀⠀⠀⠰⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⣀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢀⡐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣀⠀⠆⠀⣈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⠀⢀⠄⠂⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢹⡀⠀⣸⡆⠀⢠⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⢸⡇⢠⣿⢃⣴⡟⣠⣶⠟⢁⣀⣴⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢿⡆⣾⣧⣿⣿⣿⣿⣾⣿⣷⣾⣿⣋⣁⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢸⣷⣿⣿⣫⣭⣤⣤⣄⡀⠉⠙⠿⣿⣯⣭⣅⣀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⣦⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠘⢿⣿⣭⣉⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢿⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣟⡛⠿⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣶⣽⣿⣿⣏⠀⢨⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣟⠿⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣶⣬⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣿⡿⣷⡄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⣾⣿⣷⡈⠻⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢙⣛⣻⣿⣿⣝⣛⠛⠛⠋⠁⣀⣠⣶⣿⢿⣇⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠋⢉⣩⣿⡿⢿⣿⡿⣿⣿⣿⣿⢻⡿⠸⣷⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠟⠉⢁⣴⠿⠋⣼⡟⢡⣿⠃⢹⡇⠀⠈⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠃⠀⠸⡏⠀⠘⣧⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⢸⠻⡄⠀⠀⢀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⡘⠱⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⢰⡟⣇⠀⠏⡄⢣⢠⢖⢯⠟⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⡘⠘⡄⢠⠁⠀⠇⡠⠒⢡⠃⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠘⡍⢝⠢⣼⡼⣞⣛⠉⠭⠋⣛⡲⢽⡤⠖⡫⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠑⠢⣥⠴⢚⠋⠩⠍⠙⡓⠢⣥⡤⠚⠉⡘
⠀⠀⠀⢠⣤⣤⡀⠘⣦⢟⠕⠊⠁⠀⠀⢀⡴⠒⠉⠑⢜⢮⣴⣁⣀⠀⢀⡀⠀⠀⠀⠀⣤⡤⢄⠀⠱⣠⢊⠔⠁⠀⠀⠀⢀⠔⠂⠉⠂⠕⢆⣜⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠈⢳⡩⣹⢣⠊⣀⣤⣤⣄⢀⠎⢀⣤⣤⣤⡀⠱⣹⣔⡯⠽⠟⠁⠀⠀⠀⠀⠀⠉⢆⠉⡹⡱⠁⣀⣤⣤⣀⠠⠁⢀⣤⣤⣄⠀⢂⢣⢀⡨⠭⠋
⠀⠀⠀⢀⣀⡤⠽⡏⡆⠀⢴⣶⣶⢆⠸⡀⢀⣴⣶⡶⡄⠀⣧⢿⠤⣄⣀⠀⠀⠀⠀⠀⢀⡀⠬⠹⢇⠁⠀⡴⣲⣶⠄⢀⠀⢠⢶⣶⣦⠀⠀⡆⠇⠤⢄⣀
⠀⠀⠛⠻⠤⣄⣘⡇⡇⠀⠀⠉⠉⠀⠀⠱⡄⠈⠉⠉⠀⠀⣸⣘⣁⡠⠤⠛⠛⠀⠘⠛⠢⠄⣀⣘⠨⠀⠀⠀⠉⠁⠀⠀⠢⠀⠈⠉⠁⠀⠀⡀⡇⣀⠠⠄⠛⠃
⠀⠀⠀⠀⢀⣀⣤⢷⢡⠀⠀⠀⠀⣀⣰⣒⣁⣀⠀⠀⠀⢠⢧⣟⣳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠜⢃⢆⠀⠀⠀⠀⠀⣐⠈⠀⠀⠀⠀⠀⠠⢡⠛⠢⡀
⠀⠀⠀⠴⠟⠚⠾⠽⡷⡱⣀⠀⠀⠈⠉⢿⡋⠀⠀⠀⡠⣫⣞⠚⠺⣽⣦⡄⠀⠀⠀⠀⠴⠓⠢⠤⢼⢦⠢⡀⠀⠀⠉⠙⢏⠁⠀⠀⠀⡠⡡⡗⠒⠦⣑⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡼⡠⢛⣮⣕⠤⠄⢀⣀⠈⠴⢖⣫⣞⡑⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢑⢬⣂⠤⠀⢀⡀⠁⠰⢖⣬⣎⠁⠘⡄
⠀⠀⠀⠀⠀⢀⣼⠖⠚⠁⢠⡏⣏⡿⡚⡒⢳⠛⢯⢯⡇⠉⠓⠮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠔⠊⠁⡸⠀⢉⢶⠒⠒⡚⠻⡅⢸⠆⠙⠒⢼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠉⠀⢳⢁⡇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠆⢀⠃⠀⠰⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⡿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡎⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠚⠠⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠐⠠⠤⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠁⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢂⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢱⢄⣀⣀⣀⢠⠔⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠃⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠄⠀⠀⠀⠀⣀⡐⠀⠰⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⣧⡼⠛⠛⠀⠀⠀⠀⠀⣀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⣀⠀⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠉⠠⣿⣻⣿⠁⠀⡀⠀⠀⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⣷
⠀⠀⢀⣠⣶⣶⣿⣷⣶⣄⠀⠐⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⢀
⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠇⠊⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠒⠀⠀⠀⠀⠀⢀⡉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣦⡠⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣄⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⡇⢸⣿⣼⡇⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⡆⠁
⠀⠀⠀⢤⠀⠀⠈⠿⠿⠿⠋⠀⠂⠀⠀⠀⠀⢈⣉⣤⣿⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠉⡍⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣢⠤⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣶⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣥⣾⡦⢦⢀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⠞⠀⠀⠀⠀⠀⡆⢰⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⠞⣿⣊⡀
⠀⠀⠀⠀⠰⣶⠒⢤⠔⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠿⣿⡶⡟⢭⡙
⠀⠀⠀⠀⠀⠈⠙⢻⣶⣼⣟⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠁⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢪⣳⣷⡆⣸⡁⣠⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⡀⠁⣲⣼⡾⠛⠛⠛⠛⢿⣷⣷⣂⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣫⠷⠄⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⡵⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠶⠊⠉
⠀⠀⠀⠀⠀⠀⠐⢈⠊⡀⠀⠀⠀⠴⠀⢀⠀⣀⣠⠶⠶⣾⣿⣦⡀⠀⠀⠀⠀⠀⢀⣿⠿⠦⠒⠢⠀⠀⠀⠀⠀⠠⠀⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠔⠉⠨⢿⣿⣝⣻⠖⠀⣀⣠⣾⣿⡛⠛⠲⠄⠀⠀⠀⠀⠀⠀⢀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢫⠿⢻⠟⡿⡏⢷⠸⠄⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠀⠀⠈⠂⠋⠀⠃⣇⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢤⣀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠿⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠈⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠂⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠳⠀⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠐⠂⠈⢉⡰⠒⠦⣆⠀⠀⠀⠀⢀⠤⠀⢃⠀⢜⠀⠼⡀⠠⢀⠀⠘⠧⠤⠠⠤⣀⣀⠀⠰⣨⠀⠦⠜⣁
⠀⠀⠀⠐⠁⠀⠀⠀⡴⠋⠀⠀⠀⠈⠻⣄⠂⠀⠘⡀⠀⠀⠀⠀⠀⠀⠸⠀⡌⠀⠀⠄⠀⠀⠀⠈⡧⠠⠀⠀⠑⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠘⣄⠂⠀⡎⠀⠀⠘⠄⠠⠃⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤
⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠑⠀⢐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢊⠭
⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣎⠠⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠠⡀
⠀⠀⠐⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠰⠁⠀⠀⠰⡅⠁⡴⠁⠀⠀⢐⡀
⠀⠀⠀⠀⠢⢀⠀⠀⠈⠦⣄⠀⢀⣤⠎⡁⠀⠀⠀⠀⠀⣄⣀⣤⣀⣠⠎⢀⠄⠐⠀⠂⠀⢐⠀⠀⠀⠀⠂⠀⠐⠙⠂
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠉⠛⠀⡀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠉⠳⣎⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠒⠆⠀⢀
⠀⠀⠀⡀⠰⣀⡀⠀⠀⢈⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⣋⠁⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡠
⠀⠀⠀⢁⠀⢠⠀⠀⠐⠢⠄⠠⠵⠄⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⡼⠉⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⢉⠢⠤⣀⣀⠤⢞⠁⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⡠⠊⠀⠈
⠀⠀⠀⠠⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠁⠀⠀⠌⠀⠀⠀⠆⠀⠀⠑⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠁⠲⠃⠑⠄⠀⠀⡘⠀⠂⡀⠀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠔⠁⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠄⠀⠁⠁⠀⠰⠀⠂⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠢⠀⠀⢀⠀⠂⠀⠀⠀⠈⠐⠢⡀
⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡩⢒⠫⢖⡤⢒⠤⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠁⠢⠀⠄⠄⠀⠐⠐⠀⠉⠀⠀⠀⠀⠀⡡⢀⠅⡈⠕⠂⠉⠠⣄⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠚⢠⠀⢐⠂⢀⠁⠈⠐⠃⠐⠂⠤⠀⣀⠀⠀⠐⠳⠤⠤⠤⠄⠄⠄⠀⠀⠀⠐⣚
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠐⠁⠦⠈⠀⠘⠒⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⣂⠀⠀⠀⠈⠃⠀⠀⠀⠁⠀⠉⠉⠉⢩⠃
⠀⡊⠤⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠈⠀⠈⠁⠂⠀⠀⠁⠀⢠⠀⠀⠈⠐⠄⠀⠀⢀⠀⠠⠐⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡔⣄⠀⠀⢀⠶⡀
⠀⠀⢀⡀⢀⡀⢸⡀⢨⣃⢰⡡⢀⡇⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢇⢄⠹⡾⠟⣊⠉⠉⠓⠺⢷⡟⢀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠭⠤⣄⡠⠈⠉⠲⢄
⣀⣀⠤⢬⣻⢃⠔⠉⠀⠀⠀⠀⠀⠀⠹⣷⡡⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠳⡄⠀⠀⠳⡀
⠘⠦⣀⣩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢷
⠀⣀⢤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸
⠼⢥⣀⣲⢧⡀⠀⠀⠀⠀⠀⢀⢀⣖⣜⣿⣶⣂⡠⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⣴⠏
⠀⠀⠀⣰⡻⢓⣤⣀⠀⣀⣠⡮⣟⣿⡟⢫⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠤⠤⠤⠴⠚⠁⣀⣴⡿⠋
⠀⠀⢠⣇⡠⠜⢹⠟⢹⢿⢻⣏⠹⡏⠛⠤⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠘⡄⡴⠃⠈⠢⣀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠚⠛⠛⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢄⣀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠶⠶⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣌⡆⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣲⣄⡀⠀⠸⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢓⣶⡶⠶⠤⠤⢤⣤⠤⠴⠶⠖⢒⡶⣏⠉⠁⢀⡟⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢀⡴⠋⠀⢻⡄⠀⣠⠟⠈⠳⣄⠀⢀⡞⠀⠈⠳⣄⣸⠁⠀⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠼⣟⣁⣀⣀⣀⣻⣴⣋⣀⣀⣀⣙⣧⣞⣀⣠⠤⠤⠾⠛⠛⠉⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢤
⠀⠀⠀⠀⣿⠀⠉⠙⠲⠦⢄⣀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣀⡞⠀⠀⠀⠀⠈⣧⡀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⠄⢀⡤⠖⠚⠋⠉⠀⠀⠀⣸
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣈⡽⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠸⠋⠻⠉⠉⠀⠀⠀⠀⠀⠉⠹⠏⠻⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⣿
⠀⠀⠀⠀⣧⣠⠤⠴⠒⠋⠉⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⣠⠤⢤⡀⠀⠀⠠⣄⣀⣤⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡞⠀⠀⠀⢹⠀⠀⠀⠀⠉⠀⠀⠀⢸⠁⠀⠀⠘⡆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⢤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣤⠞⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣲⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⣤⣤⠤⠴⠖⠚⠉⠀⠀⠀⠀⢰⡒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⡤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⣿⣿⡇⠈⢿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⠀⠘⢿⣿⠏⠀⣼⡿⠁⢀⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⡀⠈⢿⡆⠀⠈⠃⠀⠀⠛⠀⠀⢸⣿⡿⠟⠀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⣿⣿⣿⣿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣠⣴⣿⣿⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠻⢷⣤⠀⠀⠀⡀⠛⠂⠀⠐⠋⠁⡐⠒⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⠀⠀⢀⣴⠋⠀⠀⢀⡀⢠⠊⠉⠉⠂⠜⠉⠉⠑⠄
⠀⠀⠀⠙⠶⠦⣄⡀⢀⡤⠒⣒⠛⢿⣶⣦⣄⡀⢈⡿⠁⠀⠀⠰⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠀⠀⠀⠈⢝⢿⣿⣯⠀⠀⠀⠀⠀⢹⠆⠀⠀⢀⣤⡀⠀⢦⣖⡀⣸⣿⡟⠛
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣠⠶⢦⡠⢤⡀⢈⣿⣿⣧⠀⠀⠀⠀⠘⢦⣒⠾⠟⠹⣿⣿⣿⠟⠿⣿⡿⠃
⠀⠲⠶⠞⠉⠉⠃⠀⠀⢰⠁⠀⣸⠀⠀⢱⠸⣿⣿⣿⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⢆⣘⣿⣄⣓⠾⠀⣿⡿⡸⠘⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⣌⢆⠀⠀⠘⢅⣠⣿⢇⣠⣴⡿⡱⠁
⠀⠀⠀⠀⣠⣾⠋⠀⠑⠤⣀⣀⢀⣀⣼⣿⠯⠊⠀⢦⣠⡀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠒⣲⣦⣄⡀
⠀⠀⠀⠔⠋⠀⠀⠀⢀⡆⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠠⠂⠀⠐⠲⡄⠀⣴⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⢤⡀⠀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢰⠁⢶⠃⢴⡆⢱⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠀⠀⠊⠉⣻⠀⠀⢠⣸⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠌⠹⣦⣤⡶⠀⠳⢶⠿⠦⣚⡻⠃⢿⣿
⠀⠀⠀⣀⣠⠆⠁⠀⢀⠔⠒⠲⡄⠀⠀⠈⠂⠀⠀⢐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⣤⡀⠥⠔⢦⡿⠛⠛⠂⠀⠘⡀⠀⠀⠀⠀⠀⢿⣿⣧⡀
⠀⣇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣴⣿⠇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠈⠻⣿⣯⣒⣤⣤⡤
⠀⠈⠓⠛⠛⢷⣄⣀⣼⣿⣶⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢀⣀⣀⣈⣻⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠈⣧⠀⠀⢸⡆⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢻⡄⢀⣾⠇⣠⡿⢃⣠⣾⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⣾⡇⣾⣿⣼⣿⣵⣿⣟⣵⣶⡾⠛⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠀⣿⣆⣿⣿⠿⢛⣋⡉⠉⠙⠛⠿⣷⣿⡿⠟⠛⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢻⣷⣻⣿⣿⣷⣿⣿⣿⣿⣿⣶⣄⠀⠈⠻⣿⣿⠿⠷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣷⣦⣤⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⣶⣬⡻⣿⣿⣿⠟⠘⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣷⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢿⣿⣿⣿⣧⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣮⡙⠿⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⣿⣯⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣶⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣴⣿⣯⢿⣧⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣤⣶⣾⡿⢿⣶⣬⣍⣁⣀⣠⣤⣶⣿⣿⢹⣿⠀⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⣤⣾⠿⢟⣽⣿⢟⣿⡿⣿⡿⢸⡿⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⡿⠋⢡⣿⠋⢰⣿⠁⠘⣧⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠸⡇⠀⠀⢻⡀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁