Fruit bowl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⣆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣟⡿⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡏⠿⠛⠁⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣀⠜⣿⣳⣟⢄⣶⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣯⣺⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣽⣾⣿⣽⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡶⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⡯⣿⣧⡿⣾⣿⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣟⢿⡻⢻⢿⣿⣿⣷⣻⣿⣿⣿⢎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⡯⣿⣽⣾⣿⣿⣷⡿⣿⡿⢿⣫⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⣮⣿⣿⣐⣏⣛⣟⣛⣛⣫⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟
⠀⠀⠀⠀⣿⠀⠀⠀⠑⣤⠀⠀⠀⠀⠰⠀⠀⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠂⠀⠤⠀⠘⠀⠀⠀⠙⢦
⠀⠀⠀⠀⣿⠀⠀⠀⠐⠀⠀⢢⠐⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣤⡀⠀⠀⣿⠀⠶⣤⣀⠘⢩⣥⠄⢠⡆⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠬⠭⠛⠃
⣿⣧⠀⠀⣿⠀⠐⣴⠉⠛⠛⠻⠶⠶⠷⠶⠴⠤⠶⠶⠶⡶⠤⠤⠴⠶⠶⠶⠒⠛⠛⠋⠉⠉
⣿⣿⡀⢀⠟⠒⠂⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀
⣿⣿⣆⠌⠀⠀⠀⠈⢟⠄
⣿⣿⣿⣷⣶⣶⣶⣶⣼⣷⣒⡄⠃⠀⠛⠂
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⡟⠀⠀⠀⠀⢀⡀
⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠞⠀⠀⣀⡀⠐⠿⣄⣲⠤⠀⠀⠀⢄⣠⡀⢀⡀⢀
⠃⠀⠉⠙⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣤⣾⣿⣿⣵⡖⢲⣯⣴⣦⣤⣤⣤⡿⠿⣷⡾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠉⠛⠛⠛⠶⠿⠟⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⣤⡼⢡
⠀⠀⠀⠀⣀⣠⠾⢑⠒⠾
⠀⢀⣴⠟⠁⠀⢀⡼⢠⠇
⢠⡿⠁⠀⢀⣴⠟⠁⠘⡆⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⣀⡴⠞⢛⡓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗
⣾⠁⠀⢠⡾⠁⠀⠀⠀⣿⢄⠴⠛⠉⠉⡄⠉⠙⢢⡘⠋⠀⠀⠀⠁⢸⡇⠀⠀⠀⢀⣀⡤⢴⠋⠁⡄
⣿⠀⠀⣼⠇⠀⠀⠀⠀⣿⠈⣆⠀⠀⠀⠉⠉⠀⠀⠹⡀⣀⣀⣀⣀⡚⠀⠀⢠⠊⠉⣿⢀⡼⠶⠖⠓⢢⡀
⠸⣆⠀⢹⡇⠀⠀⠀⠀⢻⡀⠈⢧⠀⠀⠀⠀⠀⣠⡶⠟⣩⢁⡄⠀⠈⠳⢀⡼⠂⣞⠁⠹⣗⣀⡼⠒⢻
⠀⠘⢆⠈⢷⠀⠀⠀⠀⠘⣧⠀⠈⠳⡀⠀⠀⣰⠟⠀⠈⠀⠇⠉⠀⡞⠉⠻⣌⣀⣸⡛⠛⠉⡏⢰⠤⠞⢦
⠀⣑⠦⣄⡈⠣⠀⠀⠀⠀⠈⢧⠀⠀⠙⠢⣀⠻⠀⠀⠀⠀⠀⠀⠀⢙⡶⢺⣁⡯⠀⡽⠒⣋⠷⠿⣄⣀⡾⠁
⢸⣿⠀⢠⡯⡙⠓⠶⠦⢤⣤⣤⣤⣤⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣬⠵⠖⠛⠉⠀⠀⣆⡜⡀⣱
⠀⣿⠀⠸⡇⠘⡄⢠⠞⣳⠀⠀⠉⠉⠉⠉⣙⠛⠛⠛⠛⢛⠛⠛⠉⠉⠉⡀⢀⡔⠒⣦⢀⡞⠂⡇⠳⠶⠋
⠀⢿⣀⣤⣌⡢⡃⠛⣴⢋⣀⣠⣀⡀⢴⣉⣀⣤⡴⡶⢈⣍⠀⠷⠶⠖⠛⠁⠈⣧⠀⠘⣾⠀⢠⡇
⠀⠘⣏⢷⣤⣍⢰⣶⠀⣋⣁⣠⡼⠇⠀⠈⠁⠀⡼⢁⡞⢹⡄⠘⠀⢠⡴⠖⠒⠚⠷⡄⣈⠀⣸⠃
⠀⠀⢹⡄⠀⠀⢠⡉⠀⡀⠀⠀⠀⠀⠀⠀⣠⣀⠛⠋⠀⠀⠻⠾⠀⠈⠙⠒⣲⣶⠶⢀⡛⢠⡟⠀⠀⠀⠀⠀⠠⠖⠚⠃⠤⠀⠴⠶⢤⣀
⠀⠀⠀⢻⣄⠶⠋⢹⠀⣸⠀⠀⠀⣀⠀⠀⡇⠈⣆⠀⠀⠀⣀⠀⠀⠀⢀⡾⣋⣤⡾⠋⣰⡟⠀⠀⢀⡤⠖⠛⠉⠉⣉⣡⡄⠀⢨⠵⠂⠈⣆
⠀⠀⠀⠀⠙⢦⡀⠈⠳⠋⠀⠀⠸⡉⠙⠢⣡⠀⢹⣠⡴⠋⣹⠇⠀⠀⠀⠉⠉⠘⣡⡾⠋⠀⠀⣴⠋⠀⠀⠀⠀⠈⣩⠆⠘⠚⠠⠀⠈⠐⢍
⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⢤⣤⣭⣶⣤⡘⠃⠺⢋⣤⣾⣥⣄⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⡑⠲⠦⠤⣄⣈⣉⡋⠓⠀⢁⣒⣚⣭⡤⠶⠛⡋⠁⠀⠞⠉⠹⣄⣤⡈⠳⠤⣤⣀⠀⢻⡀⠀⠀⠀⠀⣸⠃⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠛⢤⣙⠁⠸⠇⠀⣤⡄⠀⣤⠀⢉⣄⠀⢤⡄⠐⠗⣀⣷⠀⢀⠴⠲⡞⠁⣀⡟⠀⠀⠀⠀⠀⠀⠳⢦⣄⡀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⣤⣌⣀⣀⣉⣀⣀⣉⣠⣤⣴⣾⠿⠛⠁⠀⣏⣀⡴⢫⣭⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⢸⡀⠈⢳
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠶⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⣠⡶⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠶⠶⣶⣶⣶⡿⠿⣿⠟⠋⠁⠀⢶⡴⢤⡀⢳⣴⠀⠀⠀⠸⠋⠀⠀⠀⠀⠞⠉⠉⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠁⠀⠀⠀⠀⢿⣿⣷⣾⣿⠧⠀⠀⣄⠀⠻⣄⢛⣼⣿⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣯⣴⡾⣷⣿⣦⣤⣬⠀⠀⠀⠀⠀⠈⠿⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣻⡄⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣿⣿⣿⣹⣿⡟⣿⣦⣼⣿⣶⡟⣡⡀⠀⠀⠀⠀⠀⠀⠀⠙⣟
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡿⣧⠀⠀⢀⣴⡓⠈⠀⠈⠉⠓⢦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⣿⣿⣟⣿⡿⢿⣿⣿⣿⣿⣿⠾⠿⠷⣶⣴⣶⣿⣿⠷⠀⠀⠀⠀⠀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠟⠀⠀⠀⠈⠻⣿⡟⢹⠃⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠘⠙⢷⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⣾⠟⠃⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠙⣿⠃⠀⠀⠀⠀⠀⠀⠘⠆⠀⣿⣿⣾⡶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⣴⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⠀⠐⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡗⢦⠀⠀⠀⢀⡀⡠⠖⠺⠦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢑⠦⣄⡇⠀⢳⣠⠞⠁⡿⠁⠀⠀⠀⠸⣠⠏⢣
⠀⠀⠀⠀⠀⡠⠔⠒⠛⠓⠚⢦⣾⣤⣬⣇⠀⡴⠁⠀⢠⠃⠀⠀⠀⠀⠀⡏⣠⣜⣓⡹⢃⡆
⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢧⣀⠔⠁⡤⣀⠀⠀⠀⠰⡟⠉⠁⠈⠉⠻⠓⠒⠒⠦⣄
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⢧⡈⣧⣴⠥⣄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠓⠢⣼⣛⡦⠴⠊⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⡇⠈⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⡇⠀⠀⠀⠀⣀⣠⠤⠖⠋⠀⡇
⠀⠀⢳⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠤⠴⠧⠤⣤⣀⣀⣀⣀⣠⡤⠤⠤⠼⠾⠖⠒⠒⠋⠉⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣾⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⢷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠹⠀⠘⣇⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠹⣆⢀⡴⠛⠓⢦⠀⠀⠀⣀⠤⠐⠒⠒⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⣀⠀⠀⠀⠀⢙⡞⠀⠀⠀⠈⢧⣠⠊⠥⠀⠀⠀⠲⣦⠀⢠⣌⢢⡀
⠀⠀⠀⠀⣠⠤⠶⠒⠿⢤⣗⣽⡇⠀⢀⡴⠋⠀⠀⠀⠀⠀⢨⠗⢦⠂⠀⠀⠀⢸⡟⠀⠈⠉⠀⢱⡀
⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠘⢿⠿⠤⣞⡠⠀⠀⠀⠀⠀⡠⠾⢦⣾⠒⣶⠶⣤⣾⣇⡀⠀⠀⠆⠀⡇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⣳⣾⣍⣳⡔⡛⣤⣋⠉⣳⣽⣀⡁⢌⢁⡇
⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⢀⣠⡖⣧⢼⡻⢙⡮⣴⢁⡌⡟⠩⣹⠘⣹⣤⣚⣉⣳⣶
⣿⣟⢟⡖⣶⠲⢲⡶⡤⡤⣤⡤⣤⡤⣤⢼⢷⡶⡿⣬⡷⡷⢶⡿⡿⡷⢾⢻⢻⠳⡟⣟⡏⡍⢯⠏⣯⠹⠜
⢸⠀⡸⡇⠈⠁⢸⡇⠉⠀⡇⠓⠁⡇⠘⠞⢸⡇⠑⠉⡇⠙⢸⡇⠙⠁⢸⠈⠉⢠⡇⠈⠀⣇⠀⢀⣿⡀
⠸⡋⠁⠳⣀⣠⠞⢧⣀⡼⣇⠀⣠⢷⡀⢀⣼⡇⠀⣸⢇⢀⡼⢧⡀⣀⠾⣄⣠⠞⠳⣄⡼⠙⠒⠋⠀⠉⢻
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠀⠙⠋⠁⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠶⠒⠚⠉⢁⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⡇⢀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠴⣧⣰⡾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣾⢁⣼⣭⡁⢀⣴⡶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⡃⣾⣧⣤⣿⣿⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣷⣾⣻⣿⣿⣿⣿⣿⡈⠄⢊⣯⡊⠠⠀⠆⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⠶⠾⢿⣿⣷⠁⡖⠀⢀⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀⣾⣉⣿⣿⣿⣿⠋⠀⠀⠌⢻⣿⡀⠀⠀⣏⣡⠀⣁⠂⠁⡀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠋⠉⠙⢿⠛⠋⠀⠀⣤⣴⡋⠉⠉⠐⠛⢩⠇⣨⢿⡙⡗⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣙⣠⢶⣾⠃⢂⣀⣰⢿⣥⣤⣶⣶⣶⣶⣿⣫⡄⠂⠐⠛⠀⠻⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣉⠉⠉⠙⠛⠛⠳⠿⠿⠿⠛⠛⠛⠛⠛⠛⠓⠀⣀⣙⣢⡒⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣯⣥⣶⣒⣲⣒⣒⣒⣶⣦⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠋

⠀⠀⠀⠀⠀⢠⠒⢊⠉⡆
⠀⠀⠀⠀⠀⠀⡇⠘⢦⠳⢄⡀⠀⠀⠀⠀⠀⠀⠐⢫⣆
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠑⠠⡱⡄⠀⢠⠖⠉⠉⠀⠉⢿⠗⠊⠉⠉⠙⢦⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠁⠱⡀⢸⠀⠀⠀⣀⣀⠀⠀⢀⡠⠤⢤⡨⢇⡠⠎⢉⡟⠁⠀⣙⠍⣙⠦⢤⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢇⠱⠘⣾⠴⠚⠉⠡⡀⠈⠁⠙⠲⡈⡷⠀⠘⠟⢓⡠⠐⠂⠘⠀⢀⡘⠒⠢⠛⠂⡄
⠀⠀⠀⠀⠀⣇⠀⠠⠀⠀⠀⠈⠣⣸⠃⠀⠀⠀⠒⠛⠚⠍⠀⣠⠞⠉⠉⠉⢽⣜⡉⠉⠉⠙⠲⡄⢹⣄⡴⠦⠤⣼
⠀⠀⠀⠀⠀⢸⡀⠀⠣⡀⠀⠀⠐⢌⠢⣤⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢹⢀⠤⠾⠀⠀⢸⠉⢱⡀
⠀⠀⠀⡴⠒⢻⠧⠤⣄⣑⣄⡀⠀⠀⠈⠒⠭⡒⠦⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⢀⠇⠀⠐⡞
⠀⠀⠀⠓⠦⣦⣄⣀⣘⣄⣀⠉⠫⡉⠉⠙⠛⢗⠒⠒⠷⡚⠚⠒⠶⢶⠖⠒⠒⠒⠋⡉⠉⠉⠙⢤⡈⠁⣘⣧⣀⣀⠜⠁
⠀⠀⠀⠀⠀⢹⡌⢃⠀⠈⠉⠙⢫⠉⠉⠙⡻⢞⠓⠒⠒⠚⡲⠖⠀⠀⢱⢶⠒⢒⢶⠛⠒⠺⢏⠉⢉⠏⠉⢸⠃
⠀⠀⠀⠀⠀⠘⡆⠀⠡⡄⠊⠀⠀⢡⡤⠊⠀⠀⠀⠀⢀⠀⠀⠈⢦⠒⠁⠀⠑⢎⠀⠑⢖⠀⠈⠲⡊⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠹⣄⠄⠑⠀⠀⠀⠀⢡⡀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠢⣄⠀⠀⠊⠡⣀⠔⠁⠠⡔⠉⢢⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢢⡀⠀⠀⠀⠀⡀⠠⠂⠈⠀⠀⢀⠔⠁⠀⠓⢅⠀⠀⠙⢢⡀⠀⠈⣦⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠠⡀⢀⠄⠓⢄⠀⠀⠀⠈⠱⠄⠀⠀⢀⡠⠓⢤⡊⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⠘⢢⣀⠀⠀⠝⠢⢄⡊⠀⠀⢈⠿⠌⣀⣠⢞⣁⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣉⠛⠚⠛⠶⠶⠶⠾⠾⠓⠚⠶⠒⠒⠛⠉⣉⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠒⠋⠉⠁

⠀⠀⠀⣤
⠀⠀⢸⣿⣆
⠀⠀⠎⡇⠈⠄⠀⠀⡀⠀⢀⠀⠀⠚⢢⣀⠔⢸⣀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⢠⠀⠈⣴⠋⠀⠀⡤⠋⠁⠀⠐⢿⠚⠁⠀⠈⢢⠔⠉⠀⠀⠀⠀⠀⠑⢶⠒⠐⠒⢤⠀⢠⠖⠁⠉⡖⠐⠁
⠀⠀⠘⠈⠆⠀⠈⢆⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⢳⣀⠤⠔⠛⠁⠀⠀⢀⠇
⠀⠀⠀⢆⠐⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠻⠇⡀⠂⢠⠊⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⢨
⠀⠀⠀⠸⡄⠑⡀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠖⠚⠙⢣⠄⢤⡈⠠⠖⠸⢀⠎⠀⡐⠁⠀⠀⢸
⠀⠀⠀⢸⡳⢄⡘⢄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡁⠀⠄⠇⣠⡇⠀⠘⠓⢆⡠⠧⢬⡔⠒⢣⠀⠀⢀⣎⡀
⠀⠀⠀⠈⣇⠀⠈⠙⠓⠤⠄⣀⠀⠉⠢⢀⠀⠀⠌⠀⣹⠀⣀⠃⠙⠊⢣⠀⠮⠀⠀⠀⡇⢀⣠⠤⠔⠊⡙
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣒⠛⠊⠀⡉⠉⢱⠊⢢⠜⠒⠒⠓⠒⠊⠉⠁⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠱⠚⠣⡤⠺⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠔⠑⡤⠂⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⣀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠀⠀⠐⠒⠒⠂⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⠃
⠀⠀⠀⠀⠀⢠⡶⢦⡀⠀⠀⠀⢰⡏⢠⠘⢧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⣾⠀⢺⠀⢸⡇⠀⠀⠀⠀⠀⢰⠋⠀⠈⢉⣷⣶⣴⡟⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⣷⠈⣧⡀⠀⠀⣿⠀⢸⡄⠀⣇⠀⠀⠀⠀⠀⢸⡀⢀⣴⠟⠉⢩⣿⡿⣯⣀⠈⡷⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⡇⢰⡌⠻⣆⠀⢸⡄⠈⣇⠀⢻⡀⠀⠀⠀⣴⢿⡷⠛⠁⠀⠀⠀⠉⠀⠈⠛⢷⣿⣄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣇⠀⢷⠀⠸⣆⠀⣷⠀⢹⡄⠈⢷⡴⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠓⠒⠶⠦⣽⣤⠴⠶⠒⠒⢦⡄
⠀⠀⠀⠀⠀⠀⢹⡄⠈⢧⠀⠙⣦⠾⣇⠀⢻⡄⠈⢧⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⢷⡀⠈⢷⡘⣆⠀⠻⣄⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣀⣀⣰⠆⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠙⣦⡀⠙⢿⣧⡀⠘⢧⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠙⠛⢦⣙⡆⠀⠀⠀⠀⣸⠃⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠳⣄⠈⠛⢦⡀⠉⠳⢦⣀⠙⢦⡹⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⣤⠀⠹⡇⠀⠀⠀⣰⠋⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⡳⣄⡀⠉⠳⢦⣀⠉⠛⠶⢽⣶⣝⡳⠦⣤⣤⣠⠟⠀⠀⠀⠀⠀⠀⠀⠙⣫⣤⡀⣿⣀⣤⠞⢁⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⣶⣄⡀⠈⠙⠳⠦⣤⣈⣉⠛⠲⠦⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⢇⣿⣭⢷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⠉⠛⠓⠲⠶⠶⠬⢭⣽⣿⣷⣾⣧⣤⣤⣤⣤⡤⠶⠶⠶⠒⠒⠛⠋⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣉⡉⠉⠉⠉⠉⠉⢉⣁⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣗⣨⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⢎⡩⠽⣗⣻⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⡎⢠⠺⢀⢉⢉⡧⠀⠀⠐⠐⠂⠤⣠⢸⣳⣷⣚⣯⣹⣿⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⡀⠀⠀⠂⡌⠀⡇⠈⠄⠘⢿⣋⠀⠀⡀⢂⢠⣴⡠⣞⣿⣿⡟⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⣟⣋⠹⠙⣆⣇⢱⡀⠘⣢⠀⣠⠴⣿⣲⠒⠓⠉⠉⣷⠯⠳⠿⢏⠙⣃⠠⣮⡦⢠
⠀⠀⠀⠀⠀⠀⠔⠃⠀⢿⣾⠤⠉⢹⠾⠟⢸⣯⣾⢁⣊⣼⡿⢀⣀⣠⣼⠍⠐⠈⠛⠏⡋⠉⠁⠛⢆⡹⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⢈⣶⡄⠠⠡⠤⠯⣈⡳⢀⢠⡤⠞⠋⠚⠁⣤⡾⠛⠉⠉⡁⠀⣀⣉⣟⣿⣦⣀⣠⣤⡇⠹⡻⡿⠛⠢
⠀⠀⠀⠀⠀⠀⠐⠂⡋⢤⠴⢧⠶⣿⣤⠜⢏⠀⠀⠀⠀⠀⢿⣆⠀⠀⡀⣠⠀⣽⡍⠁⡈⢿⣟⠇⢸⣿⣧⣣⡆
⠀⠀⠀⠀⠀⠀⠀⣋⡡⠴⣴⠿⣤⣿⣬⣶⣻⣧⣤⣤⣤⣠⣬⣿⣤⣾⡿⠇⢈⡿⢻⣦⣤⣴⣿⡂⢹⣉⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠘⢃⣴⣿⣤⣿⣿⣟⢛⠛⠉⡒⠒⠀⠘⢛⠂⠀⠑⢛⠃⣞⣹⢿⣿⡷⣶⢾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡺⣷⡿⢿⣷⣶⠒⠒⠒⠂⠀⠀⠀⠀⠀⠐⠀⠀⠸⠟⣿⣿⠷⣷⣿⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣷⢿⡧⠀⠹⣿⣏⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡟⢀⣘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠋⠁⠀⠀⠀⠙⠻⣯⡋⡉⠀⠀⠀⠀⠀⠀⠀⣀⣁⣽⡿⠋⠉⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠷⢶⣶⡤⣶⣾⠿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠂⠀⠀⠀⠂⠙⠳⢦⣤⣄⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠁⠀⠀⠀⠀⢠⠀⠤⡀⠀⠀⠀⠀⠈⢻⡉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠤⠤⢮⣀⠁⢠⡟⠉⠙⠙⢶⠒⠉⠙⠒⢿⢤⣀⣀⣠⣄⡀⡱⠄⣠⠈⢆
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠁⠀⠀⠀⠘⣦⠜⠋⠉⠉⠉⠙⠢⣄⠖⠉⠉⠙⣏⠀⠀⠉⣩⠷⠒⠾⠗⠺⢦⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢀⣀⠈⣆⠀⠀⠀⠘⢄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⣴⢷⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡋⣉⠀⢸⠘⠿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⡄
⠀⠀⠀⠀⠀⣿⠶⢷⣄⣀⣀⡀⠀⠀⢳⡀⠀⠀⠀⡜⠀⠀⠀⠡⡾⠂⠀⠢⠀⠀⢈⣇⠀⠀⠀⠀⣀⣀⣀⣤⠷⢾⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠺⡀⠀⠀⠰⠀⡇⠀⠀⠀⡗⠒⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⠜⠱⣀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠀⠀⠀⠈⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠄⠠⠀⠄⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⣀⡠⠼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⣀⡀
⠀⠀⠀⠀⡠⠊⢁⡤⠔⠒⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠒⠤⣄⠉⠢⡀
⠀⠀⢀⡼⠁⢠⠋⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠈⢣⠀⠹⣄
⢀⠞⠁⠀⠀⢨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⣄⣀⣀⣀⣀⣤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⠀⠙⢆
⣇⢀⠞⡟⢦⣈⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣀⠞⡟⢆⢈
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣄⣀⢸⠀⡇⡇⢸⢀⣀⡤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠉⠀⣇⡇⠈⠁⠀⠀⠀⠀⠀⠈⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠁⠉⠉⢓⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⡀⠀⢉⣉⣈⢳⣴⣶⡲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡄⠀⣰⠀⠀⠀⣷⠉⠀⣿⠉⣙⣿⣿⡿⠿⢦⣀⣀⣀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⡦⣿⣿⠟⠹⣶⣦⡞⠉⢙⠶⢿⡏⠉⠉⢆⠙⡄⠀⠀⠀⠀⠀⠀⠈⣷⠾⠛
⠀⠀⠀⠀⠀⣾⡃⠀⣠⣬⣽⡏⡀⢼⣿⡉⠉⠉⠙⠷⣴⣇⡀⠀⢋⠉⣦⣿⡶⣤⠴⠲⢄⠀⠀⠀⢀⣾
⠀⠀⠀⠀⣸⣿⣷⣿⣿⡿⠋⠁⠚⠉⠉⠀⠀⠀⠀⠀⠘⢿⣷⠶⠣⣄⡟⢀⣧⣤⣀⣀⡾⠛⠛⢾⡉⢠⣵⡀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡴⢾⣷⣾⣍⣿⣿⡏⠀⠀⠀⢠⢿⡟⡇⡇
⠀⠀⠀⠀⠠⡸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⠾⣿⠟⣿⣿⣿⣿⣿⣶⣤⣀⣸⡿⣱⠃
⠀⠀⠀⠀⠀⠙⣿⣝⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⣠⣿⠿⣟⣭⡞⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⣶⣦⣤⣆⣠⣤⣤⣤⣾⡿⣿⣁⣿⣿⡿⠿⣽⣿⣟⣛⣫⣭⣷⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣯⣭⣿⣛⣛⣛⣛⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⡿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⠁⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢳⣀⣤⣤⣀⢀⣤⠀⠀⠀⠀⡏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡁⠀⠀⡴⠚⠲⡞⠳⣄⡼⠁⠀⠀⠈⠉⠋⠛⠲⡄⢠⠇⠸⣄
⠀⠀⠀⠀⠀⢀⡴⠊⠍⠀⠀⠀⠉⠑⢦⡰⠓⢴⠊⠙⣎⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⠀⠀⢸
⠀⠀⠀⠀⠀⡞⠀⠈⠈⠀⠀⠀⠀⠀⣠⠛⢲⠚⢲⡎⠉⢳⠋⢳⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢠⠛⢦⠞⠲⣴⠓⡖⢫⠷⠿⠒⠒⠒⠚⠉⠀⠀⠀⠀⣠⠞
⠀⠀⠀⢰⡚⠛⠒⠒⠒⠒⠒⠒⠒⠛⠒⠛⠓⠒⠛⠒⠛⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠚⣲
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡀⢀⡶⡇⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⣴⣦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣜⣁⠀⠀⠀⠀⠀⠀⢻⣾⠜⠁⠀⠀⠀⠀⢀⣸⡹
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⡀⢀⣾⣿⣿⣿⣿⣿⡇⠀⢀⣠⣤⣤⣜⣗⣶⣤⣤⣤⣄⠀⠀⠹⠀⣀⣀⣀⡀
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣏⢹⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⣾⣿⣿⡟⢹⣿⣿⡿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣶⣾⣿⣾⣷⣿⣿⣶⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⣀⣤⣀
⠀⠀⢿⠀⠈⠳⢄
⠀⠀⠈⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⣠⠶⣤⣤⣴⡇⠄⣟⣉⡿⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣼⡉⣳⡷⠤⡇⢂⣀⣿⡟⢠⠀⣱⠖⡚⠻⢟⠳⡤⠶⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⡩⠽⠲⢄⠈⠻⣁⠽⢦⡈⢣⡀⡨⠛⠉⢻⠟⡉⠈⡱⠞⠁⢣⡀⣀⣸⠢⡈⠉⢦
⠀⠀⠀⠀⠀⠰⡇⠀⠧⣠⣊⠉⠻⢾⢁⠤⡴⠋⠉⠙⣇⣀⡤⠷⠠⡴⠚⡓⢌⠀⡰⠋⢀⣈⠦⠃⣠⠟
⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠈⠉⠉⠛⠒⠒⠳⠤⠤⠤⠼⠧⠤⠶⠤⠞⠒⠒⠛⠚⠋⠉⠉⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠚⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⡀⢣⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⠂⢠⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠠⣀⠎⣈⠄⠂⢈⠜⡁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠘⡀⠀⣀⠀⢀⡠⢒⡁⠀⢀⣀⣀⣈⢉⠒⠤⡀⠀⡉⣸⡁⠈⡻⠀⢛⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣱⡰⣷⢹⡿⠥⡿⠋⠀⠡⠐⠀⠀⠀⣀⠨⢍⡙⠐⢌⠲⡦⠃⠀⠘⡤⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣵⢿⢿⡌⢻⣼⣷⣿⣿⣵⣞⣄⣠⣀⣄⣀⣘⣉⣀⣨⣄⣀⣐⣄⣙⠀⢀⡔⣡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠄⠀⠠⠠⠤⠤⠤⠤⠬⢽
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⠠⠤⠤⣀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠐⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠠⣒⠀⣀⢀⡀⠀⠀⠀⡔⠈⠀⣀⣀⣀⡀⠈⠢⠀⠀⢀⣀⣀⠀⠀⡠⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⠤⠤⠌⠂⠀⡌⠀⢠⠞⣡⠔⠢⡈⢣⠀⡆⠀⠑⠀⠠⠄⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠂⠀⠀⣂⠄⠀⡇⠀⢀⠀⣇⠸⠤⢃⠜⢠⠃⠀⠸⢉⡁⠈⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠘⠃⢠⠄⠀⠘⠄⠘⢄⡀⠉⢋⣁⠔⠁⠀⠠⡂⠀⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠉⠐⠂⠀⠈⠒⠤⡌⠉⠁⠀⠀⠀⠐⠃⠉⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡛⠀⠚⠂⠀⠺⠂⠐⠗⠐⠏⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡤⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⠙⣦⠀⠀⠀⢠⡾⠁⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⡇⠀⣠⠏⠀⠀⡀⠀⢙⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⠀⣠⠏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⢿⡇⢷⡏⠼⠤⠦⠤⢤⣄⣀⢄⡀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⠷⡘⢧⣺⡔⢀⠀⠀⠠⠤⠀⠈⢁⡴⠻⢷⡤⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⢈⢷⣿⣧⠠⠀⠀⠁⡀⠀⢠⡞⠡⠀⠀⠈⠢⠢
⠀⠀⠀⠀⠀⠀⢢⡀⢄⠀⠀⠁⠐⠀⠀⠉⠀⠀⠙⠛⠓⠈⠀⠐⠠⠈⠚⡀⠀⠀⡀⢁⢠⠞
⠀⠀⠀⠀⠀⠀⠈⢯⠓⠲⠤⣤⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣈⣁⡠⠴⠚⡟
⠀⠀⠀⠀⠀⠀⣀⡈⢧⠀⠀⠀⠀⠉⠉⠉⠙⠓⠓⠒⠒⠒⠒⠚⠉⠉⠉⠉⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⢮⡉⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⣙⠛⠓⠦⠤⠤⠤⣤⣤⠤⠤⠤⠶⠶⢛⣻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠤⠔⠒⠒⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡀⠀⠀⠀⠀⢲⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣾⣿⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣿⣿⠀⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⢸⣿⣇⠀⣸⣿⡏⠀⠀⣀⣀⣠⣤⣤⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⣿⣦⣄⠀⠀⢻⣿⣦⣿⣿⣠⣶⣿⡿⠿⠟⠛⠛⠛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣥⣄⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⢛⣿⣿⣿⣿⣿⣿⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⣤⣤⣤⣶⣾⣿⠿⢻⣿⣿⠻⣿⣧⠀⠀⠉⠻⣿⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠛⠛⠛⠉⠉⠀⠀⣼⣿⠇⠀⢹⣿⡇⠀⠀⠀⢈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠈⣿⣿⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⣿⠟⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠧⠀⠀⠀⠀⠘⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠿⠿⠛⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⣉⣠⣤⣴⣶⠶⠶⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⠿⢋⣠⣴⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⠾⠿⠿⠶⣶⣦⣤⣤⣤⡾⠟⣁⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣧⣂⠀⠂⠀⠀⠀⣀⣨⡿⠉⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣈⠉⠙⠛⠛⠛⢉⣉⣡⣴⡾⠟⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⡿
⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⣿⡏⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⢹⣧⠛⠋⠀⠛⠃⠈⠛⠁⠘⠛⠁⠘⠛⠛⠘⠛⠃⠘⠛⠃⠘⠛⠀⠛⠛⠃⠘⠛⠃⠘⠛⠃⠐⠓⠒⠒⣸⡟
⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣴⡞⠉⠹⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⢑⠙⠒⢤⡀⠀⢰⡏⡞⠀⠀⠀⢀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠃⠀⠀⠘⠀⠀⠈⢳⡆⣿⣼⠇⠀⠀⠀⠀⠂⠀⠱⡄⠤⣤⡤⠤⠄⣀⣀⡀
⠀⠀⢀⣀⠤⠐⠒⠂⠉⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠘⣾⡿⣼⠀⠀⠀⠇⠀⢈⠀⠀⢣⠴⠃⠙⣖⢄⠀⠀⠈⠉⠐⠒⠢⠤⣀⡀
⠔⠊⠁⠀⠀⢀⣀⣀⠀⣤⣤⢼⡀⣤⠮⡤⠤⠤⠤⠄⠤⢼⣳⣿⠀⠀⠊⠀⠀⠘⠀⠐⢹⠀⢀⡠⠜⠋⠉⠉⠈⠉⠉⠒⢄⡀⠀⠈⠙⠢⢄
⠴⠖⠒⠈⠉⣀⠠⠤⣴⠁⠈⢉⣿⠃⠀⠈⢦⠀⠀⠈⡆⠀⠙⣿⠀⠀⠀⢀⠀⡐⠀⢀⣸⢎⣁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⠉⠒⠒⠤⠄
⢰⡤⣀⡔⠉⠀⠀⠀⠈⢻⣦⣼⣿⠀⠀⠀⠀⢣⡀⣤⠃⠀⢀⢏⠀⠀⠀⠀⡐⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⢠⠀⡠⠞⢠⣤⣀⣀
⠈⠈⢱⠁⠀⠀⠀⠀⠀⠀⠱⡽⣷⠀⠄⠂⢁⡠⠟⠈⠢⢤⣪⠤⠥⠤⣤⣊⠀⣼⣏⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⡠⠚⠙⣶⣪⣍⡥⢶⠏⠉
⠀⠀⣶⠄⡀⠀⠀⠀⠀⠀⠀⠹⣼⡄⢀⡔⠁⠀⠠⡀⠠⠀⠈⠢⡀⠀⠐⠉⢉⡿⠁⠁⠀⠀⣀⣤⣾⠶⠶⢶⣶⣥⡔⠚⠉⠁⠀⠀⣾⡄
⠀⠀⢸⡆⠈⠀⠀⠁⠀⠀⠀⠀⠹⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⠸⡇⠀⠀⢠⢞⡕⠋⢀⠀⠀⠀⠀⠉⠳⠤⣤⠘⠀⢀⣿⢸
⢷⡀⠘⡇⠀⠀⠀⠈⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢿⠒⠒⢦⡀⢀⣴⣯⡏⠀⠀⠀⠑⠀⠀⠀⠀⠀⢠⠇⠀⠀⡼⣸⣼⠤
⠒⠬⣁⡛⠠⠄⣀⡀⠀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢰⠀⠀⠀⠘⢾⣱⠇⠈⠀⠀⠀⠀⠀⠀⠀⠄⣀⣎⣀⠤⠜⣛⠥⠔⠊
⠀⠀⠀⠈⠉⠐⠂⠬⠍⣁⣒⡒⠤⠤⠇⣄⣀⣒⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡃⡀⢀⣀⡈⣀⠠⠤⣄⣒⡀⠭⠕⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠂⠀⠸⠏⠉⠉⠥⠠⠌⠁⠉⠉⠿⠛⠁⠙⠒⠒⠂⠈⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠉⠑⠒⠀⠤⠤⠄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠔⠂⠉⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠒⠒⠂⠒⠲⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⢀⠎
⠙⣤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊
⠀⠈⠢⡀⠉⠁⠒⠂⠄⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠐⠂⢉⠜⠁
⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠂⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠂⠈⠉⠉⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠤⣤⠤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣠⡤⠄⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⢤⣤⢤⣤⣤⣤⣤⣠⢤⡤⠶⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠻⣦⡀⠀⠀⣠⡾⠃⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣷⠀⣿⠛⠛⠀⠈⠛⢻⡇⢸⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣿⠀⢹⡄⠀⠀⠀⠀⣼⠃⢸⡇⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠻⣧⣤⣤⣤⣄⣀⢻⡄⠘⣧⠀⠀⠀⣰⡟⠀⣼⣧⣤⣤⣤⣿⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣤⣤⣄⣀⡈⠉⠛⣧⠀⠹⣆⢀⣴⠏⠀⣼⠏⢁⣀⣤⣤⣤⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠈⠉⠙⠳⣦⣹⣧⠀⠹⣿⠁⣠⣾⣷⠞⠋⠉⠁⠀⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢙⣿⣧⡀⠘⢿⣿⡋⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⣀⣠⣤⣴⠶⠟⢻⡟⠉⢻⣦⠀⠙⢿⡻⠶⣤⣤⣄⣀⣿⠷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⣉⣉⣁⣀⣀⣤⣤⡿⠀⢰⡟⠈⢷⣄⠈⢻⣄⣀⣀⣈⣉⡉⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⡟⠉⠉⠉⠉⠀⣼⠃⢀⡿⠀⠀⠀⢻⣆⠀⢿⡉⠉⠉⠙⣿⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⢿⡄⢸⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⣿⣀⣀⠀⢀⣀⣸⡇⢸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⠀⣨⡿⠋⠀⠈⠻⣯⡁⠀⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠉⠀⠀⠀⠀⠀⠈⠻⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠒⠒⠒⠒⠒⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠋⣁⣠⣤⡶⠶⠶⠶⠒⠲⠶⠶⠶⢤⣄⣈⠙⠲⢤⣀⠀⠀⢀⠀⠀⠀⣀⣴⣾⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡈⡻⠆⠁⢀⣠⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡾⠛⠁⠀⠀⢀⡴⠒⡛⢛⡭⠟⠽⠿⠉⣻⣶⣤⣤⣀⠀⢀⠀⠉⢀⣠⡾⢿⡏⠁
⠀⠀⠀⠀⠀⢀⡴⠃⣠⡾⠋⠀⢀⣠⣶⣿⡿⡘⢱⣧⣍⡓⣉⣠⡯⠙⣟⣁⠠⡟⠷⠄⢀⣠⠶⠋⠁⠑⠄⠙⢦⡀
⠀⠀⠀⠀⢠⡞⠀⣴⠋⠀⢀⣴⡿⢫⠍⡽⡋⠀⣠⠀⠟⢳⠀⣩⠗⣚⠈⢩⣅⠉⣠⠴⠛⠋⢀⡀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢠⡟⢀⡾⠁⠀⢠⡾⢩⣤⡔⠛⢳⢿⣿⡟⢀⠰⡶⢊⢡⡎⠀⢘⡈⠩⠇⣿⣴⣄⣸⡞⡛⢆⡀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⡾⠀⣼⠁⠀⢠⡟⡤⣷⣶⡀⣸⠟⣁⣠⠏⣸⡔⠡⢤⡞⠁⢠⣤⣽⠟⣰⡧⠞⠉⣿⣿⡁⠀⣷⠀⠀⠀⠀⠈⣷⡀
⠀⠀⣸⠃⢰⠇⠀⠀⣾⠠⢁⠬⠁⣏⡉⠉⠉⠁⠀⢼⡁⠲⣶⠾⠿⠛⣋⣤⢞⡅⢀⡶⢌⠋⣈⢧⣶⣿⡀⠀⠀⠀⠀⢸⣧
⠀⠀⣿⠀⡾⠀⠀⢰⠓⢰⡞⢳⡄⠙⠃⣄⣀⣈⠛⡞⠳⠦⠬⠴⣶⡿⠋⢴⣿⣀⡘⠓⠀⠛⢯⢸⡏⢙⠌⠀⠀⠀⢠⠀⣿⡀
⠀⠀⡇⠀⡇⠀⠀⠀⠀⠘⣿⣷⣹⣷⣆⠈⠛⠻⣧⡈⢲⠟⠉⣉⣩⡇⡷⡘⢦⣠⣴⣂⡤⠂⣤⠷⢌⢻⣠⡄⠀⠀⠈⠀⣿⡇
⠀⠀⣇⠀⡇⠀⠀⣿⠴⣾⣿⣿⠁⠉⠀⢒⣀⡀⠈⣧⠌⢠⡊⢽⡟⢰⡧⡻⢈⠇⠠⣍⣤⠆⣤⣴⣯⡨⢾⡁⠀⠀⢠⠀⣿⡇
⠀⠀⣿⠀⠃⠀⠀⠈⠠⣿⠁⠙⡀⢲⠀⢀⡿⠿⣷⡇⣐⢚⣏⣆⠀⠀⡱⡡⠊⠁⢀⣶⡤⠞⢷⣇⣿⢳⣬⠁⠀⠀⢸⠀⣿⡇
⠀⠀⢻⡄⠀⠀⠀⠀⣄⣽⡷⢾⣤⣾⣿⣖⠃⣊⣛⣁⠁⡾⠁⢿⡀⢤⡜⢓⣶⣾⡿⠛⢛⣦⠀⡷⠃⣸⠏⠀⠀⠀⡆⢸⣿⠃
⠀⠀⠈⣷⠀⠀⠀⠀⠘⣷⠆⠈⣋⠉⢋⠀⠀⣼⠉⠻⣄⣀⣲⠛⠺⣦⠀⣾⠋⣩⢤⡈⠛⣯⠺⣦⣾⠅⠀⠀⠀⡰⢁⣿⡟
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⢧⡄⢉⡀⠉⠐⢀⢿⣷⢾⡿⠋⣸⣿⣷⠘⣷⣄⠃⢃⣾⠏⠀⣢⠆⣿⠏⠀⠀⠀⣰⢃⣾⣿⠁
⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠳⣾⣛⣛⣿⡷⢧⢮⣤⣤⠾⠛⢠⡟⠐⡃⠿⡿⠻⡇⠀⣨⣥⠾⠁⠀⠀⠀⡴⢁⣾⣿⠃
⠀⠀⠀⠀⠀⠘⢷⣄⠀⢄⠀⠀⠈⠻⣴⣟⠛⠠⢴⣎⣠⣤⡬⠡⣘⣎⣉⡷⠔⢂⣰⣆⡵⠃⠀⠀⠀⣠⠞⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠑⢄⡀⠀⠀⠉⠉⠓⠾⢿⣯⣽⣷⣭⣉⣀⣍⠀⠀⠈⠊⠁⠀⠀⠀⡠⠞⣡⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⡠⠔⣋⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣌⣉⠒⠢⠤⠤⢀⣀⣀⣀⣀⠠⠤⠔⢒⣋⣥⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⡖⢲⡶⢶⣶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣄⣀⡀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⣋⣉⣡⡤⠤⠶⠖⠒⠒⠒⠛⠛⠛⠒⠒⠒⠶⠦⢤⣈⡉⠛⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣉⡤⠶⠚⠋⢉⣀⣠⡤⠤⠶⠶⠖⠒⠒⠒⠚⠛⠛⠛⠉⠉⠙⠛⠛⠿⣷⡄⠀⠹⡄
⠀⠀⠀⠀⣠⠞⠉⣠⠶⠋⠁⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡿
⠀⠀⠀⡼⠁⢀⡞⠁⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⢀⡼⠃
⠀⠀⢸⡇⠀⠘⣇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⣀⡴⠋
⠀⠀⠀⠳⣄⠀⠈⠛⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⠒⠋⠉⠀⣀⣠⡴⠚⠁
⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⠀⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣤⠤⠶⠚⠋⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣄⣀⣀⣀⣤⣤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠿⠿⠟⠛⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠻⠿⠿⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡠⢖⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⡲⢄
⠀⠀⠀⠀⡎⡔⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡴⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠈⢢⢳
⠀⠀⠀⠀⢇⠘⠦⣀⣤⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢦⣄⠴⠃⡸
⠀⠀⠀⠀⠈⠳⢄⣀⠉⠒⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠉⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠈⢏⠉⠓⠒⠤⠤⠤⣄⣉⣉⣉⠙⠓⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠚⢉⣉⣉⣉⣠⠤⠤⠤⠒⠚⠉⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠤⠒⠒⠋⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠶⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠶⠿⢛⣷⣀⠀⠀⢀⣀⣠⣤⣶⠶⠟⣛⣻⣭⣧⣤⡶⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⡯⡆⠛⢀⡚⠩⡬⢻⣷⣿⣛⣭⣭⡶⠶⠿⠛⣛⣉⣩⣥⣤⣶⠶⠾⠟⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣩⡥⠛⠯⢀⡙⠣⠴⠀⣿⣟⣭⣥⡶⠶⠾⣟⣛⣻⣭⣽⣷⠷⠶⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⡚⡍⣩⡤⠷⣶⣞⣫⣭⣭⣷⠶⠾⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠿⠾⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣤⡶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⣴⡿⠙⢛⡛⠉⠁⣀⠙⣛⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠟⠛⣋⡡⠆⡀⠉⠩⣤⡄⠙⠁⠉⣡⡝⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠶⠿⠉⣀⣤⠆⣉⠀⡈⠋⠀⠶⠶⠤⠋⢋⠀⠐⠷⣤⡌⠛⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢋⣤⡿⠉⠁⠛⢃⣈⣈⠺⢿⡟⠋⠘⣉⠉⢧⣤⡃⠀⠙⣂⡀⠻⢷⣶⡆
⠀⠀⠀⠀⠀⠀⢰⣿⠛⠡⠟⠉⢀⣐⣛⣁⣀⣈⣉⣀⣐⣒⣤⣀⣛⣋⣀⣀⣈⣁⣀⣀⣉⣁⡀⠳⠈⣻⣆
⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣧⠉⠋⠀⠛⠃⠀⠚⠂⠒⠒⠀⠒⠒⠀⠲⠶⠀⠲⠖⠀⠶⠶⠀⠰⠶⠀⠐⠒⠂⠀⠛⠃⠘⢻⣿
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠿⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⡶⠶⠿⠛⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠷⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⢿⣿⣦⡀⢀⣴⣿⡿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⢸⣿⣿⠀⠙⠿⠃⠘⠿⠋⠀⣿⣿⡇⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠁⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣄⠻⣿⣷⡄⠀⠀⠀⠀⢠⣾⣿⠟⣠⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⠛⠛⠛⠛⠛⠻⢿⣦⡘⢿⣿⣦⠀⠀⣴⣿⡿⢃⣴⡿⠟⠛⠛⠛⠛⠛⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠉⠳⠌⢻⣿⣷⡈⢿⡟⠡⠞⠉⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⣀⡴⢂⣼⣷⡈⢿⣿⣧⡐⢦⣀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣤⣤⣤⣤⣤⣴⣾⠟⣡⣾⣿⠏⠀⠀⠻⣿⣷⣌⠻⣷⣦⣤⣤⣤⣤⣤⣽⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠋⣴⣿⡿⠃⠀⠀⠀⠀⠘⢿⣿⣦⠙⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⢸⣿⣿⠀⣠⣶⡄⢠⣶⣄⠀⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⣿⣾⣿⠟⠁⠈⠻⣿⣷⣿⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠷⡾⠃⠀⠀⣤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣹⡃⠀⠀⠀⠹⡄⠀⠀⡜⠲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠓⣄⢀⡇⠀⣰⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣀⡤⠶⠦⡌⠈⠐⣋⠁⠀⣠⠴⣏⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠏⠁⠀⢀⠴⠒⡤⠰⡌⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠀⠀⡇⠀⠙⠲⠶⢤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣻⡅⠀⠀⠙⣆⠀⠀⠀⠛⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢻⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⡀⣀⠀⣀⢀⡀⡀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠃⠘⠋⠘⠒⠛⠀⠀⠃⠃⠘



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢡⠀⠠⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⢐⢀⢀⠂⠀⣀⣁⣈⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡠⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠒⠒⠉⠉⡙⠈⢩⠀⠄⠉⠀⡤⠋⢁⠀⠈⠉⠑⠒⠒⠤⢄⣀⠀⠁⠀⠉⢀⡤⠊⠁
⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡤⢀⣸⠠⠀⡤⠃⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡀⠐⣔⠘⡄⠀⡇⠀⠐⠀⠀⠅⠀⠀⣀⠀⠉⠀⠀⠀⣀⠀⠈⠈⡄
⠀⠀⠀⠀⠸⣄⡀⠀⠀⠄⠀⠈⣡⠀⢀⠀⠀⠱⠬⠃⣙⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡠⠚⠁⠀⠐⣀⠼⠃
⠀⠀⠀⠀⠀⢇⠙⠷⣦⣄⣀⡀⠀⠀⠀⠀⡀⠒⠐⠀⢀⢀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣃⣀⣤⠴⠚⢁⡘
⠀⠀⠀⠀⠀⠘⣤⡞⡁⠉⡍⠙⡛⠓⠶⠶⡶⢶⣤⣤⣤⣤⢤⢤⢤⠤⠤⠶⡶⠖⢶⢛⠋⣉⠉⠒⠲⣤⢐⠃
⠀⠀⠀⠀⠀⠀⠈⢷⠲⠸⠀⢉⠁⡄⠬⢬⢰⢁⣁⢱⣀⡁⢊⢐⣤⠑⢀⢀⢇⣈⡱⢈⣊⡠⢧⢀⣀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡬⠁⡈⠙⠿⣧⡸⠘⣶⢅⡊⢤⡱⣾⢸⣰⡎⠀⠈⣺⠈⢁⡾⠋⠉⠃⢭⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⡬⠤⣸⡏⢁⢰⡎⠠⠀⢨⣉⣿⠃⠢⠄⡴⠓⢹⡟⣇⣱⠀⠀⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣁⠰⠚⠛⢮⣻⡟⢶⢑⠢⡈⢻⡧⢲⠀⣤⢂⣼⣿⠡⠼⣥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠀⠰⠻⠻⣯⠳⣧⡿⢟⢁⣴⠟⠯⡀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣬⣵⣿⢁⣿⠨⣾⣟⣛⣦⠼⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠭⠉⠉⠉⠉⠉⠉⠄⠀⠈

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

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⠈⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡽⠉
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢿⣿⣿⡄
⠀⠀⢀⣀⣀⣤⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣀⣀⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠁⠀⠈⢿⣿⣿⣦⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣴⣿⣿⡿⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⣴⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶
⠀⠛⠛⠛⠛⠋⠹⣿⣿⣧⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣾⣿⣿⠋⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆
⠀⣠⣤⣤⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣤⣤
⠀⢿⣿⡿⠿⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠛⠛⠿⠶⠶⠶⠿⠿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⢀⣀⢤⣄⢄⡠⣄⢤⡰⣄⢠⡀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⣉⡡⣄⣶⣽⣷⣯⣿⣾⣿⣿⣾⣷⣿⣮⣷⣼⣦⣳⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣩⣶⣿⣿⣾⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣿⣷⣾⣿⠿⠿⠛⢋⣭⣤⣶⣶⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣿⠟⠷⣄⠀⠀⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣷⣾⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⣷⣰⣏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠉⠛⠿⣧⣀⡀⠀⠀⢀⣿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠐⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢱⣦⣀⠀⠙⠛⢿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠚⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢯⡳⣄⠀⢾⢿⡟⠁
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣝⢿⣿⣦⠀⢀⠃
⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠄⠀⠀⢼⡫⣷⣿⣿⡆⢸
⠀⠀⠀⣾⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣝⢮⡻⣿⡇⢸
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢮⣻⣷⣿⣿⡇⣸
⠀⢀⡟⢠⡇⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⢠⣨⡳⣿⣿⣿⣿⡇⣿
⠀⢸⠇⣼⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡳⣽⢿⣾⣿⣿⣿⢣⡇
⠀⢸⠀⣿⣿⣿⣇⡇⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⢀⢤⣳⡳⣝⢾⠿⣽⣿⣿⡟⣼⠁
⠀⣼⠀⣿⣿⣿⣿⢿⢻⣰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⣯⢷⡳⣽⣮⣶⣵⣮⣿⡿⢱⠇
⢠⡟⠀⢿⣿⣿⣿⡾⣟⣏⣯⣷⢷⢲⣰⣴⡰⣆⣦⢶⢶⣳⡽⣞⣷⡻⣽⣮⣷⡿⣾⣿⣿⣿⣿⡿⣡⠏
⣾⢀⡀⣼⣿⣿⣿⣿⣻⣿⡾⣞⣿⣯⢷⣻⣳⡹⣞⣯⢯⢷⣻⣝⣯⣿⣝⣮⣿⣝⣾⣿⣿⣿⠟⣵⠏
⠻⣮⣛⠻⠿⢿⣿⣿⣿⣿⣿⡽⣿⣾⣯⢿⣷⣿⡽⣾⣯⣿⣻⣿⣾⣿⣟⣿⣿⣿⣿⣿⠟⣡⠞⠁
⠀⠈⠉⠛⠛⠶⣬⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣯⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣬⣭⣭⣭⣩⣭⣭⣭⣽⠶⠾⠛⠋⠁
⣿⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⠶⠿⠿⠟⠻⠛⠛⠛⠛⠛⠻⠿⠿⠿⠷⢶⣶⣶⣤⢤⣀⡀
⠀⠀⠀⠀⣠⠴⢚⡭⠖⠋⠉⢁⣀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⠉⠉⠓⠮⣝⠲⢤⡀
⠀⠀⠀⢰⡇⠀⣏⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣈⠇⠀⣷
⠀⠀⠀⢸⡏⠲⢬⣓⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣖⣩⠴⠊⣿
⠀⠀⠀⠈⡇⠀⠀⠀⠉⠙⠛⠛⠿⠿⠷⠶⣶⣶⣶⣶⣤⣤⣤⣴⣶⣶⢶⡶⠶⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⡤⠤⠴⠒⠋⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣦⡀⢀⣴⣿⣿⡿⢿⣿⣿⡿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠟⠁⢸⣿⣿⡇⠀⠙⢿⡿⠃⠘⢿⡿⠋⠀⢸⣿⣿⡇⠈⠻⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⡀
⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀
⣰⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡄⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⢠⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣆⠈⢿⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⡿⠁⣰⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠻⣿⣿⣷⡀⠀⣾⣿⣿⠟⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠈⠻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⠙⢿⣿⣿⣄⠘⠿⠋⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁
⠀⠀⠀⢀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⣠⣶⡄⠹⣿⣿⣷⣄⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⡀
⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠁⣴⣿⣿⡿⠀⠈⢿⣿⣿⣦⠈⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⠏⢀⣾⣿⣿⠟⠀⠀⠀⠀⠻⣿⣿⣷⡀⠻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠃⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠘⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠈⠻⣿⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢺⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦⡀⢸⣿⣿⡇⠀⣠⣾⣷⡄⢠⣾⣷⣄⠀⢸⣿⣿⡇⢀⣴⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣿⣷⣾⣿⣿⠟⠁⠈⠻⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⣿⡄⠀⠀⣿⣿⡀
⠀⠀⠀⢸⣿⣇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⣿⡀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⢸⣿⣇⠀⠀⢻⣿⡆⠀⠀⣠⣴⣾⣿⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣿⣿⡀⠀⠸⣿⣧⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠈⣿⣿⠀⣼⣿⠟⠁⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⣠⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣄
⠀⠀⢠⣾⣿⠟⠁⣿⣿⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⠈⠻⣿⣷⡄
⠀⠀⣿⣿⠁⠀⠀⠈⠁⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⣿
⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟
⠀⠀⠀⢿⣿⡿⣿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟
⠀⠀⠀⠸⣿⣷⠈⠻⣿⣷⣄⡀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⢀⣠⣾⣿⠟⢡⣿⡿⠁
⠀⠀⠀⠀⢻⣿⡆⠀⠈⠛⠿⣿⣿⣿⣿⠿⠿⠛⠿⢿⣿⣶⣤⣀⣀⣤⣶⣿⡿⠿⠛⠿⠿⣿⣿⣿⣿⠿⠛⠁⠀⣾⣿⠃
⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠋⠉⠙⠓⠲⣄
⠀⠀⠀⢀⣤⡶⠤⠤⣀⠀⢠⡴⠶⠒⠒⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⣠⡤⠚⠉⠀⠀⠀⠀⠀⠑⠮⠆⠀⠀⠀⢀⢈⣃⣀⣤⣤⡤⠤⠤⡤⣤⣤⣤⣄⣀⣀⡀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠚⠁
⠀⠉⠙⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢽⠋⠁⣀⢩⡤⠤⣤⣧⣤⡀⠀⠀⠀⠀⠉⠉⠙⠋⠄⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⡉⠁⠀⠂⠀⠠⠤⠤⠴⠤⡀⠸⣿⠛⠉⠀⠀⠀⠀⠀⣀⠈⠉⠿⢿⣷⡦⠤⣤⣤⣄⡀⠀⠀⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣸⣷⠶⠂⠀⠀⠈⠀⠀⠀⠈⠆⠠⠀⠀⠀⠀⠀⠛⠛⠻⠶⢬⣈⢢⡀
⠀⠀⠦⣤⣤⣴⣶⣥⣤⡤⠾⠿⠛⠚⠛⠛⠛⠛⠋⠉⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠣⣷
⠀⠀⠀⡄⣿⣿⠻⠭⠁⠀⠀⠁⠈⠁⠉⠉⠁⠈⠁⠈⠉⠙⠻⠿⢍⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠒⠀⠀⢰⣿
⠀⠀⠀⣷⡈⠳⣦⡀⠀⠀⡀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠦⣤⠄⢀⣠⠖⣫⡟
⠀⠀⠀⢹⡹⣦⣈⠉⠛⠶⢤⣬⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠨⠂⠉⠀⢀⣀⣀⣤⠶⠚⢉⣤⠞⢩⡇
⠀⠀⠀⠈⣇⠀⠈⠙⠲⠤⢄⣀⡉⠉⠙⠋⠙⠛⠒⠒⠒⠒⠲⠶⠖⠒⠲⠖⠚⠛⢛⣉⣁⣤⡤⠶⠞⠉⠀⠀⣸
⠀⠀⠀⠀⠘⢦⠄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠿⣿⣛⢛⠻⡻⣛⢛⣛⡿⠿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢟⣫⣭⣴⣼⣯⣩⣽⣜⠂⠓⠯⡜⡱⣋⢽⢒⡎⣭⣛⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⣫⠞⢋⢀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⣦⠙⢛⣉⣬⣥⣤⣤⣴⣮⡟⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠛⠅⣰⠋⢰⠋⢉⢀⠇⠀⠀⠐⠚⠀⢀⣤⡶⠟⣿⠉⡩⣤⣰⠶⢶⣶⢸⡇⣳⣝⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⡉⣼⠁⠀⠀⠀⠂⠋⡀⠐⠀⠀⢀⡴⠋⡕⢶⠀⣿⠀⡆⣝⠀⠂⣸⢻⢸⡇⣿⡶⣻⡽⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠐⠠⢀⡇⠀⠠⠀⠀⠐⠀⢼⣿⠄⣰⠟⡴⢖⡌⠨⡄⢸⡇⠣⠉⠠⠤⠁⠺⢸⡇⢿⣿⡽⢞⣎⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠈⠀⠄⢸⠀⠀⠀⢀⣀⣠⣤⣤⣄⣼⣏⡰⢜⣌⠖⠂⣃⣸⣷⡴⠶⠶⠞⠛⠛⠻⡟⠛⠷⣼⠋⠭⢆⢿⣿⡄
⠀⠀⠀⠀⠀⠀⣸⢻⡏⠐⠀⡀⠐⣘⣧⣤⠞⢉⡍⡤⢤⠀⣿⠉⡉⠛⢦⣩⡴⢻⢉⡄⢸⡆⠀⡚⢃⠋⢿⢸⡇⠀⢠⠀⠙⢦⡙⡜⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⣠⠔⠋⢉⠉⠻⡄⠋⢃⢓⢸⡆⢻⡄⠆⠀⠃⢻⡄⢠⢼⠠⠄⣷⠰⠦⣬⣉⡺⣸⠃⠀⠈⠀⠀⠀⠹⣦⢹⣿⡆
⠀⠀⠀⠀⠀⢸⣧⡟⣠⠈⢀⠐⠀⠀⠀⠀⠹⣆⠈⠀⢈⡴⠛⠻⣄⠑⢤⡌⡇⣀⣼⡦⠶⠿⠶⠶⢶⣍⣡⡏⠀⠐⠂⠀⣤⡀⣀⢸⡎⣿⠇
⠀⠀⠀⠀⠀⢸⣿⡇⠙⠄⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠋⡀⢒⠠⠊⠀⢠⣼⣿⡉⠔⠀⠀⠀⠀⡰⢀⡼⣿⠰⣿⠖⠐⠂⣈⣀⡍⠀⡇⣿⡄
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠞⠙⢦⡐⠃⠀⢀⡴⠟⡉⢹⡙⠲⠦⡤⠴⣶⠟⡋⢀⠈⢷⠀⠀⠂⠀⠈⠉⠀⡼⠃⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠐⢀⠑⢄⠀⢀⡤⠞⠁⡄⠲⣤⠙⠳⣤⠟⠀⠀⠀⢸⡇⡀⠤⢀⡀⣿⢸⡇⠤⣛⡈⣧⠀⢠⡄⠀⠀⠎⣕⢸⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⢀⠸⢂⡿⣏⡠⠚⢜⡦⡱⢈⡱⠇⡿⠀⠀⠀⠀⣼⡁⠀⠚⢠⢠⡟⠸⢧⣅⡃⣇⠸⡆⠀⠀⣠⠌⢄⡄⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠥⡸⡇⠀⠑⠦⣌⣙⠂⠃⠘⠃⢷⡀⠀⢀⡼⠁⣉⠛⠒⠒⣾⠗⠶⢤⣌⣉⡉⢀⣇⢀⡴⣡⠐⡾⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠠⠸⠆⠀⠤⡀⠉⠉⠉⠛⣛⡛⢷⡚⢋⡠⢖⡍⢻⠆⢀⡿⠀⠆⠤⣀⣉⠙⢻⡟⣩⠾⢏⣙⣽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡠⢠⡧⠀⠀⠁⠀⠀⠂⠘⠿⠃⠈⠳⣌⠁⣬⣂⣝⠃⣼⠃⡘⠄⠉⢑⣾⠀⣼⢡⡏⢡⢬⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⣠⡱⡄⠀⠀⠠⠄⣰⢀⠐⠂⠀⠈⠛⢦⣝⣋⣼⠇⢰⣜⠒⠤⢼⠇⣰⠇⣶⢘⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣘⢦⡀⠀⡼⡀⠠⠀⠀⠐⠒⠀⠀⠀⣹⢟⠳⢦⣬⣉⣒⠋⣰⡟⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣯⣖⡦⠤⠀⠤⠤⠤⠴⠒⢒⢚⠱⠜⢙⡓⠆⠭⣉⣭⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠙⠿⣿⣿⣿⣶⣶⣤⣿⣴⣤⣮⣧⣬⣼⣶⣶⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣴⠚⠛⢳⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢏⠀⠈⠖⠀⠀⠠⡭⠉⠈⠙⠻⡟⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠁⠀⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡛⠉⢀⠀⠀⠁⡀⠀⠆⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠴⠀⠀⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠁⣿
⠀⠀⠀⠀⠀⠀⢀⣸⡇⣠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⣿⣄⡀
⠀⠀⠀⠀⢀⡴⠋⣼⠁⠠⡄⠀⠀⠓⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠠⢠⣏⠈⣷⡄
⠀⠀⠀⠀⢸⣧⠀⢿⣝⠀⠀⠀⠘⠀⠀⠀⠘⠍⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⠟⡇
⠀⠀⠀⠀⢸⡈⠳⢦⣈⠓⢦⣄⡁⠀⠊⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠲⠀⠀⣀⣤⠞⢉⡴⠋⢰⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠈⠓⠦⣌⣙⠶⠶⠶⢦⣤⣤⣌⣂⣀⣀⣀⣀⣀⣀⣀⡤⠴⠶⠞⣁⡤⠖⠋⠀⠀⡾
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⢤⣤⣄⣉⣉⣉⣉⣉⣡⡤⠤⠖⠚⠋⠁⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣈⠉⠓⠲⠶⠤⠤⣤⣤⣤⣄⣤⣤⣤⡤⠤⠖⠛⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣤⣤⣀⣤⣤⣤⣤⣤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡝⣦⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣷⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⡼⣽⣿⣿⣿⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠈⠑⢢⣄⣤⣴⡞⡕⣾⣿⣿⠇⠀⣼⡃⠀⠀⢀⣀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠱⣴⣿⠋⢴⣶⣿⠟⠁⢸⣿⣿⡄⠀⢹⣧⣶⣿⣿⡏⣿⣷⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣷⡄
⠀⠀⠒⡒⣀⠀⠀⢸⢀⠀⠀⠘⣧⣼⢋⠥⣴⣦⡄⠀⢿⣿⣧⠀⣸⡿⠛⠻⣿⢇⣸⠟⡻⢿⣯⣤⠤⠤⠤⠤⠤⠶⠟⠛⠁
⠀⠰⠟⠉⠟⠄⠀⢸⠀⣠⣶⣦⠈⠛⠉⠐⡿⡿⣿⠀⠘⣿⣿⣶⠋⣴⡿⠃⠜⠏⠑⠈⠿⡦⢹⣿⣷⡄
⠀⠠⢴⠆⢲⠠⠀⠸⡀⠽⠋⣱⢠⠞⠁⠀⠀⠀⠐⡄⠀⣼⣿⣿⣷⣤⠊⠁⠀⠀⠀⠀⠁⠶⣾⣿⣿⠇
⠀⠀⠞⠠⠏⠀⠀⢠⡙⠀⣶⠁⡚⠀⠀⠈⢾⠀⠀⣷⣎⢻⣿⡿⠟⡇⡄⢀⣰⠼⠄⠴⣄⣆⠹⡀⢸⢠⣄⣀⡀
⠀⠀⡯⡀⡀⠀⠀⠀⣏⡉⠉⠰⠞⠀⠀⠸⡾⠀⡀⠀⢈⡇⠀⠀⠀⠉⢋⠈⠉⠀⠀⠀⠉⠨⠛⢀⡎⠀⠲⡜⠁
⠀⠞⠁⠓⠃⠀⠀⠀⠀⢧⣀⡀⠂⠠⣤⡤⠔⠊⠀⣀⠾⢦⣤⠀⠀⠀⠘⠤⣀⣀⡤⠶⠂⢀⡤⠜⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢲⣬⠗⡶⠋⠽⠷⢾⠏⢹⣦⠱⣖⠲⢶⡘⡏⣤⠞⠉⠉⠁⠀⠀⠒⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠥⢁⠀⢧⠀⢀⠀⢠⡆⣿⡄⠰⠟⠢⠉⠀⠀⠉⢧⡀⠀⠀⠀⠀⢾⠧⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⡍⠂⢀⣙⣾⠿⠾⣵⠏⠀⢿⠁⡆⠖⡷⣤⠒⡢⣓⢐⣿⡄⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣤⡴⠚⠙⠉⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠛⠓⠼⣤⣾⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⢀
⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⠀⠈⠀⠀⠀⠰⠆⠀⢰⡇⠀⠈⣂⠀⠀⠀⠒⠠⣾⢿⡦
⠀⠀⣴⡿⠋⠀⠠⠀⠀⠀⠀⠀⠠⠖⠀⠛⢷⣄⠀⠀⠀⠀⣠⡟⠉⠉⢳⠀⠀⠀⠀⠤⠀⠀⣸⣿⠀⠀⠋⠀⠀⠀⠀⣸⡟⠚⣿⠐
⠀⢸⡿⣀⢠⡆⣠⠀⠠⠄⠀⠀⠠⡄⢰⡀⡌⣿⡄⠀⠀⠀⢹⡿⢷⡾⣿⠈⠀⠀⠀⠀⣀⣠⣿⣿⣇⣀⠀⠀⠀⠀⢠⣿⣤⣤⣿⣧
⠀⢸⣇⣸⣯⣋⢀⡠⠀⠀⠀⠀⢄⣈⡭⣽⣇⣿⡇⠀⠀⠐⠻⣿⣷⣾⣿⠙⠀⠀⠀⠀⡉⠀⢉⠉⠙⠛⠃⠀⠀⠀⠴⣟⣻⠿⣛⣿⡄
⠀⢾⣿⢹⣚⣗⣧⠁⠀⠢⣤⡀⠀⠘⣺⣻⠟⣿⡗⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠈⠉⠈⠁⠁⠁⠀⠀⠀⠁⠀⠈⠀⠀⠉⠁
⠀⢸⡟⣾⡏⠉⠁⠀⢠⣶⠿⠁⠠⠷⢟⢻⡟⣻⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣶⡄⠀⢀⣶⡀⠀⢀⣶⠀⠀⢀⠴⠀⠛⡢⠲⢀
⠀⢸⡗⣿⣥⠄⠀⠀⢸⣿⡄⠀⠀⢠⣤⣼⡷⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠛⢧⡀⣠⠿⢦⠀⠘⠻⣄⠀⠀⢀⠀⠉⠁⢰
⢠⣾⣇⣿⠀⠶⢀⠄⠀⣹⣿⣀⣐⣿⣿⣺⣿⣿⣇⠀⠀⠀⢠⣦⣼⣇⣀⡀⠀⠀⡅⢀⣸⠇⣇⣶⢸⠃⣄⣦⣸⠀⠀⠸⣶⣶⣶⣯
⢸⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠙⠿⣿⡿⠟⠁⠀⠀⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⠀⠀⠈⢻⣏⣽⠏
⢰⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⠆⠀⠀⡀⣀⡐⣐⣐⡀⠀⠀⠨⠭⠍⠀⡭⣭⠩⢤⢩⡭⡍⠀⠀⠀⠀⠐⠂
⣼⣿⣟⣿⣿⣿⣿⢷⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣀⢀
⢹⣿⣿⣿⣿⣿⣿⣧⣬⣭⣬⣴⣾⣿⣿⣿⣿⣿⣿⡃⠀⠐⠂⠀⣡⣶⣀⠶⢀⣀⠀⠀⠤⠈⠀⠀⠀⢈⠑⠢⠀⠀⠀⠂⢻⣿⠀⠈
⢺⣽⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠶⣀⣿⣿⣿⡂⣞⠉⠀⠀⠀⠀⠀⣿⡄⠀⢙⠦⠀⠀⢾⡀⣸⣿⣷⣤⣿
⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⠁⠀⠐⣃⣽⣿⣿⣿⣷⣯⣌⠀⠀⠀⡄⢀⣿⣧⣤⢨⡇⠀⠀⣿⣿⡟⠛⢿⣿⣿
⠀⠀⢀⣠⡙⣋⡁⠈⣉⣛⣛⡉⢀⢈⣙⣋⠀⠀⠀⠀⠀⠺⠿⣿⣿⣞⠿⣿⣿⠟⠀⠀⠀⣷⡘⠻⠟⣃⣿⡷⠀⠀⠛⠷⠿⠿⠿⠾⠛
⠀⠀⠀⡇⠗⣧⣇⣀⣇⢸⣧⣇⣼⣠⣏⣹⣇⣀⣀⣀⣀⠀⠖⠚⠉⠏⠁⠒⠐⠒⠀⠀⠀⠉⠛⠻⠟⠛⠋⠁⠀⠀⠂⠰⠱⠆⠏⠯⠸
⣶⣶⣶⣶⣶⣾⣹⢫⣯⣿⣭⣽⣿⣿⣽⣯⣯⡿⣿⣹⢿⣷⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣾⣾⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣷⣷⣽⣧⣧⣾⣽⣯⣯⣤⣿⣷⣶⣤⣭⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠴⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡿⠏⠁⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡞⠻⠷⣦⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠒⢀⣤⣈⣴⣴⣶⣦⣴⡿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠉⠉⢿⣿⣿⣿⣿⣷⣄⣴⣶⣶⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡦
⠀⠀⠀⢰⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠈⠀⠀⠈⠉⠱⣾⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠆
⠀⠀⢀⣠⣿⣴⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣿⣿⣟⣉⣻⣿⠟⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⡠
⠀⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⠼⠉⠙⠀⣹⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠈⠙⣿⡿⢻⣿⣿⣿⣽⣿⣿⣮⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⣷⣶⣶⣴⣦⣤⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠛⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢵⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢀⣀⣤⣥⣴⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⠱⣾⣿⡿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠿⠛⠋⠿⠛⢿⣿⣿⣿⣿⣧⣤⡎⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⠙⠛⠛⢀⠀⠀⢴⡆⠈⠙⠛⠛⠉⠁⠀⠀⠛⠋⠻⠿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣄⣰⢟⡃⠀⠀⠀⢀⣤⣴⣶⣤⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠁⠀⣀⡀⠿⣿⡿⠿⣽⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⠶⢾⡉⣉⡉⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⣶⢀⡀
⠀⠀⠀⠀⢠⣾⣿⣻⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⠛⣶⣿⣿⣿⣿⣷⣤⠀⠒⠂⠀⠀⠁
⠀⠀⠀⠺⣿⣿⣿⡿⠿⠉⣀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣷⣦⡀⠰⣶⣄⡀⡀⢀⣀⣄⣤⣠⣄⣸⣟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠟⠛⢩⣿⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣹⠿⠿⠟⠉⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠦⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠉⠉⣿⣿⣯⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⣽⣿⣿⠉⠉⠉⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢸⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣧⣤⣄⣀⣀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣀⣀⣠⣤⣼⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⠀⠀⠀⠀⠉⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠉⠀⠀⠀⠀⢸⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⠀⠀⣀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⣀⠀⠀⠀⠀⢸⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡟⠛⠋⠉⠉⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠉⠉⠙⠛⢻⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⣀⣿⣿⣟⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣿⣿⣀⣀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣿⣆⣠⣴⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠠⠠⠒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⠸⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣴⠛⢏⡞⠠⣻⡿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⡿⠃⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⢩⠉⣟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡍⠀⡟⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣬⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡕⠋⢢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⢿⡥⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡷⢾⣻⣭⢵⣿⣿⣿⣿⣷⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⢿⣿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣋⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠄⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡷⠄⠴⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠧⠀⢾⠦
⠀⠄⠀⡀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⣧⠀⢠⣇⣤⣶⣄⠀⠀⠀⠀⠀⠀⢠⡆⡀⡸⣄⠀⡸⣀⣀⣶
⠀⡁⠀⠉⢀⠈⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡂⠀⠉⣳⡍⠁⠀⣚⠁⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢈⢦⠁⠀⠀⡋
⠂⡀⠀⠉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡒⠚⡟⠁⠙⡟⠒⣺⠗⠀⠀⠀⠀⠀⠀⠘⢗⠒⢫⠎⠀⢳⡐⠒⡺
⠀⠀⠂⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣧⠆⢶⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⡤⠐⢼⡷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣾⠿⢻⣶⣤⡀⠀⠀⠤⡤⠤⡐⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠛⠛⠁⠈⠀⠆⠀⠀⠀⠀⠀⠉⠴⠂⠂⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣸⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠒⠄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠿⣷⣶⡶⡛⠋⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⣀⠔⠀⣀⡀⠀⠈⠀⠀⣴⣦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣄⡀⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡁⠐⠀⠀⠀⠀⠈⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠐⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢀⣂⣄⠀⠀⠠⠠⠀⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣻⣿⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠠⢤⡚⢂⣀⠡⣀⠀⢀⠄⠀⠆⠀⠀⠀⠈
⠀⠀⢰⡄⠀⠀⠃⠀⠀⠈⠀⠀⠂⠀⠱⠀⠀⠀⠀⠀⡀⠀⢀⣠⣤⣤⡶⠀⠀⠀⠀⢐⠁⠀⠀⠀⠁⠀⠙⡇⠘⢠⠀⠀⠀⠀⠀⠐⠿⠿⠦
⠀⢸⣿⠀⠀⠀⠌⠀⠰⡄⠐⠀⠀⠂⠀⠀⠀⠀⠀⠈⠤⡴⢿⣿⣶⠟⠁⠀⠀⠀⠀⠈⠣⢀⠀⣀⣴⡄⢰⡗
⠀⠘⠿⣄⠀⠀⠃⠂⠀⠈⠑⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠋⠀⠉
⠀⠀⠀⠉⠉⠀⣧⠀⠀⠀⠀⠀⠀⠀⣀⠸⠒⢀⡰⠶⠄⠀⠂⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⢦⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢈⡀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⢺⢿⠁⠀⢠⠞⠓⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠁⠀⠀⠀⠀⠠⡀⠑⠀⠂⠈⢀⠀⠀⠀⠀⣠⠔⠉⠟⠀⠀⢘⠀⠀⠀⠀⠀⠉⢹⠀⠀⢀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⡠⠋⠓⠒⠒⠊⠁⠀⣠⣼⣗⠉⣆⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⣠⠎⠀⠀⠀⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⣰⣿⡷⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⡂⠀⠀⠀⠀⠀⣻⡾
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢦⠉⠙⠛⠚⠉⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠴⠀⡤⠈⠛⠳⣄⠁
⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⠄⠀⠠⠀⢠⡀⠀⠀⣑⠀⠀⠀⠀⠀⢰⠁⠀⠠⠄⠠⡆⠀⠀⠀⠀⠘⠁⠀⠀⠀⢡⡄⣿
⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠈⠣⠔⠃⠀⠀⠀⠀⠈⢼⣇⠀⠀⠐⠂⠃⠀⠀⢧⠀⠃⣀⠀⢀⠀⠁⠀⠀⠀⠀⠘⢄⣀⡀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠆⢀⣀⠚⣳⠴⡀⠀⠀⠀⠈⠻⠧⣤⡤⠒⢢⡀⠀⠈⠳⢄⣀⣀⣀⡀⠐⠀⠀⠀⡀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡞⠉⠀⠀⠀⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢼⣆⡀⠀⠀⢀⠼⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⢳⡬⠁⠉⠀⢠⠚⠂⡀⠀⠀⠀⠀⠀⠈⠀⣅⢠⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⠱⠄⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣐⣁⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣦⣀⡀⣠⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠈⠻⢷⣬⣀⠰⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠚⣛⠻⣿⣧⢱⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⡴⠋⠤⡄⢠⣾⡟⡛⠳⣿⡘⣮⢸⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⠈⡇⠀⠈⢀⡀⠴⠃⣿⡟⣏⠿⣤⣿⡗⡟⡼⣱⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠒⠁⡼⠰⠡⣤⣤⠀⢻⣷⡜⢷⡈⠻⣿⠓⣱⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠓⠆⠀⠀⡄⠾⠆⣸⣷⡧⢤⡀⣘⢦⣰⣿⢿⣦⢹⡰⢣⢞⣩⣴⣟⡄⣧
⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⠂⣼⡇⢤⡽⣂⡄⠀⣧⢠⡆⣿⣿⡜⠜⡝⢿⡟⣟⢿⡏⣿⢞⣵⣿⣛⣻⣽⡾⠃⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡀⡆⢇⣶⢿⣷⡀⣴⣿⡇⢠⡘⢧⣣⣻⣞⢾⣆⣽⢘⣿⡜⣼⢱⢯⣾⡿⠿⠛⣭⣺⠇⣼⣿⠃⡰
⠀⠀⠀⠀⠀⠸⣮⣧⡘⣦⡙⠂⠻⣷⢹⣿⠁⣾⣿⣦⣽⣷⡉⣾⣿⢿⣻⣥⡾⣿⢏⡟⣩⣶⣿⣛⣭⣵⣿⢟⣡⡶⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣝⣳⣦⣌⡳⣽⣷⣿⣯⣛⣾⢯⠁⠘⠓⣛⣙⡛⢿⡿⡜⣾⣿⡿⣏⣭⡴⢶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⢠⡶⣓⢲⣾⣭⣿⣿⣿⣿⣿⣿⠿⠡⢍⠈⣥⣘⣶⣼⣿⣿⣷⣬⣛⠿⢯⣾⠿⢋⣴⣿⣿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠹⣧⣌⣻⣟⣻⣽⣿⢿⡟⡛⢠⣤⣐⣿⣷⣿⣿⣿⢻⣿⣼⣿⡟⣿⣿⣶⣶⣶⡿⢿⣿⣿⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣽⣄⣿⣿⣾⢿⠿⣟⣿⣿⣿⣿⣿⡙⣯⣿⠇⣸⣿⡷⠟⣛⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢨⣀⠀⠀⠀⠈⠻⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠿⠿⠿⠟⠛⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⣄⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⣶⣒⡒⠛⠛⠛⠛⠋⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⣒⣲⣶⡄
⠀⠀⠀⠀⣯⠉⠉⠉⠉⣿⠛⠛⠛⠛⢻⡗⠒⠒⠒⠒⠒⣶⠒⠒⠒⠒⠒⢲⡖⠒⠒⠒⠒⠒⣿⠛⠛⠛⠛⠛⡿⠉⠉⠉⠉⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢷⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⢰⠇⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⣧⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡟⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⣦⠀⠀⠀⠸⣆⠀⠀⠀⠘⡇⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠀⠀⠀⢀⡞⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⠀⠀⠘⢧⡀⠀⠀⢹⡄⠀⠀⠀⢿⠀⠀⠀⢀⡇⠀⠀⠀⣼⠁⠀⠀⢠⡞⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠈⢳⡄⠀⠀⢻⡄⠀⠀⢸⡆⠀⠀⢸⠃⠀⠀⣼⠃⠀⠀⣠⠏⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠙⢦⡀⠀⠻⡄⠀⠀⢷⠀⠀⡿⠀⠀⡼⠃⠀⢀⡼⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠶⠾⠿⠶⠶⠿⠶⠶⠾⠷⠶⠷⠶⠾⠷⠶⠶⠿⠶⠾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣀⡴⠚⣲⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣿⣿⣿⣿⣿⣿⣁⣠⣤⣴⣚⣥⣶⣶⣿⣿⣿⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⡇
⠀⠀⠀⠀⠀⢀⡤⠤⢴⣶⠤⠶⣚⠛⢻⣿⣿⡏⣩⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣻⡇
⠀⠀⠀⣠⡞⠁⠀⢰⡋⠀⢰⣿⣿⡄⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⢟⣡⣾⣿⡿⡿⠁
⠀⠀⣼⣿⡇⣀⣄⠀⠹⠂⢸⣿⣿⢰⣿⣿⣷⢸⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢚⣿⣿⣿⡿⣽⠃
⠀⠀⣿⣿⡇⣼⣿⠂⠀⢸⡆⣿⣿⢸⣿⣿⣿⣾⡿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⡿⣱⠃
⠀⠀⢿⣿⣧⣿⣿⠀⠀⣿⣇⠸⣿⡞⣿⣿⣟⣉⣁⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢸⣛⣯⣴⠃
⠀⠀⠀⢿⣿⣿⡟⢀⣰⣿⠿⠦⢍⡀⠙⢿⣿⣿⢿⣿⣿⣿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡀⠀⠀⠈⢳⢄⠈⣿⢧⠖⠉⠿⠿⠛⠿⣿⣿⣿⣯⣭⣭⣭⣙⣛⣛⣛⣯⣭⡭⠞⠁
⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣥⣄⣀⣀⣀⠁⣷⣸⣰⣀⣁⣠⣤⡴⠛⠁⠀⠈⠀⠀⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠶⠿⠿⠟⠻⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⣿⣷⣮⠵⠒⠚⠩⡉⠀⠀⠀⠈⠉⡭⠉⠓⠒⠮⣵⣾⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠟⠉⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠙⠻⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢀⡠⠔⠒⠢⣄⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⢀⡀⠀⠘⠀⢀⣀⡄⠀⢠⠋⣴⡆⢈⠱⡀⢀⠎⢠⣶⡏⠀⡈⢣⠀⣠⣀⠀⠈⢆
⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠠⠀⠾⠿⡟⠁⠀⠸⡀⢻⣿⠟⣠⠃⠘⡄⠸⢻⣿⣿⠃⡸⠀⠈⢻⠿⠆⠘⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢣⠀⠀⠀⠉⠒⠒⠚⠁⣀⢀⣘⠢⣄⣉⡠⠖⠁⠀⠀⡎⠀⠀⠀⡳⠤⠤⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⢣⡀⠀⠶⣿⠆⠀⣾⠉⠛⠉⡇⠰⢶⣶⠎⠀⢀⠞⠀⠀⢀⠎⡔⠈⠁⢢⠑⡀
⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⠀⠘⠲⠶⠞⠁⠀⠀⠀⢀⡴⠋⡠⠄⠠⠼⢸⠀⠀⠀⡠⢀⠃
⠀⠀⠀⢀⣠⣲⣶⡀⠀⠑⠀⢸⠁⠀⠀⣀⣤⣤⣤⣤⣉⠓⠢⠤⣀⣀⣀⣀⡀⠤⠔⠊⠉⠀⠀⡁⢏⠉⡢⠸⢤⠐⣊⠄⠃
⠀⠀⠀⠀⣿⣿⡿⠀⡠⣁⣀⣸⣄⣰⣾⣿⣿⣿⣿⣿⣮⠳⡄⢀⠀⠀⠀⠀⢠⠀⠀⠀⡶⣒⠒⠙⠢⠬⡧⢀⠼⡋⠉⠁⠢⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢳⠀⠑⠤⠤⠴⠋⠀⠀⢀⡇⡏⢹⠒⢤⠥⠔⠲⡄⠀⡟⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⣿⣿⣦⣄⣠⣼⡿⢿⣿⣿⣿⣿⣿⣿⡿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⢟⡵⠃⢠⣂⣐⠢⣀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠈⠀⠀⠀⡇⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣿⣿⣿⣿⢟⡥⠋⠀⠀⠸⣿⣿⣶⣶⣼⡀⠀⠀⠠⣇⡇⢸⠀⠤⠀⠀⠀⡇⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⡠⠜⠉⠉⠙⢯⡋⠀⠀⣀⣀⣀⡙⠿⠿⠿⠋⠀⢀⣀⣀⣀⠙⠺⣄⣄⢀⣀⣠⠇⠤⢧⠔⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⡲⠋⠀⠀⠀⠉⢢⠀⠀⠀⡖⠉⠀⠀⠈⠑⡞⠁⠀⠀⠉⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠁⠈⠉⠙⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠠⣤⣤⣠⣤⣤⣤⣤⣀⢀⢠⡄⢀⣠⣤⣤⡄⣤⣤⢠⣤⣠⣤⣄⡤⢠⣤⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠙⢿⣿⣯⣻⢿⠿⠻⠛⠡⠻⣿⣿⣛⢿⣿⡜⢿⣏⢿⣧⡙⠿⠆⠿⠃⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠄⢀
⠀⠀⠀⠀⠀⠀⠙⣯⡿⣿⡆⢀⡲⠯⠀⠨⡉⠻⣷⣽⣏⠈⠛⠀⠙⠋⠀⠀⠂⠀⣴⣿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⣰⣶⣍⡃⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⡿⣻⢷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠙⠃⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⢈⣛⣻⣿⢗⣻⠵⠋⠈
⠀⠀⠀⠀⠀⣠⡀⢠⣼⡛⠈⠤⠀⠀⡀⠀⠀⠀⢀⠶⠀⢟⣴⣦⡀⠀⣾⣿⣿⠿⠟⠋⠁⠀⠰⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⢨⣡⡾⠮⠉⠀⠀⠀⠀⡀⠀⠀⠀⠈⠄⠀⠀⢈⣻⣷⠀⠈⠖⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠖⣀⠀⠀⢉⣄⠀⢋⠉⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠈⠋⠀⢤⡉⠃⠰⠷⠂⠀⠖⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠘⣆⠹⡍⢚⣡⠶⣶⠿⠿⠆⠀⢸⢄⡀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠔⠙⠊⠉⠉⠁⢃⠨⠀⣐⡊⠁⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⢀⠒⠀⠀⠃⠀⠀⠀⠀⠠⠦⡀
⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠐⠂⠀⢀⠦⠀⠀⠀⣀⠀⡘⠟⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡒⠰⡷⣀
⠀⠀⠀⠠⠀⠐⠐⠂⠀⠀⠂⢠⡄⢸⡇⢀⠲⡈⣛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⢄⡚⣠⡄
⠀⠀⠀⢀⣀⢐⣢⣴⣤⡿⢂⣿⢃⡿⠁⣴⡌⢋⣍⠀⠟⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⡐⠀⠀⠀⡄⠀⠰⠠⢙⠛⠮⠰⡦⢸⡦
⠀⠀⠀⢭⣴⣿⣛⣿⣭⠶⣛⣵⠟⠁⠂⢀⣤⡀⠄⢴⠆⡰⠆⡘⠁⠀⠀⠀⠀⠀⢐⠂⠀⠰⡾⢱⣷⠀⠀⠈⠆⢺⡿⡈⢸⣇
⠀⠀⠀⣽⣭⡭⠿⠷⢟⡛⠉⢠⣤⠛⠀⣿⣿⡗⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⡀⠠⠀⠀⠀⠀⠶⠐⠃⢄⡀⠄⢻⠠⣶⠁⣼⡏
⠀⠀⠀⢶⣶⣶⣶⠟⠋⠁⠀⠈⠁⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢒⠀⡀⠀⠀⠙⠈⣬⢹⣶⢎⠆⢀⣰⣿⡁
⠀⠀⠀⢹⣿⣛⠉⠀⠄⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⢶⣤⣤⣥⣬⣶⣿⠿⠏⠁
⠀⠀⠀⣩⣾⠭⣤⡀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠁⠀⢆⠀⣥⢀⣉⡄⢠⡄⣄⠛⠂⠀⠀⢟⠐⠀⠀⠈⠋⣶⠙⠃⠌⠃
⠀⠀⠀⠚⠛⢛⣋⣀⠂⠀⠠⠀⠀⠨⠀⠁⢠⢈⣵⡾⣷⣿⡟⣷⢶⢀⣄⢻⡿⠿⣿⠆⡈⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢔⡻⣻⣿⡍⡀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣿⡇⣿⢿⣧⣿⣾⡇⣿⡘⣿⣇⣿⠀⠀⣠⣴⡟⣿⢨⠀⠐⠀⢠⡄⠀⣰⢁
⠀⠀⠀⠋⠊⠛⠁⠚⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠃⠛⠈⠛⠀⠀⠈⠉⠛⠛⠛⠓⠓⠂⠈⠁⠀⠙⠚⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢄⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠻⡀⠀⠀⠘⠀⠁⣄⠀⠀⠀⢠⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⠀⢁⡀⠀⢰⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠤⢄⡀⠀⠀⢸⠀⠀⠘⣦⠀⣀⡀⠀⣤⠌⣠⠛⠁⠀⡆⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⠅⠀⠀⠈⣿⠏⠹⢦⠍⢰⠇⠀⠀⢰⠁⢀⡾⢁⠀⠀⠀⠀⣀⠤⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠈⠳⣶⠀⠀⢀⡌⠀⠆⠈⢻⡇⠀⡆⠀⣎⣰⠏⠀⠌⠀⢠⠄⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠉⠳⢤⣽⠀⠀⣼⠁⠀⠀⠀⠀⢱⡀⠇⢠⡿⠁⠀⣾⡄⠈⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠰⢶⣶⣦⣄⢀⡀⠈⠳⣄⠀⠈⠳⢦⡟⠀⠀⢀⡀⠀⠈⣷⣶⠎⠀⢀⡾⠋⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢌⡋⢤⡉⠠⠙⣦⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⠃⠀⣰⣏⣀⣀⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⣀⠙⢷⡀⠀⠀⠀⠻⣤⡁⠀⣰⡦⠚⠃⠉⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⡀⠀⠙⢀⠹⣶⠘⠛⠂⣤⣄⡀⠘⣧⠞⠁⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠙⠦⡀⠳⣄⠀⠀⠈⠉⠲⣦⡀⠀⠀⠀⢀⠀⣤⣼⠀⠒⠒⠀⠀⠉⡡⠿⠟⠁
⠀⠀⠀⠀⠀⠈⠓⢂⡀⠶⠄⠘⠂⠀⠛⠶⢶⠀⠹⠆⠀⠀⠀⠀⠀⠻⡄⣀⡴⠞⠋⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⡖⠒⢀⠤⢄⣀⠳⠀⠸⠦⢄⠀⣀⠀⠤⠾⣁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠖⡄⠐⠀⠉⠛⠻⣦⣀⠀⠛⠁⠀⠀⠀⠈⠳⡆⠁⠀⢀⡄⢀⣀⣀⠠⠐⠒⠚
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⠦⡄⢠⣄⠢⡔⢄⠀⠀⠙⠲⣤⡀⢀⣤⠄⠒⠚⠒⠂⠰⢿⣦⠈⠉⠉⠐⠒⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠼⣿⣦⣤⣄⠀⠀⠈⠃⣀⡀⠆⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⡀⣤⣥⡴⠶⠖⠈⢉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠛⠷⢶⣋⡉⠿⠶⣉⣀⠀⠀⠀⢀⣀⠴⠟⣤⠤⠞⠋⠀⣀⡀⠀⠠⢤⡤⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡒⠂⢠⠈⠳⠖⠠⢀⠈⠛⠷⡁⠀⠀⣀⣀⡈⠁⣤⠶⠋⢉⡄⠐⠀⠉⠁⠀⢠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣶⣶⠞⠿⠓⠚⠓⠨⢷⣄⠀⠹⠒⠀⠀⠈⠙⠛⢠⣤⢀⡈⠀⠈⠁⢴⣀⠤⠌⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢈⣧⣤⣤⢠⡶⠒⠂⢠⡈⠣⣄⠘⣀⠀⠀⠀⢠⡴⠒⠻⡷⠖⠂⢠⣄⡉⠀⠀⠱⠃⡀
⠀⠀⠀⣀⠀⠀⡌⠁⠲⡀⠸⡇⠀⡤⠁⠤⠀⠀⠀⠘⠆⠙⣄⢉⡷⠉⠹⢦⣤⠈⠀⠈⠀⠁⠄⠘⡉⠀⠂⢲⠀⠑
⠀⠀⠀⠈⠓⢰⡿⠀⠀⣾⣶⠷⠦⣤⠄⣰⡆⠀⢰⡷⡤⠚⢻⡶⢀⣤⣀⠁⠀⠈⢠⡌⢱⣣⣄⠘⠗⠀⠈⠀⠶⡈
⠀⠀⠀⠀⣠⡋⠀⠀⡰⠋⠃⡀⠀⠀⠀⠙⡛⠃⠀⠛⠆⠀⠀⢳⣀⡄⢩⣐⡦⠈⠛⠀⢀⠍⠛⢳⡆⠀⠀⠀⣀⠙⠀⠀⠰⡆
⠀⠀⠀⡐⠿⠃⠀⠰⠁⠀⠀⠑⠀⠀⣀⠊⠀⣀⡤⢴⣤⣴⣞⠉⠁⡧⠈⠁⠐⣦⠄⠛⢫⡤⠀⡀⠘⣂⡀⠀⠁⠀⠀⢠⠄⠃
⠀⢰⡤⠃⢀⢀⡼⢤⡀⠀⢀⣤⠲⡖⠙⠓⢾⡋⠀⣸⡆⠀⠙⢇⠁⠀⠀⠀⡌⠁⠀⠀⢸⠀⠀⢹⡞⠉⠉⠖⠂⠀⢠⡦⠀⣤⠰
⠀⢸⠇⢀⡼⠁⠄⠀⢹⡟⠉⢀⡴⠃⠀⠀⢀⠉⠈⠉⠳⠀⠀⠺⣷⠶⠶⢤⡿⠀⠀⠀⠊⠀⠁⠰⡇⠀⠀⠋⣀⣼⡏
⡀⠘⢀⡌⠳⠖⠀⠀⠀⠛⠰⠂⢡⠀⠀⠀⠸⠂⠀⠀⠀⠀⣠⠞⠁⠀⡀⠀⠘⢣⡀⠀⠀⠀⠀⠀⢧⡀⠀⡀⠀⢸⡇⠀⠀⠰⡆
⠈⣄⡿⠁⠀⠀⠣⠄⢀⣀⠀⠀⠀⠀⢀⡼⠟⠛⡟⠓⠦⣠⡏⠀⠀⠀⠁⠀⠀⠀⣿⣠⠤⠴⣶⠴⢎⡁⠀⠀⠀⠸⣇⠠⠎⠠⡇
⠀⠉⠰⣧⠈⠳⣄⢀⡜⠋⠘⠓⣄⣠⡟⠀⠀⠀⠁⠀⠀⠹⠇⠀⠐⠀⠀⠀⠒⠂⣼⠃⠀⠀⠀⠀⠀⠙⢦⡤⡖⠢⡀⠀⠀⣠
⠀⢠⣾⣹⠆⠀⠘⣿⡀⢀⠀⠀⠈⠿⠀⣤⡴⠀⣆⠀⠀⠀⡃⠀⣀⣤⣤⣤⣄⢀⣿⠀⠀⠀⡀⢠⡤⣴⠟⠀⢀⡄⠀⣦⠐⢠⡦
⠀⢮⡄⠉⠀⢄⠀⠛⠑⠞⠀⠄⠀⠘⣇⠀⠀⠀⠈⠁⠀⠈⣡⠞⠁⠀⢄⠀⠈⠛⣏⠉⠀⠉⠁⠀⢠⡏⠀⠀⡞⠐⡿⠁⠘
⠀⠾⢫⣴⠶⢄⡀⠰⣄⣤⣄⣀⠀⠀⢙⠶⠉⠙⠋⠁⠶⣤⡏⠀⠀⠀⠈⠀⠀⠀⠈⣣⠶⠆⠀⢶⡜⠃⠀⢉⡀⠼⠇⣀⠀⡟
⠀⢠⠸⡇⠐⠀⠙⣶⠋⠀⠉⠈⠛⢶⡎⠀⠀⠀⠃⠀⠀⠈⢷⠀⠙⠛⠁⠀⠙⢠⠟⠁⠀⠀⢰⠆⢱⣆⣰⠋⢥⡀⣀⣥⣴⠇
⠀⢸⣧⠀⠛⡀⠀⠘⣷⠴⢀⡀⠀⠀⢻⡀⠢⣤⠀⠠⠄⠀⠠⣧⣠⣤⣤⣄⣰⠇⠀⠀⠀⡰⠃⠤⠋⢨⠋⠠⠜⢁⠙⠁⢼⠆
⠀⠸⠙⣧⡀⠑⢤⡀⢡⠀⠈⠑⠂⠀⢀⣧⠀⠀⠀⠀⠀⣠⡴⠋⠁⢠⠇⠈⠳⣆⠈⠁⢈⣤⠒⠶⢦⡀⠀⠀⠀⡮⠠⠂⣠
⠀⠀⣠⠀⠑⣄⠀⣨⡽⠶⣤⡀⣠⠖⠉⠉⠉⠉⠱⢦⠾⠁⠀⠀⣠⠘⡀⠀⠀⢸⣤⠖⠉⠀⠀⣷⠀⣴⣶⠶⢢⡀⢀⠾⠋
⠀⠀⠙⣶⡆⠀⢻⡁⢰⡄⠀⠹⣧⢀⣀⢀⡀⠀⠀⠈⣦⠀⠈⠉⠀⠀⢉⠁⠀⢀⣏⣀⣀⣀⡴⠛⠻⠃⠈⡇⢀⡼⣾⠃
⠀⠀⠀⠘⢷⠄⠈⠁⠙⢠⠀⠀⠙⡄⠀⠀⠑⠠⠄⠠⠛⢀⡠⠤⠛⠋⠁⠀⠙⠧⡀⠀⠀⠀⠀⠀⠇⢀⡀⠁⢨⠟⡀
⠀⠀⠀⠀⠀⠂⣰⣧⣀⡀⢑⡀⠠⣧⡤⠒⠒⠲⠒⠢⣴⠏⠀⡀⠀⠀⠀⣠⠀⣀⡿⠒⠒⠛⢶⣞⠓⠀⢀⡘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠙⣯⠙⣇⠉⠁⠺⠏⠀⠀⠀⠀⠀⠀⠈⢣⠈⠉⠐⠀⠁⠉⠸⠋⠀⠀⠀⠀⠀⠛⠓⠫⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠂⠀⠀⠐⠄⠁⠂⠀⠶⠐⠂⠐⢷⣀⠀⠀⠀⢀⣇⠀⢀⠀⠒⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢌⣀⣸⣆⠀⠀⠀⠀⣠⠆⠉⠉⠛⠀⠈⢙⡟⠉⣀⠤⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣾⣿⣶⣶⣦⣤⣤⣤⣯⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠱⡀⠀⠀⣏⠀⡇⠀⠀⠀⢀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⢄⠀⠀⠘⡆⣇⠀⠀⠈⠉⠀⠀⢀⡔⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⢣⠀⠀⠳⠏⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠺⣉⠑⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢣⠀⠀⠀⢀⡤⡀⠀⢠⠎⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠃⠀⠀⠀⡔⠒⢦⡘⢆⠀⠀⠑⢄⣀⠎⠀⢸⢀⠇⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡠⠃⣀⠴⠃
⠀⠀⠀⠀⢀⠤⠄⠤⠤⣀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠠⠊⢀⡤⠒⢑⠀⠀⠸⠑⠊
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⡠⠤⠊⠀⠀⠀⣤⠊⢳
⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠤⠤⢄⠉⠁
⠀⠀⠀⡠⠤⢄⠀⠈⠉⠉⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⡠⢄⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣄⠀⢀⡠⣀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⠆⠀⠀⡠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⢸⠀⠀⠈⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡠⠊⠀⠀⡞⢠⢲⠀⠀⠀⠀⡴⡄⠀⢣⠀⠁⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⡹⠀⠈⠒⡩⠆⠀⠀⠀⠓⠃⢸⠀⠀⣤⠀⠡⠘⠤⠠⠂⠀⠀⠀⠀⠈⠢⢄⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠰⡁⣠⠞⠁⠀⠀⠀⠧⠄⠀⠀⠀⠀⠀⡆⠀⠀⡄⠉⠁⠀⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⠙⠂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⢬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⣁⣠⣤⣴⣶⣶⣶⣶⣦⣤⣄⣈⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣤⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣤⡈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⣠⡾⠋⢻⣿⣿⡿⠋⢁⣤⡴⠖⠲⠦⣤⡈⠙⢿⣿⣿⡟⠙⢷⣄⠙⢿⣦⡀
⠀⠀⠀⠀⢠⣾⠏⢀⣾⡟⠀⠄⠘⣿⡟⢀⣴⣿⠃⣠⣶⣶⣄⠘⣿⣦⡀⢻⣿⠁⠠⠀⠻⣷⡀⠹⣿⡄
⠀⠀⠀⢠⣿⠃⣠⣿⣿⣷⣶⣤⣤⡿⠀⣼⠟⢁⣠⣿⣿⣉⣻⣄⡈⠻⣧⠀⣿⣤⣤⣶⣾⣿⣿⣄⠘⣿⡄
⠀⠀⢀⣿⠇⢠⣿⣿⠿⠋⢁⣠⣤⣤⣄⣀⠀⠻⣿⣤⣼⠛⢿⣿⠟⠀⣀⣠⣤⣤⣄⡈⠙⢿⣿⣿⡄⠸⣿⡀
⠀⠀⣸⡟⠀⣾⡿⠋⣠⠾⠛⠋⢠⣄⠈⠛⠷⣆⠈⠛⢿⡶⠛⠁⣰⠾⠛⠁⣠⡄⠙⠛⠷⣄⠙⢿⣷⠀⢻⣇
⠀⠀⣿⡇⢰⣿⠃⢰⠃⣠⣶⢶⣿⠛⢲⣶⣦⠈⣧⠀⢈⣁⠀⣼⠁⣴⡶⣶⣿⠛⣶⣶⣄⠘⡆⠘⣿⡆⢸⣿
⠀⠀⣿⡇⢸⣿⠀⣿⠀⢻⣧⣴⡿⢷⣿⣿⡿⠀⣾⠀⢈⡁⠀⣷⠀⢿⣧⣼⡿⢶⣿⣿⠟⢀⣿⠀⣿⡇⢸⣿
⠀⠀⣿⡇⠸⣿⡄⠸⣷⣄⠈⢿⣧⣼⣿⠁⣠⣾⡟⠀⢈⡁⠀⢻⣷⣄⠈⣿⣧⣼⡿⠁⣠⣾⠇⢠⣿⠇⢸⣿
⠀⠀⢹⣧⠀⢿⣷⡄⠙⢿⣦⡈⠛⠛⢁⣠⡿⠏⢀⣤⣾⠷⣤⡀⠹⢿⣄⠈⠛⠛⢁⣴⡿⠋⣠⣾⡿⠀⣼⡏
⠀⠀⠈⣿⡆⠘⣿⣿⣶⣄⡈⠙⠛⠛⠋⠉⠀⣴⣏⣹⣿⣤⣾⣿⣦⠀⠉⠙⠛⠛⠋⢁⣠⣾⣿⣿⠃⢰⣿⠁
⠀⠀⠀⠘⣿⡄⠙⣿⣿⡿⠿⠛⠛⣿⠀⢻⣦⡈⠙⣿⣏⣹⣿⠋⢁⣴⡟⠀⣿⠛⠛⠿⢿⣿⣿⠋⢠⣿⠃
⠀⠀⠀⠀⠘⢿⣆⠈⢿⣦⠀⠂⢀⣿⣧⠈⠻⣿⡄⠙⠿⠿⠋⢠⣿⠟⠁⣼⣿⡀⠐⠀⣴⡿⠁⣰⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢷⣄⣼⣿⣿⣷⣄⡈⠛⠳⠶⠴⠞⠛⢁⣠⣾⣿⣿⣧⣠⡾⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡈⠛⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠛⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⡉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⢉⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠾⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣌⣉⣉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢋⣉⣤⠴⠖⠚⠋⠉⢉⣁⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠭⣭⣷⣦⣄⠈⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡴⠞⢉⣠⠴⠚⠉⠁⣀⣤⠴⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⢻
⠀⠀⠀⢀⡴⠋⢀⡴⠋⠁⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡼
⠀⠀⠀⡞⠀⠀⣾⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⣠⠞⠁
⠀⠀⠀⣧⠀⠀⠹⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠉⠀⣀⡴⠚⠁
⠀⠀⠀⠈⠳⣄⡀⠀⠉⠛⠲⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠚⠛⠉⠉⠀⣀⣠⡴⣶⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠴⠖⠚⠋⠉⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠤⠤⠤⠤⠴⠶⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠞⣛⣛⣛⣋⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣙⣛⣛⣛⠳⠶⠶⠦⣤⣤⣀⡀
⠀⠀⠀⣀⣤⠶⠛⣋⣭⣤⠶⠶⠟⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⠶⣤⣭⣙⠛⠶⣦⣀
⠀⢠⡾⠋⢀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⡀⠙⢷⡄
⠀⢸⡇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡇
⠀⠀⠻⣦⣄⠈⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠶⠛⠁⣠⣴⠟
⠀⠀⠀⣿⠉⠛⠶⣦⣄⣈⡉⠙⠛⠛⠷⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠾⠛⠛⠋⢉⣁⣠⣤⠶⠟⢹⡟
⠀⠀⠀⢿⡄⠀⠀⠀⠈⠉⠛⠛⠳⠶⠶⢶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⠶⠶⠾⠛⠛⠉⠁⠀⠀⠀⣸⡇
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠙⠛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠉⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢰⡔⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⣗⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣿⠾⠛
⠈⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣷⠉⣷⠀⢠
⠀⠢⡀⠀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⡰⢻⢁⣦
⠀⠀⠐⡞⠀⠀⠀⠑⢦⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⢀⣿⢷
⠀⠀⠀⠑⠀⠀⠀⠀⠈⣇⠀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⣿⡾⣫⣾
⠣⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠀⢀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⣷⣿
⠀⠁⠀⠀⠀⠱⣝⠆⠈⠀⠀⠐⠁⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢠⠾⠁⣜⠅⠀⠂⠉⠳
⠀⡖⠀⠀⠀⠀⠘⠋⠘⠓⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠁⠀⣸⠐⠀⠀⠀⠀⠦
⠀⡄⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣟⠀⠀⠀⠀⠀⢠
⠀⠃⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⣾
⠀⢽⢸⠀⠀⠠⠀⠀⠀⢀⠄⠀⠘⡆⠀⠰⠀⠃⠆⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⠌⠠⡆
⠀⠸⠀⠆⠀⠘⠄⠀⠂⠀⡃⠐⢆⡀⠀⠣⠄⠠⠊⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠁
⠀⠈⠇⢠⠀⠀⠀⠀⣀⠒⠂⣶⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣏⠀⠀⠀⠀⡏
⢦⡀⠐⠈⡇⠀⠈⠀⠘⠗⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠴⠻⠀⠀⠀⡸⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡆⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⢰⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⠛⠿⣿⣷⣄⡀⠀⠀⣿⣿⠀⠀⢀⣤⣾⣿⠿⠛⢻⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⠀⠀⠈⠙⢿⣿⣦⡀⠈⠁⣀⣴⣿⡿⠋⠁⠀⠀⠘⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄⠀⠀⢀⣠⣾⣿⠟⠉⢀⡀⠈⠻⣿⣷⣄⡀⠀⠀⢠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣧⣤⣶⣿⡿⠋⠁⠀⠀⣿⣿⠀⠀⠈⠙⢿⣿⣶⣤⣼⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠇⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠸⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣤⣤⣤⣤⡄
⣿⣿⢹⣿⡇
⣿⡿⡤⣿⡇
⣿⣿⣿⣿⡇