Jolly text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡶⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣏⠔⠀⠀⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠁⠉⠀⠉⣽⠏⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⡠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣾⠃⢰⡿⠀⠀⠀⠀⣀⠀⢀⡄⠉⠉⠁⠰⠊⢄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢀⠄⠸⠁⠀⠀⠀⠀⣸⡏⠀⣼⢇⡔⠀⠀⣼⠃⢣⡟⠐⠀⠀⠀⠠⣀⡸⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢫⡀⠀⣀⣀⠀⠁⠀⣿⢀⣠⡿⠉⠀⠀⢠⡟⠁⣼⠇⠀⣤⠀⣴⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢈⡟⠁⢀⣡⠄⢺⡏⠀⣼⢣⡶⠉⢢⣾⠁⢠⡟⠀⣰⡏⢠⡟⠀⣠⡶⠟⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣴⠋⠸⠀⣿⠁⢠⡿⠘⢧⠀⠂⠛⠄⠈⠓⠂⠈⢁⣽⡷⠟⠋⢀⣀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⢀⠇⣸⡟⠀⢸⡇⠀⠀⠲⡄⠀⢠⡟⠂⣴⠞⢻⠏⣴⠋⢠⡞⠠⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢠⡿⠁⠀⠘⣧⡀⠀⠠⢁⣠⣾⠋⠸⠁⠠⠋⢸⡯⠀⣼⠇⠀⡄⢠⡆⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠀⣀⠤⠬⣉⣤⠾⠋⢱⡏⢀⡴⠄⢀⡤⣿⠃⢠⡟⠀⣸⠃⣸⠇⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣴⠋⠁⠀⠀⣾⠃⠸⣇⠀⠜⠀⠿⠄⠘⠓⠀⠈⠀⣿⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢧⣀⠀⠀⢠⡿⢀⡀⢀⡴⠒⠒⣤⣀⠠⠤⠤⠖⣾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⣼⠇⠀⠀⣿⠄⢠⠎⠉⠆⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⡆⣰⡏⠀⠀⠀⢿⡀⡈⠢⠈⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠨⣷⠋⠀⠀⠀⠀⠀⢹⠷⠄⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠛⠀⠀⡄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣾⠃⣸⠂⠀⠀⠀⢸⡇⠀⢰⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⣐⣁⡀⢠⠗⠄⢹⡇⠀⣾⠃⢰⡇⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⢸⣧⠃⣰⠇⣿⣎⠁⢸⡇⠀⢸⡇⢸⡇⢰⡟⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢀⡏⠀⢿⣈⣵⢸⡇⣀⢸⠃⠈⠷⠊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠸⣄⡼⠀⠉⠁⢀⡀⠀⠘⢒⠂⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⢏⠲⢂⡼⠁⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠛⢻⡇⣰⠖⣆⠀⣿⠀⠀⣶⠀⠁⣩⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣺⡇⡟⢴⠢⠀⣿⠀⠀⣿⠀⠐⣿⡄⣸⡀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⢾⡁⢿⣀⣴⠀⣿⠀⡀⣿⠀⠀⠙⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⣀⡿⠈⢦⣈⠁⠀⠉⡍⠁⢿⣀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠁⣠⠀⠈⠙⠒⠚⠁⠀⠀⠁⣾⠩⠆⣟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢠⣠⡄⡄⠀⠀⠀⠙⠢⠴⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡚⣃⠄⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣜⠬⢋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡆⣸⢶⠀⠀⣴⠋⠂⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣷⠰⢡⡟⠀⡆⡘⣺⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠀⠀⠀⠀⠀⠀⣇⢸⣼⠙⡅⣧⠇⢿⠀⠀⢸⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠁⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⣰⠁⠀⠀⡇⠸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢶⡄⢰⡀⠀⡇⠀⠀⢸⡇⠂⣾⠸⢀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠁⠈⢷⡀⠀⠀⠀⢸⡇⠀⣿⠁⢸⡇⠀⡿⢀⣤⡀⡀⠀⠀⡄⠀⢀⠠⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⠑⠀⠀⠀⠀⡇⠀⢹⠀⠸⡇⠀⡇⠈⢛⠁⣥⡄⠀⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⢄⠄⠀⠀⠀⠰⠆⠀⠀⠀⢉⡏⠀⠀⢸⠀⠇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠻⠀⣹⠸⠏⣁⡄⡀⠀⠰⡆⠀⣇⠀⢸⠃⠀⠀⣾⡐⢸⣇⠃⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⡑⢾⣿⡿⢊⡫⠁⠀⠀⢰⡇⠀⠘⣆⠀⠀⠀⠀⣿⠁⢸⡏⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⣡⡎⣩⢹⣄⠋⠃⠂⠀⢸⡇⠀⠀⠈⠃⠀⠀⠀⢸⠀⠀⠇⠀⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠿⠄⠋⠁⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⡀⢠⣤⣄⡀⠀⣀⠀⢈⣤⣤⡀⣤⣤⣤⡄⣀⠀⠀⣀⠀⠀⣠⠀⢈⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠈⢸⡇⠀⣿⢸⠁⠀⠘⡆⣿⢠⡟⠁⠀⣿⠀⣿⠀⠀⣿⡆⢠⣿⠀⢠⣿⡇⣾⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣅⣀⡏⢸⠀⠀⢠⡇⣿⢸⡇⠀⠀⠃⠀⣿⠀⠀⣿⢻⡌⣿⠀⣾⢹⠇⣿⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⢈⡇⢸⣀⣰⠟⠀⣿⠈⠳⢤⡀⠀⠀⣿⠀⠀⣿⠈⠁⣿⢰⣏⣸⡀⠻⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⢸⡇⢸⡻⣄⠀⠀⣿⠀⣶⠀⢸⡇⠀⣿⠀⠀⣿⠀⠀⣿⢸⠇⢸⡇⣴⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠃⠸⠀⠘⠇⠘⠃⠈⠃⠀⠷⠀⠻⠤⠞⠁⠀⠛⠀⠀⠛⠀⠀⠛⠙⠀⠘⠃⠙⠆⠞⠃




⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⠎⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣑⠊⡹⠋⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣑⠚⠉⢲⡤⢎⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡴⠛⠺⢅⣀⡤⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠋⠉⠉⠉⢉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡀⠀⢠⠀⠀⠀⠀⡇⢸⣘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⡌⣡⠄⠀⠀⠇⠀⣿⠈⡆⣞⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠛⠙⠜⠀⠀⠀⠃⠚⠈⠀⠣⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡤⠀⠀⢀⡤⢤⠀⠀⡠⡤⢄⠀⠀⡠⢠⢄⠀⠀⡠⣠⢄⠀⣤⡤⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠺⡶⡃⢰⢋⡔⣁⡇⠘⣾⡭⢯⡆⢸⡴⢻⢞⠀⣌⠔⣡⠊⡁⢋⡔⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⢲⣡⣴⢈⡃⡽⢃⡬⠊⡔⣡⠆⢀⠁⠁⣎⡥⣋⠔⢡⢊⡝⢋⡄⠀⣋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡹⢤⠜⡝⠰⣊⠟⣱⠇⢣⢊⠔⡡⠗⣏⠧⡤⢊⠇⢩⡔⡡⢫⠂⣏⡆⠀⣇⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⣄⠈⠉⠉⠁⠀⠀⠈⠉⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠒⠀⢈⣈⣉⣉⡁⢁⣉⢈⢈⠉⠈⠈⠉⣫⠉⡏⠈⠈⠉⢁⠉⠉⢈⠁⢉⣉⣈⣉⠀⠉⠈⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⢠⣧⡇⠀⠀⠀⠀⠀⠀⠀⡁⡿⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠰⢀⣀⣀⠇⠀⡤⣴⣾⠛⠻⣗⣦⠀⢰⣀⣀⣛⠄⢿⣀⣀⣐⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠾⡹⠛⠀⠐⠒⠓⠬⠷⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⣀⣠⣤⡀⠀⠀⠀⣀⣀⣠⣤⡄⠀⠀⠀⣀⣀⣠⣤⣄⠀⢀⣀⣀⣀⡀⠀⢠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠂⠀⣠⡾⠻⠋⠻⣿⡄⠀⠀⢹⣿⣿⢣⠃⠀⠀⠀⠹⣿⣿⢣⠂⠀⠸⣿⣿⡏⠁⠀⠀⢻⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣿⡇⠀⠀⠀⢹⣿⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⣿⣿⠈⠀⠀⠀⢻⣿⣇⡀⠀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⢾⣿⡇⡀⢰⣿⣿⡄⠀⢰⣿⣿⡆⠀⢀⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⡅⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠫⠎
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⣿⡗⠁⠘⢻⣿⠔⠀⠀⣿⣿⠃⠀⠘⣿⡿⠣⠃⠀⠀⠀⠘⣿⡿⠃⠂⠀⠀⠀⠀⠀⠻⣿⡟⡈
⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⣠⣿⠁⠀⠀⠈⣿⣦⣀⣰⣿⡟⠄⠀⠀⣿⣇⡀⢀⣠⣾⠁⠀⣾⣿⡀⢀⣠⣾⠰⠀⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠘⠻⠿⠿⠟⠈⠀⠀⠀⠻⠿⠿⠿⠿⠿⠸⠀⠻⠿⠿⠿⠿⠿⠰⠀⠠⠾⠿⠿⠧⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢃⠀⠀⢰⡟⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣾⠷⠖⠃⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠁⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⢀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⣴⡏⠀⢸⡿⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠉⠙⠛⠒⡶⠧⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢾⠀⠀⠀⠀⢀⠔⢰⣿⠀⠀⣿⠃⢀⠆⠀⠀⣴⠋⡅⣴⠇⡔⠀⠀⠀⠀⡇⠀⢸⠄⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠀⠀⢀⠔⠁⠀⣾⡇⠀⢸⣿⠖⠁⠀⠀⢰⡯⠊⢰⣿⠐⠀⠀⠀⢀⡀⠈⠛⠉⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣤⠆⠒⢂⠀⠀⣸⣿⠴⠒⣿⠇⣀⡀⣀⠀⣿⠁⠀⣾⠏⠀⢠⡗⠀⣼⠇⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣼⡖⠉⣿⡇⠀⢸⡿⣸⡏⠁⠸⢺⡟⠀⣰⣿⠀⡠⣾⢃⣰⡟⢀⣠⣶⠟⠋⠀⠀⠀⠀⠂⠰⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣴⠋⢠⡇⢰⣿⠁⠀⣿⠇⠹⢇⣀⠜⠈⠓⠊⠀⠙⠈⠀⠈⣀⣾⡿⠟⠋⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⡼⠀⣾⡏⠀⢸⣿⠀⠀⠠⠤⡄⠀⠀⢰⠞⡂⢀⣴⠟⢻⡏⣰⡟⠁⢠⡟⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠑⠊⠁⣸⡿⠁⠀⠘⣿⠀⠀⠀⠀⡜⠀⢀⣿⠞⢰⡟⠁⢠⠟⢀⣿⢀⠂⣾⡥⠋⡀⠀⢀⡀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⡴⠟⠁⠀⠀⠀⠙⠳⠤⠄⣊⣤⠾⢻⡇⠀⢀⠁⣀⡁⠀⣼⡟⠀⢰⡟⠀⢀⡿⠀⣼⠃⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠛⢒⣶⡞⠋⠀⠀⣿⠃⢠⡿⠙⠀⡽⠈⣿⠃⠀⣾⠇⠀⢼⡇⣠⣿⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢰⡟⠁⠃⠀⠀⢰⡿⠀⠸⣧⡀⠴⠁⠀⠛⠀⠊⠉⠃⠀⠀⠁⣼⣇⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⡄⢀⠄⠀⢀⣾⡇⡀⠀⢀⣴⠖⠛⠒⣄⣀⣠⡤⠤⠴⠖⢲⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡠⠬⢄⠀⠀⢰⡿⠀⠀⠈⣿⣇⠀⣠⠞⠉⡇⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢸⠀⠀⣿⠃⠀⠀⠀⣿⡈⠆⢿⣀⡴⠁⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⢸⡇⣼⠏⠀⠀⠀⠀⠘⢷⣼⠀⠀⠀⠀⠀⢀⡤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⢀⠏⠛⠒⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠓⢦⡀⠀⠀⠀⠀⢀⣀⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⣠⣾⠏⠀⠀⠀⠀⠀⢈⡿⠀⠀⢀⣴⡟⠉⠀⠀⠀⢹⡆⠀⠀⠀⠀⡞⠁⠀⠀⠙⢷
⢀⡤⠒⠀⠒⠲⠤⣄⣾⡿⠁⣰⣿⠃⠀⠀⢀⡀⢀⣀⡾⠁⠀⢀⣾⡟⠀⠀⠀⣀⡤⣼⠧⣀⠀⠀⠀⢳⣄⣀⣰⡆⠈
⢿⣤⡄⠀⠀⠀⠀⢸⣿⡟⢲⣿⣧⣀⣠⣾⡡⠴⠚⠙⡆⠀⠀⣾⣿⠁⠀⢀⣾⣏⠔⠃⠀⠈⣷⠀⠀⠀⠉⠉⠉
⠀⠁⠀⠀⠀⠀⠀⠸⣿⣁⣿⣿⠀⠀⢿⣁⡤⠀⠀⢀⡇⠀⢰⣿⡿⠀⠀⢺⣿⠁⠀⠀⠀⢀⡟⢀⡀⠀⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣼⣿⣁⠀⠀⡼⠁⣠⢾⣿⡇⠀⠀⢿⣿⠤⠤⠤⠖⠋⢠⣿⠃⢸⣿⡄⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⢿⣿⠈⢉⡞⠁⠉⠀⢸⣿⡇⠀⠀⣸⣿⡆⠀⠀⠀⢀⣿⡟⢀⡟⢻⣷⡴⠋
⠀⠀⣠⡶⠚⢶⣦⡀⠀⠀⠀⣀⠤⣀⠀⠙⠋⠁⢀⣤⡶⠒⢦⡙⠷⠤⠞⠁⠙⠿⣦⣠⠴⠋⠈⠉⠁⠀⣨⣿⣇
⠀⠀⠛⠀⠀⠈⣿⣇⠀⠀⢾⣁⣤⠄⢳⡀⠀⠀⣾⡟⠀⠀⣼⠃⣠⡞⠉⠉⢶⡀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢸⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣸⣿⣧⣀⣸⣇⣀⣼⣿⡧⠄⠚⠁⣸⡿⠀⠀⠀⣸⠃⣀⡤⠀⠀⢠⣤⢰⡇⠀⢸⣿
⠀⠀⠀⠀⢀⡀⣿⣿⠒⠉⠘⣿⡇⠀⡿⠀⠀⢸⣿⡇⠀⠀⢠⣿⡇⠀⢀⡴⠃⣴⣿⠁⠀⢀⣿⣿⡄⠻⠤⠼⠋
⠀⢀⠤⠊⠁⢀⣿⡇⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡗⠊⠉⠀⢠⣿⡇⠀⢀⡞⢹⣿⣇
⣠⠋⠀⠀⠀⣸⡿⠀⢀⣤⡴⠶⢦⣄⡀⠀⠀⠘⣿⣧⠀⠀⣸⣿⣇⠀⠀⢀⡞⠙⠓⠒⠋⠀⠈⣿⣿
⡏⠀⠀⠀⣴⠟⠁⢰⣿⠏⠀⠀⠀⠈⢻⣆⠀⠀⠘⠿⣦⡴⠃⠙⠿⣦⠴⠋⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀
⠙⠢⠴⠚⠁⠀⠀⠘⣿⣄⡾⠃⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⢀⣿⡏⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢺⡟⠛⠓⠲⠶⢤⣄⣀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⢛⡾⢧⣄⣀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠙⠛⠲⣶⡿⠥⠤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⢀⣠⠞⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡴⠀⣀⡀⠉⠀⠀⣀⡀⠀⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠉⠻⠉⠀⠙⠁⠀⢀⣾⠏⡇⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣰⠃⠀⣾⠇⢸⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⢰⣿⠀⠀⣸⣿⠇⠀⢠⡶⢤⡀⠀⢠⣿⡿⠁⠀⢸⣿⣠⠏⣠⣤⡀⢰⣶⠈⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⣼⡏⠀⠀⣿⣿⠀⠀⠈⠳⢤⣽⡤⢺⣿⠀⠀⠀⣾⡟⠁⠀⢸⣿⠀⣸⡏⠀⠹⠟
⠀⠀⠀⠀⠀⠀⠐⣿⣏⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣴⡿⠂⠈⡇⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡏⢠⣿⣇⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⢠⣿⡷⠶⠻⣿⡇⠀⠀⣿⡇⠀⢠⡇⢸⣿⡄⠀⣸⢻⣷⣀⣼⣿⣧⡾⣸⣿⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣴⣄⣀⣤⡶⢻⣿⡇⠀⠀⣿⡇⠀⢸⣿⣧⣀⣼⠁⠀⠻⣿⣶⠏⠀⠻⠟⠁⠈⠉⡴⢻⣿⠀⠀⠀⠠⣶⣦
⠀⠀⠀⠠⣦⠀⠙⠛⠛⠁⠀⢸⣿⣷⠀⠀⢻⣿⣦⠟⠈⠛⠛⠁⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⣿⠀⠀⠀⠀⠉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⣴⡏⢈⡇⢠⡞⢹⡄⠀⠀⠀⢿⣴⣿⡟
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⢰⣿⠁⡼⢡⣿⠁⣸⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠐⣶⣷⡞⠀⠺⠆⠀⠀⢀⣠⣴⡟⠁⣠⠤⣄⠀⠀⣸⣿⠞⠁⢸⣿⠜⠁⢸⣿⡆⢸⣿⠀⠀⠀⠀⢙⣿⣿⣅
⠀⠀⠀⠀⠐⠉⠻⠉⠀⠀⢀⣤⡾⠟⠁⢸⡇⠀⠘⣲⠤⢷⡔⣿⣿⠀⠀⣾⣿⠀⠀⣼⣿⠀⣼⣿⠀⠀⠀⠀⠉⢹⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⢸⣇⢀⣾⡿⠁⠈⡇⢿⣿⠀⠀⣿⣿⡀⢠⣿⣇⡴⢹⣿⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣤⣦⡀⠈⠛⠗⠀⠀⠀⢸⣿⢸⣿⡇⠀⢀⡇⠸⣿⣄⡼⠁⠻⠷⠏⠙⠛⣡⠾⣿⡏⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣤⣶⡄⠀⢸⣿⠘⣿⣇⢀⡼⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⣰⠃⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⠏⠁⠀⠀⣾⡿⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣿⠃⠀⣠⣤⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣰⡿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠻⠾⠟⠁⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠀⠀⠶⠀⠸⣿⠇⠀⠀⠀⠠⣤⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠴⠛⡿⠓⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⣾⡇⣴⣶⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣿⣿⠿⠓⣠⣤⣤⠀⢸⣿⠇⣼⣿⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠉⢸⣿⣿⠀⣸⣿⠟⢙⡇⣾⣿⠀⣿⡇⠀⠛⠿⠤⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⢸⣿⣿⠀⠸⣿⣿⠀⣿⡟⠀⣼⠁⣿⡇⢸⣿⠇⠀⠀⢀⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣀⣠⣬⣥⠀⠙⠻⠛⠁⠈⠿⠁⢸⣿⠀⠀⣰⡟⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⡄⢡⡄⠀⣿⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠘⣿⣿⠀⠀⣠⣤⡄⠀⣼⣿⢀⣿⠇⠀⣬⡍⠋⢡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⣿⠁⢹⢠⣿⡇⣾⣿⠀⣸⣿⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⣿⣿⢸⣿⡇⠀⡿⢸⣿⢃⣿⡇⠀⣿⣿⣠⡴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠏⠀⠻⠧⠞⠁⢸⣿⢸⣿⡇⠀⠈⢉⣩⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠟⠋⣀⣠⣤⣤⣤⣤⣤⣍⣀⠛⠃⠀⢠⡾⠋⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠉⠉⣉⣩⣭⣍⣙⣂⠀⠸⢧⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡏⠀⢰⡆⠀⣴⣿⠟⢛⠛⠛⠛⠛⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠶⠞⠁⠀⢿⣷⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠐⢦⡀⠀⣿⣿⠃⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⣴⣿⠇⠀⠀⢹⡀⣿⣿⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⡏⠀⠀⠀⢸⣷⣿⣿⠁⣴⣶⡆⠀⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣿⣿⠤⠤⠐⠂⡾⢹⣿⣿⡜⣼⣿⠃⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠂⠹⣿⡆⠀⣀⠞⠁⠈⣿⡟⢰⣿⡏⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⢉⣩⠥⣄⡀⠀⣀⠀⣿⣿⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⡟⣰⡶⠀⢻⣤⠟⠀⢿⡇⠀⣠⠞⢁⣤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⢀⡠⢼⣿⡇⠀⢸⠇⠀⠀⠈⠛⠛⠁⣴⡿⠁⠀⠀⢸⠂⠀⠀⠀⠀⢀⣴⡆⠀⢀⡀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⡁⠀⢸⣿⡇⣠⠏⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⢠⠏⠀⠀⠀⠀⠀⣼⣿⠁⠀⣿⣿⠀⠀⠀⢀⡟
⠀⠀⠀⠀⡠⠖⠉⠀⠀⣿⡇⠀⠀⠉⠉⠁⣠⢖⣪⡐⠲⣄⠀⣿⣿⣀⡤⠞⣡⡾⠛⠉⠛⡆⠀⣿⡏⠀⣠⣿⣿⠀⠀⢠⠞
⠀⠀⢀⡞⠀⠀⠀⠀⠀⣸⡇⠀⠉⣿⣿⡀⢿⣿⡟⠀⣀⣿⢺⣿⡟⠀⠀⣰⡿⠀⠀⠀⡠⠃⢰⠿⠧⠴⠃⣿⣿⢀⠔⠁
⠀⠀⠘⡄⠀⠀⠀⠀⣠⠟⠀⠀⠀⣼⣿⡇⢿⣿⠋⠁⣴⠃⠀⣿⡇⠀⣰⣿⡟⠒⠚⠉⠀⢀⡏⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠈⠀⠀⠐⠊⠁⠀⠀⠀⡠⣿⣿⠀⠈⠛⠗⠚⠁⠀⠀⠈⠛⠚⢩⣿⡇⠀⠀⠀⢀⡞⠀⠀⣠⠖⢉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣠⠋⠀⢀⡾⠁⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠊⠁⠀⠀⢾⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣷⠀⠀⢠⣾⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡏⠀⠀⣾⣿⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⢰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⡇⠀⠀⣿⣿⡄⠀⠀⢀⣤⣤⡀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⣷⠀⠀⣾⣿⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣿⣿⠀⢠⢿⣿⣇⠀⣰⣿⠟⠛⠟⢀⣨⣿⣿⣷⠀⠀⠀⣿⣿⣿⣄⡜⢿⣿⣄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡶⠃⢸⣿⣿⡀⣿⣿⡀⠀⠐⡏⠀⠈⢿⣿⣆⣤⠞⠁⠈⠉⠁⠀⠈⠉⠁⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⠈⣿⣿⣇⠙⠿⣷⣤⠞⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⣿⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⡇⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⡗⠀⠀⠈⠛⠛⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢀⣿⠃
⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⡶⠃⠀⣾⣿⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣤⠀⢸⣿⣿⡿⠀⠀⢀⣾⣿⡇⠀⣴⡆⠀⠀⠀⠉⠉
⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡟⠀⠀⢿⣿⡇⠀⠀⠈⣿⣿⡷⣠⣿⡿
⠀⠀⠀⠈⣿⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣼⣿⣿⡀⢀⡀⠉⠛⢃⠠⢶⣶⠛⠋⠁
⠀⠀⠀⠀⣿⣿⡀⢠⣿⡟⠀⣤⠀⠀⠀⡼⢿⣷⣀⣴⠏⠈⠛⠛⠉⠀⠀⡰⠋⠀⢻⣿⠃
⠀⠀⠀⠀⢸⣿⡇⣿⣿⣇⠀⢹⣧⡤⠞⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠸⣿⣷⠘⢿⣿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠸⣿⣧⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣿⣿⠀⠀⢠⣾⡿⠟⠛⠻⢿⣿⣄⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢹⣿⣧⣠⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⠀⢠⣿⡟⠀⠀⠀⠀⠈⣿⣿⠀⣿⣿⡄⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⣿⣿⠀⣾⣿⠀⠀⠀⠀⠀⢠⣿⡿⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣿⣿⠀⢻⣿⣄⠀⠀⠀⣠⣿⣿⠃⠀⣿⣿⣇⣀⣤⣄⡀⢸⣿⣿⠀⢀⣀⡀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⠿⠀⠀⠻⣿⣿⣶⣿⣿⠟⠁⠀⠀⢿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⡄⢹⣿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣧⠀⠀⠀⢠⣾⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⢀⣴⣶⣶⣶⣶⣦⡀⠀⢹⣿⡇⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⢻⣿⣇⠀⢠⣿⣿⠟⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⠟⠉⠀⠀⠙⣿⣿⡀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢻⣿⣷⣿⣿⠏⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢠⣿⡏⠀⠀⠀⠀⠀⣸⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣤⠀⢠⣿⡏⢸⣿⡄⠀⠀⠀⠀⢠⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠃⠈⢿⣷⣤⣀⣠⣴⣿⡿⠁⠀⢸⣿⣷⣶⣶⣶⣶⠀⣿⣿⣧⣤⣤⣤⡄⢸⣿⡏⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠛⠛⠃⠘⠛⠃⠀⠀⠀⠀⠘⠃





⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠷⡆⢰⣿⣭⣧⠀⠀⡀⠀⢿⣿⠇⢀⣀⡀⠀⠀⢰⣦⣤⡤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣻⣦⠀⢠⣏⠀⠀⣆⢻⠆⢹⡏⠁⣰⣿⢿⣷⡀⠇⣼⣿⢻⣿⣆⢠⡞⠀⣀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢦⡀⠈⣧⣤⣨⠿⣄⣸⠀⢰⣿⡏⢸⣿⠇⢠⣿⡟⠀⣿⣿⠀⣻⣾⣅⣠⠞⢩⣤⠄
⠀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⢠⣤⠀⠀⠀⢀⣤⣤⣀⠉⠀⣸⣿⣇⣿⡟⠀⢸⣿⡇⢸⣿⡟⠀⠋⣀⡀⠩⡤⠟⠿⠊
⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣿⣿⡆⠀⠀⣿⡇⠈⢿⣷⠀⣿⣿⣿⡟⠀⠀⢸⣿⣇⣼⣿⠇⠀⢰⣿⡇⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣠⣿⣿⡇⠀⣾⣿⡿⣦⣸⣿⣇⣽⣿⡏⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⣼⣿⡇⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠉⣿⣿⡇⠀⣿⣿⡇⠀⢹⣿⠏⠘⣿⣧⠀⠀⠀⠀⣸⣿⣿⠀⠀⣰⣿⣿⣷⡀⣴⣿⢿⣿⡇
⠀⠀⠀⠀⣀⡀⠀⣿⣿⡄⠀⢸⣿⣧⠀⣸⣿⣿⣤⣿⡟⠀⠀⠙⢿⣧⣀⣀⣼⡿⠋⠻⠷⡶⠿⠋⡈⠙⠛⠛⣁⣼⣿⣿
⠀⠀⠀⠰⣯⣿⡀⠸⣿⣇⠀⠈⢻⣿⣦⣿⠇⢈⣩⣁⠀⠀⢀⣀⡀⠈⠉⠉⣁⣤⣄⠀⠀⣤⠴⠺⣇⢀⣴⡿⠋⠁⣿⣿
⠀⠀⠀⢀⣬⣉⡽⠃⠈⠋⠀⠀⠀⠈⠉⠁⠀⠸⣶⣿⠂⣴⣿⠋⣿⡆⠀⣼⣿⠋⣿⣷⠰⣯⡖⣰⡋⢾⣿⡁⢀⣼⣿⠟⣶⣷
⠀⠀⠀⠻⡽⠟⢠⡆⢴⣦⡀⠀⠀⠀⣠⡴⠶⣦⣄⠀⢰⣿⡏⣸⡿⠁⢠⣿⡿⢀⣿⣿⠀⡟⠉⠉⠁⠈⠛⠻⠟⢛⣁⣴⣌⣉
⠀⠀⠀⢀⣼⠓⣾⢧⡄⢻⣿⣆⠀⢰⣿⣇⠀⠈⣿⣷⢸⣿⣿⠟⠁⠀⢸⣿⣇⢸⣿⡏⠀⠀⢀⣿⣿⠀⠀⣿⣿⣄⢹⡓⠆⢹⡀
⠀⠀⠀⠘⣇⠘⣁⣼⠄⠀⢿⣿⡆⣿⣿⡟⠛⠲⢾⣿⡿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⣆⠻⠖⠛⠃
⠀⠀⠀⠀⠿⠋⢁⣴⡾⠟⢻⣿⣿⢸⣿⣧⠀⠀⣼⣿⠇⢻⣿⣆⠀⠀⠀⢸⣿⣿⠃⠀⠀⢠⣿⣿⣿⡄⢠⣿⡿⢻⣿⡆
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⢠⣿⣿⠀⠙⠿⠷⠾⠿⠋⢀⠀⠙⢿⣦⣄⣴⣿⠟⠻⣷⣤⣴⡿⠟⠉⠻⢿⡿⠟⠁⠸⣿⣷
⠀⠀⠀⠀⠀⢿⣿⡇⠀⢀⣾⣿⠏⢀⡴⠂⠀⣰⠶⢖⣫⣷⣦⣄⡀⠩⢥⣄⣀⣀⣀⡴⣄⣀⡀⠀⠀⢀⣤⣶⠶⠾⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠿⠷⠿⠛⣡⣤⡟⠀⢴⡞⠋⡴⠋⣹⡀⣿⠈⠙⢦⡀⠀⠙⣿⡛⠲⠈⢹⠃⠀⣼⣿⠋⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣻⣿⠀⠀⣇⣀⣀⣸⠉⢁⣿⣄⡀⠀⣿⣿⣿⡆⣹⠴⠶⢼⡄⠀⠻⢿⣦⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠟⠁⠉⠉⠀⢿⣿⢿⡷⠀⠙⠿⠜⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣠⣰⣶⡖⠀⠀⠀⠀⠙⠉⠁⠃⠃⠀⠀⠀⣺⣶⡂⣠⡀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣩⡶⣻⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢝⡿⢭⣉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⣹⠣⠀⠀⢤⡤⠠⠄⡖⠆⠀⢲⡖⣦⢠⡀⡤⠄⠀⠀⢿⡌⠙⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣉⣀⠀⠀⠀⣿⠘⡇⠳⡄⠀⢸⡇⡿⢹⢳⡇⠀⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢹⡇⠀⠀⠙⠀⠁⠉⠁⠀⠈⠁⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠀⢸⡀⠀⠀⠛⠉⠀⢀⡤⡄⠀⢠⡔⣤⠀⢀⡴⠛⢳⠄⢠⡖⢢⡀⠀⣤⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣯⠀⠈⠛⠶⠦⢤⣤⣀⠸⡟⠁⢀⣿⣰⢻⡄⡸⠓⠲⣤⠔⢾⡗⢺⠗⣻⡷⢛⡇⠀⠀⠈⣿⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢠⡖⠀⠀⢹⡆⠙⠒⠋⠉⠁⠀⠉⠀⠠⣏⠞⠀⠘⠷⠋⠀⠙⠁⠘⠧⠴⠃⠀⣺⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠤⠚⣀⠀⣤⣄⠀⠀⢀⡴⠲⡄⠀⣀⠀⠀⣴⡦⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠉⢷⠘⣧⢸⠀⠀⣼⠃⢠⢇⡾⠉⣷⠀⣟⡹⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢰⡄⠀⠀⢠⠀⠀⠘⠇⠙⠋⠀⠀⡿⢀⠎⣸⡇⢠⡏⠀⠉⠀⠙⠒⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠙⣗⣿⡊⠀⠀⠀⠰⣦⠀⠀⡤⢤⡀⠘⣧⠎⠀⢻⣇⡾⠀⠀⠀⢀⡀⠀⠀⠀⠰⡇⠀⣼⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠑⡾⢿⠂⠀⠀⠀⠀⠘⣇⣠⣷⢦⣷⠞⢷⠀⠀⢸⡟⠀⠀⣴⠀⣼⣿⠀⣠⠄⠨⡿⡾⢇⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡃⠀⠀⣀⡴⣿⠁⢿⣄⡟⠀⠘⢧⣤⠏⠹⣄⣰⠛⠚⣣⣿⠛⠁⢀⣈⡟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⡟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⢁⡟⠀⠀⠸⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠰⣼⣄⣠⢀⠀⠀⣶⣄⣶⠀⢀⢀⡍⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠝⠿⠓⠀⠘⠿⠃⠀⠚⠟⠝⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣥⣤⣬⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⡿⡿⢯⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣷⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣁⣽⡿⠋⣽⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⡟⠉⢻⣿⣿⣿⠁⢸⣿⣿⢋⣿⣿⠟⠉⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⡿⠀⣾⣿⣿⣿⡟⠀⢾⣿⠇⢸⣧⣿⣿⣶⡟⠛⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⣸⣿⡇⢸⣿⣿⣿⣿⣇⠀⣾⣿⠀⢸⣿⠋⣿⣿⣇⡀⠀⠹⣿⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢀⣾⣿⠀⢸⣿⠏⣨⣯⣷⡀⢻⣿⠀⣼⣿⡀⠘⠿⢻⣿⣄⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠻⣿⠇⢸⣿⣿⠀⢸⣿⡀⠛⣻⣿⣷⣤⣵⡄⢸⣿⡿⣤⣴⣿⡿⠛⣆⠀⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣿⠀⣼⣿⣿⠀⢸⣿⣿⣿⠽⣿⣿⣿⣿⣿⣦⣭⣾⣿⣄⣿⣷⡀⠸⣆⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢀⡿⣿⣿⣇⠈⠿⢿⣯⣷⣿⠟⣿⣿⣶⣿⣿⣿⠁⠸⣿⣿⣧⠀⢻⡆⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠃⣼⠿⣿⣿⣻⢷⣶⣿⣿⣿⠃⣼⣿⡟⢡⣽⣿⣿⣄⡀⠙⣫⣿⣧⠈⣿⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣵⠋⡗⣽⡿⠀⢀⣾⣿⡇⠀⣿⣿⡇⠘⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⢹⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣶⣼⣷⣯⣶⡟⠁⢀⣾⣿⣿⠁⢈⣿⣿⣿⡀⠙⣿⡟⠋⢿⣿⣿⣿⣿⣧⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠀⣠⡿⠻⣿⣿⠀⢸⣿⣿⣿⣷⡄⠘⢧⣶⣿⡿⣿⣿⣿⡿⣸⡇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣭⣁⣤⣤⣾⡟⢀⣴⣿⣿⡇⢸⣿⣋⣻⣿⣿⣦⣄⠙⠛⣹⣿⣧⣍⣵⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣙⣿⣧⣘⣻⣾⣿⣷⠀⢿⣿⣿⣿⣿⡿⠻⢿⣿⣿⡿⣷⣭⣵⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⠛⣾⣻⣷⣌⣛⣯⣿⣿⣤⡧⡀⣿⣿⣦⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁


⣶⣶⢶⢶⢷⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⡾⣶⡶⣶⣶⢷⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡵⠒⡄⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⢣⣿⠁⢠⡧⠁⠀⠀⠀⠀⢠⣼⡇⠀⢀⣾⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣾⡇⢠⠏⠀⠀⠠⣪⠵⣄⠘⣿⡇⠀⠀⣿⠃⠀⣴⡆⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⣿⠖⡱⠊⢹⡇⣼⡏⡴⠢⡄⣿⡇⠀⠈⣿⣤⠀⣿⠂⠀⣼⣇⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠄⣿⣸⠁⠴⣾⠃⣿⠛⣧⡀⡇⣿⠃⠀⠀⣿⢬⠀⣿⠀⠀⢿⣿⠀⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡇⠀⣼⠁⠀⢻⣇⢈⣴⡁⢿⡀⢀⡀⣿⠀⠀⠨⠷⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⢰⣇⠀⣰⠆⠙⠛⠋⠀⠈⠉⠉⠀⠻⠤⠴⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠀⠀⠀⠀⠫⠒⠉⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⣰⢊⠑⠆⠰⣾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡿⠀⠀⠀⠀⢿⡈⠓⣁⣳⠃⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⠿⣾⠁⣠⣮⠤⡄⠨⣸⡇⠀⠀⢠⣶⠀⠉⠚⣫⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠋⠀⣠⣿⢈⣿⢁⣀⡃⠀⣿⣧⠀⠀⣾⡇⠀⠀⢴⣿⡃⠀⣾⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⢿⣿⢸⡏⠸⠇⢸⡄⣿⡟⠀⠀⣿⡇⠀⠀⢸⣿⡇⢠⣿⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠒⢺⣇⠈⢿⡀⢀⣾⠀⢻⡇⠀⠀⢹⡇⡀⠀⠀⠙⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣼⠇⠳⣄⠉⠛⠁⠀⠈⠙⡛⠋⢸⡇⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣕⣀⣪⢾⡻⠁⠀⠈⠻⣶⣠⡤⢄⣸⡟⠀⠈⠷⠶⠃⣠⠤⡀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢀⣦⠀⠀⠀⠈⠉⡋⠁⠀⠀⠀⠀⠀⢸⡏⠰⠃⢸⡇⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⡠⢄⣅⠤⡀⠀⠀⠀⠀⠈⠳⢤⣤⡟⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⡀⠁⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⢖⡒⢌⢢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⠬⠟⣸⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠚⠁


⣿⠿⠿⠿⡿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⣤⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠹⣷⠀⢠⡇⠀⠀⣸⡿⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢿⢿⣆⠀⠀⢻⣇⢸⡇⠀⠀⣿⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠙⢿⣄⠀⠀⢸⣄⣿⣧⡀⠈⣿⣼⠀⠀⢸⡿⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⣠⠿⣧⡀⠈⡇⠀⠙⣿⠄⠸⠿⠀⠀⠾⠧⣤⣴⠇⠀⠀⠀⢀⣴⠋⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⠈⢿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠉⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣷⠄⠀⠀⠀⠀⣠⡤⢤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠀⠀⠀⠈⠙⠲⢄⣀⡴⠋⠀⠀⠈⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢀⡟⠓⠦⠤⠤⠔⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡇⣰⡞⠙⢦⢸⡇⠀⠀⣿⠀⠀⠹⣇⢀⡞⠀⠀⠀⠀⠀⠔⠈⠁⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢼⡇⣿⠀⠀⢸⢸⡇⠀⠀⣿⠀⠀⠀⢹⡞⠀⠀⠀⠀⡔⠺⠤⠤⣀⠔⠒⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇⠹⣆⣠⠟⢸⣇⣀⡆⣿⣀⡰⣀⢈⠃⠀⠀⠀⢸⠁⡀⠀⠀⢀⡁⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠁⠀⠈⠉⠉⠀⠉⢉⡞⠁⠀⡇⢠⠖⢢⠀⠀⠑⠚⠓⠊⠀⠈⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⣼⠁⣠⠎⠀⢸⢀⠇⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣻⣇⣰⠀⠀⠀⣀⡿⠊⠀⠀⠀⢸⡏⠀⠀⠀⢀⡇⢀⡾⡆⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠂⠉⠈⠓⠁⠈⠉⠉⠀⢧⠀⠀⠀⡠⠊⠙⠦⣀⡠⠊⢈⠝⢺⡗⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣒⣉⣀⠀⠀⠀⠀⠀⢰⠁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠊⠀⠀⠀⡔⠉⠉⠙⢆⠀⣠⠴⠊⠉⠀⠀⠈⢳⠀⠀⠀⠀⠸⣀⠜⠁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣠⠤⠞⢫⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⡆⣿⠀⢻⠀⣿⠙⣦⢸⡇⣼⡋⢱⠞⢹⡏⠳⢹⣇⠀⣸⡇⠀⣸⡇⠀⣴⡋⡳
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡀⣿⠶⢾⠀⣿⢾⡋⢸⡇⠸⣧⡀⠀⢸⡇⠀⢸⠙⣴⠏⡇⠀⣇⣿⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠴⠃⠿⠀⠼⠀⠧⠘⣧⠾⠏⢱⠘⣷⠀⠸⠇⠀⠼⠄⠉⠀⠇⠸⠀⠸⠇⠫⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠠⣶⠶⣾⢐⡏⣿⣉⠀⠀⢀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢹⠆⠐⢻⠋⣿⠻⣧⡀⠀⠀⣿⠀⣿⢻⡇⣿⣀⠀⠀⢈⡳⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⣿⠀⣿⣀⣸⠇⠀⠀⠟⠀⠋⠈⠁⠉⠁⣀⠀⠠⣍⣏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⡀⠀⢀⡤⠲⡄⢠⣗⠌⣽⠃⣙⢾⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⣤⠀⠘⣿⠀⠀⣀⣄⠀⢠⡴⢲⣶⠀⢿⣄⢠⣿⠧⢠⠇⣿⡟⠀⣿⠀⠈⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣿⠀⠀⣿⠀⣼⠅⠁⣠⣿⢁⣾⡿⣰⢣⠻⡆⠻⠴⠊⠀⠈⠀⠀⣿⠀⢀⣠⠤⠒⠂⠒⢦
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠰⠋⠀⣸⡿⠀⢿⡤⠔⠉⠻⠛⠀⠉⠁⠈⣊⡥⠴⠶⠲⠶⠶⢤⣄⣽⣞⠉⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣀⡴⠟⠁⠀⣀⠀⢀⣤⣄⢠⡶⠆⢠⡞⠁⠀⠀⠀⠀⢀⡠⠞⠉⠙⣦⠙⠂⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠐⣾⠛⡾⢹⡇⢸⣧⣿⢸⠗⠀⠘⠷⣤⣀⡤⠴⠚⠁⠀⢀⣀⡀⠋⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⠸⣇⣸⠇⢸⡧⠟⠻⠶⠂⠀⠀⠀⠀⠀⣴⠚⢳⣠⡟⠀⢹⠀⠰⣿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⢚⠀⠀⠀⠋⠀⠉⠁⠀⣀⣀⣀⣤⣴⡾⠋⠀⠀⠀⣾⠃⠀⣼⡿⠀⢠⠇⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢢⣻⡗⣉⠀⠀⣠⠴⠖⠚⠋⠉⠉⠁⠀⣾⡟⠀⠀⠀⠀⣼⡇⢀⢼⣿⠁⡰⠃⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢦⣹⣯⠖⠀⣾⠁⠀⠀⣰⡆⠀⠀⠀⣼⡟⠀⠀⠀⠀⢰⣿⠔⠋⢸⡟⠊⠀⢰⡶⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠺⣷⠊⠀⠙⠓⠒⠛⠉⠀⠀⠀⣸⡿⠁⣠⠆⠲⡄⣼⡇⠀⠀⣿⡇⠀⢠⣿⡇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡾⠋⢻⡇⠀⢰⡿⠁⣼⡿⣄⢠⡧⢿⡇⢀⠜⠻⣧⠴⠃⠻⣧⠞⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠞⠁⣠⡿⠁⠀⢿⣇⣠⠟⠀⠈⠉⠁⠀⠀⢀⣠⢤⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⡟⠁⢀⣀⣤⠤⠤⠄⠀⣀⣀⣀⣠⡞⠁⢀⣸⠟⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠴⠞⠋⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠣⣀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⢒⡒⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠎⠀⡀⠉⠁⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠃⣎⢨⠆⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⡀⠀⢎⡁⠀⠀⠀⠀⣶⣾⣶⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣷⣶⠊⠉⠁⠀⠀⠀⠈⢻⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠐⡤⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢄⣊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡞⢀⣀⠠⠤⠠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣉⣙⡽⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡴⡶⠉⢀⣠⣤⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⢺⣸⠀⠀⠀⠀⠀⢀⡴⣿⡿⣋⣤⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠰⣰⡹⠂⠀⠀⢀⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣹⢗⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠲⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣾⣇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢲⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢲⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠐⠎⡞⠁
⠀⠀⡠⢒⠲⢈⠉⠉⠙⠒⠒⠦⡤⢄⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⡔⡸⠁
⠀⠪⡞⠕⠠⣀⣦⢄⣀⣀⣀⣰⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡠⢱⣧⣤⣤⣄
⠀⠀⠉⠘⠊⠀⠀⠀⠈⠁⠀⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋⠀⠀⠀⠃⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢖⣋⠭⠭⢗⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⠔⠋⠤⠤⢀⠀⠈⠪⡻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡴⠃⠀⠀⠀⠀⠀⢡⠀⠀⢡⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠞⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢧⣀⣀⣴⣿⣥⠀⠀⣀⡀⠀⠀⠉⠁⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣈⡥⠼⠛⢋⣉⣁⣀⣶⣉⣑⣦⡀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢛⢙⠏⠛⣉⣱⢀⠄⢉⠙⣿⣙⠻⣷⣌⠓⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡻⠘⣤⠿⠟⠺⣐⣿⣷⠏⠉⡲⠀⡹⢧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⡷⠚⠁⠀⠀⢀⣉⠉⠙⠀⡴⡁⢀⣛⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⣀⣀⠀⢉⡷⠀⠈⠛⢱⣯⣭⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠙⠓⠛⠉⠉⠉⠉⠛⠻⣥⣒⣒⠒⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠠⠤⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣂⠀⠀⠈⠙⠂⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⡄⣀⣀⡀⠠⠄⠀⠀⠀⣀⡞⢙⠂⢤⡥⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢒⡦⡤⠶⠦⣬⠰⠚⠁⡙⠻⢦⣤⣧⡴⠞⢢⡀⢄⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣄⠀⠀⠀⠙⠺⢦⡀⢆⠀⡄⠀⢻⠳⣦⡀
⠀⠀⠀⣀⠴⠚⢋⣁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡹⣄⠘⢧⡈⠙⢦⣄
⢀⡴⠋⠁⢠⡴⠋⠀⠀⠀⢰⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢳⡦⠿⠃⠀⠙⢷⣄
⣿⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠙⣧
⠹⣦⢠⡿⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⠃⠀⠀⠈⢷⡀⠀⠸
⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠁⠀⠀⠀⠀⢸⣧⠀⢠
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣤⡾
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢟⢦⣷⡀⣠⠀⠀⠀⠀⡠⠄⠀⣀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆⣻⠀⠉⢷⡘⠀⠀⣰⡟⡗⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡰⠊⡿⠀⠀⠈⢿⣧⡾⢟⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇⠧⣇⠀⠀⠀⣼⠷⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⡀⠀⠘⡶⢷⡀⢰⡀⢹⣆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⠢⢍⡛⠻⠾⣶⣮⣷⣌⣷⣈⢻⣅⣉⠲⡀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡶⠞⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠐⠂⠤⢤⣉⣉⢉⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣉⣉⣡⣤⡴⠾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⣤⣄⣀⠀⡔⠁⣾⠉⣿⠉⡟⡏⢙⡟⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠛⠻⠿⠿⣶⣿⣤⣿⣥⣾⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣤⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⢀⣾⠃⠀⠀⠀⠉⡏⠉⠉⠉⠋⣻⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠉⠁⠀⠀⠀⠀⠀⢻⠦⣤⣦⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣛⠀⠀⠀⠀⠀⠀⢀⡏⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣁⣩⠀⠀⠀⠀⠀⢰⠋⣀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⣷⠀⠀⠀⠀⠀⡆⡀⢳⡄⠉⠶⠤⠄⠀⣀

⠀⠀⠀⠀⠁⠀⠀⠰⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⢤⣀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠘⢫
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣀⠀⠀⠉
⠀⠀⠀⠐⠢⠤⡤⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡛⠦⡔⣀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣷⣦⣭⣡⢀⣼⣿⣀⠀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠀⠀⢀⣤⣾⣿⣏⠻⣿⣷⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡡⠀⠀⠀⠀⠀⠀⠙⢻⣯⣤⣤⣶⡿⠛⠛⠛⢿⣿⣿⣿⣿⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠤⢶⣶⡆⣤⣄⠀⣠⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣭⣽⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⣿⡀⠀⠀⣀⣠⣤⣸⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⠎⠀⣼⣿⣿⣿⣿⣆
⠀⢫⡗⣋⣩⡛⣿⣯⡶⠶⡶⣠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣠⣴⣿⠛⠅⢀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠁⠊⠉⠀⠀⠀⣾⣾⣿⣿⣿⡟⠁⠀⠀⠀⢀⣰⣶⣿⣿⣿⠗⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢧
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣀⣠⣴⣶⣿⣿⣿⣿⣷⣶⡤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠺⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠇⠀⣸⣿⣿⡟⠋⠉⠀⠉⠉⠛⠛⠛⠛⠓⠛⠛⣿⣿⣿⣿⣿⣿⣭⣿⣿⣧⣽
⠀⣠⣤⣄⣠⣴⣿⣿⣷⣬⣣⣶⣿⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡶⠁
⠀⢶⣬⣙⠛⠋⠀⢈⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⢡⣦⣿⣿⣿⣿⣿⡿
⠀⢼⣿⣿⣿⣄⡴⣻⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣍
⠀⠘⢿⣿⣿⣿⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠨⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⠤⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠓⠀⠀⠀⠈⠛⠛⠛⠉⠉⠉⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢤⠠⣄⡀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠪⠐⢀⡡⢒⠔⣩⢿⠏⣠⡗⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⡀⡤⠀⣠⠠⢴⠂
⠀⠀⠀⠀⢀⡀⠀⢀⡤⢋⡔⢁⠔⢡⡟⠔⢡⡇⢀⡞⠀⣠⠖⠀⠳⢤⠞⠀⠆⡤⠀⠀⣠⠀⠀⢠⠄⠁⠰⠈⣀⠴⠋
⠀⠀⠀⢔⠉⠁⠀⠲⠳⠃⠀⠎⣠⡟⠜⢀⡾⠀⡟⠀⢰⡇⠀⠀⠠⣏⠀⠀⢸⡁⠀⠐⣇⢀⢠⡎⡀⠊⠘⠩
⠀⠀⠀⢔⢀⠀⠀⠀⢀⡀⠈⠛⠋⠀⠈⠉⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠣⠠⣄⣀⡹⡂
⠀⠀⠀⢱⡈⠀⠀⡴⢋⠏⠀⢠⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡜⢀⡼⠁⠀⠀⠀⡀⠀⠀⠁
⠀⠰⠉⠈⠝⢀⡾⠗⠁⠀⠀⡿⠀⠀⠀⣄⡴⠀⣨⠀⢠⠀⠀⢀⡾⠣⢠⡶⠀⡄⠠⡈⠉⣀⠀⣀⠀⢸⡏⠀⠀⠔⠂⣤⠆
⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⢴⡇⢰⠀⠀⢸⠁⢰⡏⢀⡈⣷⠊⢹⡁⣠⡟⠀⡼⠁⢸⠁⡞⠁⢸⠁⠀⠀⣻⠂⠠⠊⠉
⠀⠀⠀⠀⠀⠘⠷⠖⠊⠁⠚⠀⠙⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡶⡒⠀⠀⠀⠈⠠⣄⢜⣀⢠⠒⠀⠀⠀⢀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠢⠈⠀⠀⠀⣀⡤⠘⢳⠓⢄⠀⠀⠀⠀⠱⣅⣢⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣓⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠒⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠒⠀⣀⠑⢦⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠓⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠉⠀⠡⠂⠀⠀⠈⠁⠺⡄⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢆⡀⠁⠀⠀⠀⡇⢀⠔⠉⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⣈⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢟⡆⡁⠠⠊⠀⠀⠀⠀⠀⢀⡤⠠⢀⠀⠀⠀⢱⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠎⠀⡠⠔⢢⠀⠀⠀⢀⡎⠀⣸⣿⡇⠀⠀⠔⠀⠀⠘⣄⢀⡰⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠜⠀⢸⠀⣼⣿⣇⠀⠀⠘⠤⠤⠛⠋⡁⠀⢎⠀⠀⢀⠀⡇⣌⠁⠠⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠚⠈⠐⠚⡫⠷⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⡇⠀⠈⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⡲⠄⠀⠀⠘⣇⣀⡰⠖⠺⢔⠢⠄⣀⠀⠀⠀⢠⠒⠒⠦⣴⠚⠑⠲⡌⠲⣄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⠐⠹⣄⣠⠔⠊⠘⠀⣧⠀⠀⠀⠁⠀⠀⠀⠀⠐⠃⠀⢄⡀⠀⠱⠀⠀⠁⠀⢻⠳⣄⣠⠘⠛⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡽⢄⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⢄⡀⠈⠃⠀⠀⢀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠛⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠃⠀⠀⠀⠂⠐⠁⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠡⡀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢆⠀⣇⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⢀⣀⣀⡠⣜⡄⠀⠀⢀⣼⡀⠀⣦⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⢠⡟⠳⢤⣀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣌⠉⢰⠋⢀⠴⠚⠉⠀⢳⡀⠌⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡸⢿⣄⠀⠀⠀⠁⠀⠙⡄⠆⠀⠀⠀⠀⠀⠠⠤⠃
⠀⠀⠀⠀⢠⠏⢻⠀⠀⠀⠀⢀⠀⠉⢻⠇⠀⠀⠀⠀⠀⠀⢳⣄⠀⠸⠀⠀⠀⠀⠀⢠⠞⡅⠀⠙⠳⢤⡀⠀⠀⠀⠘⡀⡄⡸⠀⠀⠁⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠃⠄⢤⠀⠘⢄⠀⠀⠀⠀⠀⠀⠈⠓⢆⠀⠀⠀⠀⣴⠋⢰⡤⢄⠀⣠⠀⢘⡄⠀⠀⠀⡷⢡⠃
⠀⠀⠀⠀⠈⢆⣀⠀⠀⠀⠘⠶⠊⢸⠇⠀⠈⠑⠤⣀⣀⠀⠀⠀⣄⠈⡀⠀⠀⠀⠿⣄⠘⠞⠀⠇⢉⠀⠊⠀⠀⢀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⢈⡅⠒⠤⠤⠤⠖⠋⡰⠀⠀⠀⠀⠀⡏⠑⢤⠀⠈⡆⠈⢄⡠⢄⡀⠀⠀⠀⣠⠇⠈⠳⠤⢤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⢄⣠⡤⠞⠁⠀⠀⠀⢀⠼⢃⡤⠾⠒⠊⠁⡼⠀⠉⠐⠛⠛⠋⠉⠓⠀⠀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⣁⣀⣀⣀⣀⣠⢴⡏⣠⠀⠀⢀⡴⠖⠾⣥⣀⠀⠑⣤⣀⠀⢀⣀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠘⣧⠘⢆⡀⢟⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠂⠂⠀⠀⠂⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⠈⠀⠑⠘⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠛⠛⠛⠛⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⠀⠀⠀⣆⠒⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠀⠀⠠⠉⠅⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠀⢠⣷⠀⠀⣠⠤⠀⠀⠀⠀⠀⠘⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⣀⠀⠀⠈⠀⠀⣼⣿⠀⠇⠀⣀⠀⠀⢀⣀⡀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠰⠆⢀⣾⡟⠃⠀⠀⠀⢰⣿⡇⠐⠀⣼⡏⠀⠀⠚⢿⠇⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣤⠄⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⠁⡄⠀⠀⠀⠀⣶⣿⣧⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣼⡏⠀⠀⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⣿⡀⢰⣶⡆⠀⠀⠙⢿⣿⣷⡀⢠⣦⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢰⣿⠃⠀⢸⣿⠄⠀⣰⡿⠂⠒⠘⣿⡄⠀⣿⣿⠀⠀⢿⣧⡀⢀⠆⠈⢻⣿⣷⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣠⡀⠀⣾⡏⠀⠀⢼⣿⠀⠀⣿⣇⣀⠀⠀⠙⠿⠶⠻⣿⡀⠀⢈⡿⠿⠋⠀⠀⣀⢻⣿⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠨⠿⡏⠀⣿⡇⠀⠀⢸⣿⠀⠀⠈⠉⢡⠀⠀⠀⠀⠀⠀⠙⢧⣤⠞⠀⢰⠎⠄⠹⣿⡆⢻⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠘⣿⡇⠀⠀⠈⡱⠖⠠⠀⠀⠀⢰⡦⠀⠀⠀⣠⣤⠁⠀⠀⢻⣿⡄⢻⣿⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⡏⠠⠊⢀⠀⠙⢿⣦⠆⠀⠀⠘⢠⡞⠀⠀⢀⣀⠀⠀⠀⣿⣿⡄⠀⢀⠀⢿⣷⠀⢿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢶⠟⢁⡠⢄⡀⠑⠤⣀⢀⡀⠀⠀⢰⣿⠁⠀⠀⣿⠉⠂⠀⠀⠘⠻⣿⡶⠋⠀⠈⣿⡇⠘⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⡋⣾⡇⡅⠀⣰⣿⡿⠁⠀⠀⣿⡟⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢿⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠰⠋⠙⠀⠙⠂⠚⠁⣴⣿⡿⠁⠀⠀⢸⣿⡇⠀⠀⠀⢻⣿⡀⠀⣀⣴⣀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢁⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠻⣿⣄⠸⠛⠏⠀⠀⠀⠀⠀⠀⢻⠀⡼⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⣀⣀⣤⣾⣿⠿⠋⢠⣾⠏⠍⠆⢸⣿⡇⠀⣀⡀⠀⠀⠙⢿⣦⣀⠀⣠⡆⠀⢠⣄⣠⠇⢠⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⠉⠁⠀⠀⠀⣿⡏⠀⡰⠀⠀⣿⡇⠀⠙⠃⠀⢀⠃⠀⠉⠻⠿⠋⠀⠀⢦⣈⣁⡤⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠘⠛⠀⠀⠙⠛⢉⠀⡠⠀⠸⣿⡀⠀⠀⢀⠊⠀⡴⠒⣢⡀⠀⢀⣤⠀⠈⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⢀⣈⣷⡥⠴⠀⠈⠻⠶⠒⠁⠀⠀⡃⢬⠟⡇⠀⠀⠉⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠆⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠤⣄⣀⣀⣀⣀⠤⠤⠴⠒⠚⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⢠⡟⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣾⠥⠚⠀⠀⢿⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠁⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⡀⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣰⡏⠀⣼⡇⠀⠀⠀⠀⣠⡀⢀⡤⠀⠉⠉⢒⠞⢤⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠸⠁⠀⠀⠀⠔⢀⣿⠀⢠⣿⢀⠌⠀⠀⣾⣡⢣⡟⠐⠀⠀⠀⠐⢄⣠⠇⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⣀⣀⡀⠀⠀⣼⡏⣀⣼⡟⠁⠀⠀⢰⡟⠁⣼⠇⠀⣤⠀⢰⡆⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠀⣰⡤⢶⣿⠉⢠⣿⣰⡶⠁⣦⣿⠀⢠⡟⠀⣠⡟⢀⣿⠀⢀⣴⡾⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⠞⢹⠀⣸⡇⠀⣼⡇⢻⡀⢠⠊⠿⠐⠘⠃⠊⠈⠃⣹⣷⡾⠟⠉⢀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡼⢀⣿⠁⠀⣿⠀⠀⠤⢄⠀⠀⢠⠖⠆⣠⡴⢟⡟⣡⡞⠁⣰⠋⡘⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⠊⠀⣼⠏⠀⠀⣿⡀⠀⠀⢠⠀⢀⣾⠎⢸⠋⢀⠞⢁⣿⠠⢠⡿⠊⢀⠀⢠⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⠋⠀⠀⠀⣈⡛⠒⣂⡴⠞⢹⡇⠀⣠⡡⢤⠀⣸⡏⠀⣼⠃⠀⡿⠀⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⣼⠿⠉⠀⠀⣾⠃⢸⡇⠈⡸⠁⣿⠁⠠⢿⠀⠘⠧⢰⡟⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢸⠃⠀⠀⠀⢰⡿⠀⠈⠓⣀⣥⣄⡀⠀⠀⢀⣀⣀⣠⣾⠷⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⠊⠀⠀⣿⠏⠁⠂⣾⠋⠀⡠⠞⡏⠉⠉⠉⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢰⠀⢰⡟⠀⠀⠸⣿⠱⠸⡁⡠⠁⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⣠⡿⠁⠀⠀⠀⠙⢦⡇⠈⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣏⠀⠀⠀⠀⠀⠀⡼⠉⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢐⣾⣷⠀⣠⡄⠀⠀⣠⣤⠀⠻⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠈⠀⠀⠈⠀⠀⣰⡟⢸⠁⠀⣴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣿⠀⠀⣠⣤⠀⠀⢀⠀⠀⠀⢀⣿⣡⠏⠀⣼⡇⣰⠃⠀⠀⢀⡀⠶
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣸⡏⠀⠀⣿⡏⠀⠀⣯⠙⢦⢀⣸⣿⠁⠀⢠⣿⠖⠁⢸⣿⠀⣸⡇⠀⣶⡆
⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⣿⡇⠀⢸⣿⠇⠀⢀⣤⡍⠹⡏⣿⡇⠀⠀⢸⣿⠀⠀⣸⡿⠀⣿⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⣿⣧⣤⢼⣿⠀⠀⣾⡿⠀⢀⡇⢻⣿⠀⠀⣼⣿⡀⢀⣿⣇⡼⢹⣷⠾⠛⠛⠛⠃
⠀⠀⠀⠀⠀⢠⣄⠀⣀⣤⢾⣿⡇⠀⢸⣿⠀⠀⣿⣷⠀⣸⠃⠘⢿⣦⣼⠃⠻⠿⠟⠘⠛⣱⢻⣿⠀⠀⠀⣠⣤
⠀⠀⠀⢠⡄⠘⠿⠟⠋⠁⢸⣿⣇⠀⠈⣿⣧⣼⠋⠛⠟⠃⠀⢀⣀⠉⠁⠀⠀⠀⠀⠀⣸⠁⣼⣿⠀⠀⠀⠉⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠉⠁⠀⠀⠀⠀⣴⡏⢸⠀⣴⠚⡆⠀⠀⠀⢻⣴⣿⠏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⢰⣿⢀⡞⢸⡏⢀⠇⢀⠀⠀⣀⠉⠁⠀⠀⠀⣶
⠀⠀⠀⠀⢐⣾⣿⠁⠘⠃⠀⠀⣀⡴⢾⠃⠠⡖⠦⡄⠀⣸⣿⠊⠀⣿⡷⠋⠀⣿⡇⢨⣿⠀⠀⠀⠀⣹⣿⣯⡀
⠀⠀⠀⠀⠈⠈⠃⠀⠀⢠⣴⠟⠋⠀⣼⡄⠀⣹⡒⠺⡖⣿⡇⠀⠀⣿⡇⠀⢸⣿⠁⣼⣿⠀⠀⠀⠈⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⡇⣼⣿⠁⠀⡇⢸⣿⠀⢰⢻⣧⣀⣾⣿⡼⢉⣿⡶⠶⢶⡄
⠀⠀⠀⠀⠀⠰⣿⡇⠀⠈⠉⠀⠀⠀⣿⡇⣿⣿⠀⢀⡇⠈⠿⣶⠏⠀⠙⠋⠀⠀⡴⠋⣿⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠀⢰⡿⠛⠃⠀⣿⡇⠘⢿⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⣿⡇⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢻⣤⣾⠟⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠴⠟⠁⢀⡀⠀⣶⣦⠀⠀⠀⢀⣠⡆⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡉⠁⠀⠀⠀⡨⢿⡿⠄⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⢀⣴⣶⣆⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⢻⣇⠀⠀⠀⣿⣯⠀⠀⠀⣹⡇⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣽⣿⡁⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⢾⣿⣶⣶⣾⠋⠹⣷⣶⣾⣿⡇⠀⠀⢀⣼⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣶⣶⣿⠏⠹⣿⣶⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣦⣀⠀⠙⠻⣿⣿⣶⣾⣿⡿⠟⠋⠀⣀⣴⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣶⣤⣛⠻⠿⠿⠟⣃⣤⣶⣿⡿⠛⠋⠉⠁
⠀⠀⣰⣶⣤⣤⣾⣿⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠉⠻⣿⣷⣦⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⣴⣿⡿⠟⠋⠁
⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠿⣿⣶⣤⡀
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣾⡿⠛⠉⠀⠀⠀⠀⠉⠛⢿⣷⣦⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠉⠛⢿⡿⠛⠛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣴⣿⣿⡆
⠀⠀⢠⣤⣤⠀⠀⠀⠀⢠⣿⣦⣀⣤⡟⢳⣤⣀⣴⣿⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣾⣿⣿⣿⣧⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣼⣿⣿⣿⣿⡄
⠀⠀⣼⣿⣿⣧⡀⠀⠀⠀⠹⣿⢿⣿⣤⣴⣿⡿⣿⠋⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠙⠿⠿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠟
⠀⠀⠻⠿⢿⣿⣿⣦⣄⠀⠀⢿⣾⣿⡿⣿⣿⣷⡏⠀⢀⣠⣴⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡟⠉⠀⠉⢹⣿⠉⠉⠉⢹⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣬⡻⣿⣿⣿⡿⢟⣥⣶⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣴⡟⠹⣦⣤⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣯⣽⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣿⣿⣦⣦⣿⣿⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣷⣿⠿⣿⣿⡿⣿⣾⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⠿⠋⠁⠀⠀⠈⠙⢿⣷⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⡿⠛⠁⠀⠻⢿⣿⣿⣿⣿⣿⠿⠀⠈⠙⢿⣿⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣴⡆⣤⣤⡀⣶⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡄⠀⠿⠙⠃⠛⠞⠳⠿⣾⠃⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣳⡄⠈⠉⠀⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀⠾⠛⠁⢀⡀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠛⢛⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠳⢟⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣛⠿⠁⠀⠀⠀⣄⣠⣴⣄⣀⡀⠀⣹⣿⣿⣿⡿⠀⠀⠀⡀⣠⡄⠀⠀⠀⠙⣵⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⠁⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⡆⢠⣙⠛⠉⢡⣼⣶⣾⣿⣿⣿⡏⠀⠀⢰⣴⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⠿⢿⠿⣿⣿⣿⠃⣘⣋⣶⣦⠸⣿⣿⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠏⠈⠁⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣆⡶⣶⢶⢶⡶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⣿⣿⣿⢉⣻⣿⣿⣿⣟⣿⣻⣿⣿⣿⣧⣃⣿⠸⣿⣿⣿⣉⣹⣿⣿⡇⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⠽⣿⣯⣿⣿⣿⣯⣿⣿⡿⠿⠿⠿⠁⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠆





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠒⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡶⣶⡶⣤⡀⠀⠀⠀⣾⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡤⣬⣷⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠘⣿⡌⢻⡄⠀⢸⣿⣿⣿⣴⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠶⠾⡿⠿⢥⡤⣤⣤⣤⣤⣤⣤⣬⣙⣳⣄⡴⠋⣿⣿⣿⣿⠟⠁⠀⠀⢹⣧⠀⣷⠀⠀⣿⣿⡍⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣸⠇⡤⡄⠰⢒⠆⢠⠴⠆⡎⠉⠉⠱⣋⡀⢠⣀⡈⣿⠁⠀⠀⠀⠀⢸⣿⠀⢻⠀⢀⠛⠛⢷⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⡈⠀⠉⢁⡀⠸⣌⢸⡁⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⣼⣠⣾⣷⣤⣬⣧⣶⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢿⢈⡟⣶⣒⠉⠑⠛⣋⢠⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⠞⡵⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⣤⡟⠘⡅⠙⣿⣿⣿⡿⣱⠟⠀⢀⡴⠛⠁⠀⠀⠀⠀⣨⣽⡶⠿⠛⠁⠊⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠙⣷⣤⡳⠀⠙⠛⠛⢱⠏⠀⠀⣸⠀⠀⠀⠀⠠⠰⠛⠛⡉⡠⢀⢀⡴⢲⣿⠸⣏⠛⠻⣿⢿⣿⢿⠟⠛⢁⡌
⠀⠀⠀⠀⠀⣀⡴⠞⠋⠘⢷⣾⣟⣮⠙⠷⠦⣤⣤⠞⠳⣄⠀⢿⣦⣀⠀⠀⠀⠈⠀⠚⠁⠁⠁⠉⠀⣿⠛⠛⢻⣃⠀⠀⠀⢁⣀⣀⡴⠞
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠹⢿⣭⣀⣀⣠⠾⠁⠀⠀⠈⠓⢈⣳⣥⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠞⡷⠶⠟⠓⠛⠛⠛⠛⣿⣿⣍
⠀⠀⢰⠟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⡀⠀⠀⠀⣠⡴⢿⡀⠀⠉⠛⠒⠒⡶⠶⠿⠿⠯⠽⠿⠾⠿⠿⠿⠿⠿⠷⠿⠿⠿⡝⢷⡀
⠀⠀⡟⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣴⠏⠀⠀⢻⠄⠀⠀⠀⠀⡇⡞⠉⢉⣉⢩⣭⡍⢩⣭⡍⠉⣩⡏⠉⠙⡆⡇⠈⢳
⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠁⠀⠈⠉⠀⠈⠁⠀⠉⠀⠈⠉⠁

⠀⢠⡀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣐⡉⠄⡿⢃⣀⡄⠀⠀⢀⠠⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡗⢦⢀⣧⣀⡀⠃⠀⡄⡀
⠀⠀⣉⠱⠰⠞⢫⠁⠀⠳⢮⡛⠾⠲⠁⣶⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⢇⣴⠈⠜⢾⠉⠵⣮⡁⣀⠙⠀⠴
⠀⠀⠁⠀⠈⠶⣘⣄⡶⢈⡄⠱⢦⡁⣢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢓⠚⢻⡴⢠⣥⣄⢠⠂⣩⣿⡶⠛⠁
⠀⠀⠀⠀⠶⠃⠉⡤⠀⣿⡃⣀⠃⠝⠉⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠐⢀⣦⠃⡊⠁⠠⡦⣀⠫⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣷⠁⠀⠁⠀⠀⠀⠉

⠀⠀⢀⡀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡦⡀
⠀⠀⠈⠅⡆⠀⣠⠞⠁⠀⡀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡾⠥⢀⢀
⠀⠀⠀⢘⣧⢀⡡⡨⣩⡌⣣⡾⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠄⡸⡅⠒⠀⣼⡱⢋⠀⣀⣈⠻⠃
⠀⣀⠀⢸⡿⡯⢻⠀⡉⣞⠷⢻⠇⡐⠳⣤⠀⠀⠀⠀⠀⠀⠙⠋⠁⢎⠊⡟⠑⠷⣍⢨⠙⢢⢢⡜⠋
⠀⠀⠀⡮⠳⠵⠛⠴⠇⣈⠚⣵⡔⡒⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⣤⠄⣈⠁⠸⣾⠆⣯⡏⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠁⠀⠶⠘⢱⡖⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⣠⡀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄
⠀⠉⠁⢁⢟⣣⡄⠠⣝⠄⠀⠀⣤⠤⠞⠁⡀⣴⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⣒⣦⣤⠌⠀⠀⢀⠈⠑
⠀⠘⠃⠀⢞⡯⡀⠄⠘⠀⠐⠙⠶⣤⡁⡜⠟⠀⠀⠀⠀⠀⠀⠀⠤⢀⠟⠭⠅⠀⠀⢦⡘⢯⣄⣁
⠀⠀⢶⠄⠁⠏⣛⠰⣞⠋⣠⣠⣊⢨⠟⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠖⣸⡐⣿⡄⠻⢃⠙⠰⠺⠯⠤
⠀⠀⠀⠀⠀⠀⣈⠁⠂⠹⠉⠡⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠯⠵⠊⢀⠸⢟⡀⠰⠆⠤⣤⡀⡃
⠀⠀⠀⠀⠀⠀⠉⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠃⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠤⣖⣴⢳⡧⣡⡆⡽⣷⢆⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⢿⢣⡇⣿⢻⣻⡘⣍⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡖⡌⣳⢣⢈⠁⡍⡉⡂⢅⢊⣠⢄⠀⠀⠀⢸⣿⣿⣿⡟⡽⣷⣽⢿⣷⣾⣾⣿⣷⣿⡾⣿⣿⣿⣿⣿
⠀⠀⠀⠸⢱⠷⡱⠇⢏⢦⡄⡄⡿⡆⣾⠿⢮⡆⠀⠀⢸⣿⣿⣿⣣⣷⣿⣋⣾⡎⡟⣿⣿⣜⣿⣷⣭⡇⣿⣿⣿
⠀⠀⠀⢰⣰⠂⣦⡄⠠⠾⣐⢃⠀⢀⣀⡠⠛⠁⠀⠀⢸⣿⣿⣿⣿⢯⡿⡟⣿⣟⣽⢿⡿⣿⡿⣿⣻⣷⣿⣿⣿
⠀⠀⠀⠀⢿⠈⣼⣰⢳⡴⡟⣹⡶⣶⣶⢏⠋⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⢹⢻⠚⡇⣿⡞⣫⢙⢻⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠩⠇⠸⠃⣳⠏⡀⠋⠭⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⣿⣸⣿⢻⣾⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣠⠊⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠤⢀⡀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⣠⠖⢋⠡⣐⠒⠀⠈⠉⠉⠀⠀⠀⠁⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡴⢋⣄⣈⠔⠋⠀⠈⠉⠉⠉⠉⠉⠉⠐⠒⠢⢬⡀⠑
⠀⠀⠀⠀⠀⢀⠄⠀⡞⢠⠞⡠⠁⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡈⠳⣼⡀
⠀⠀⠀⠀⢀⠀⠤⠄⢧⢉⠜⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠘⡗⢒⠢⢄
⠀⠀⠀⢠⠊⠀⠀⠀⠘⡏⠀⠀⠀⠀⣴⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠦⠀⠁⠀⢹⠀⠆⠀⠱
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⣤⣶⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡇⠀⠀⢸⠀⢸⠀⠀⡀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢿⣿⣿⠇⠀⠀⠠⠀⠠⠀⠀⠀⠻⣿⠿⠁⠀⠀⣸⠁⣌⠀⡰
⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⣄⣈⠁⣉⣠⡆⠀⠀⠀⠀⠀⠀⢠⢇⣀⡠⠜⠁
⠀⠀⠀⠀⠀⠈⠙⠶⠦⠾⣄⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⡠⠋⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠣⠤⠜⠁⠀⠀⠀⢀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⢃⣈⣙⣒⠦⠤⣤⣄⣀⣀⣤⡤⢤⡖⠋⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⣀⣡⠀⠀⢆⠀⠢⠀⠔⠀⡄⠀⢫⡖⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠂⠤⠀⠊⡀⠀⠀⠣⣀⣀⠔⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠡⡀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⢀⢀⣑⣧⣴⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡜⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡼⠁⡸⢠⡄⠤⠤⠀⠀⠀⠄⠐⢂⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⡰⠃⠺⠷⠴⠀⠿⠄⠘⡖⠀⠋⢻⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠂⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡴⠻⡟⠃⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣼⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡠⠿⡇⠀⢶⣄⠀⠈⠀⠐⠂⠉⠉⠁⠉⠀⢠⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠁⠀⠀⠹⢄⡀⠀⠀⠀⠀⠒⠒⠂⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⢨⡍⢳⣤⣄⣂⠀⢀⣠⣼⠋⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢂⣤⠀⢀⠄⠻⣿⣤⠀⠈⡅⠀⠀⠀⠉⠹⢉⡟⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢘⡿⠆⢈⠀⢰⠿⠃⠀⣄⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠂⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⣠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢲⠀⠀⠀⠀⢠⣿⠳⠀⣠⠀⠀⠈⠐⡇⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠐⠀⠀⡜⠏⠀⠀⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢡⣤⡤⢀⣀⠀⠀⣼⠌⠀⢠⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠘⠟⠁⠀⠈⡰⣻⠟⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⡾⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠑⡢⡀⣠⠄⡀⣀⠔⣊⠩⠀⠀⠀⠀⠁⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠁⣀⠤⠤⠤⠤⣤⣀⡀⠀⣽⠁⠀⢹⣾⠥⢀⣀⣀⣀⣀⣀⠀⠁⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠰⢎⡙⠲⠤⠤⠤⠒⡋⠩⠵⠞⠢⠴⠿⠖⢉⠉⠳⠤⣀⣀⣀⠽⠓⢦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠉⠃⢀⠀⠀⢀⡀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠖⠊⣀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⠁⠀⠊⠁⢉⡉⢋⣀⡈⠥⠬⠒⠒⣬⠉⠂⠀⠘⢖⠒⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠙⠉⢠⢈⠀⡆⠀⠀⢛⣀⠠⠭⠄⠒⠒⠲⠀⢢⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡆⠠⢄⣀⣀⠤⠼⠐⠒⠂⠉⢉⡴⠂⢀⣴⠋⠄⠊⢉⠃⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⡴⠂⣰⡆⢠⡞⢁⠆⠀⠀⣾⡧⠃⢸⡧⠊⣶⠀⢰⡇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠘⠀⠓⠉⣼⣅⣾⠓⢡⡾⠁⡶⣿⠀⢀⢿⡇⢀⠿⡄⣼⡇⠀⠀⠀⠀⠙⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠄⢠⠖⢹⡿⠀⢿⡀⡼⣇⠰⠁⠙⢒⣡⡀⢩⠗⠂⢤⣟⡔⡂⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠀⢘⠀⠛⠀⠀⡠⠥⢄⢀⡾⢩⠂⣾⢡⠃⠀⠀⢐⣅⠀⠀⠀⠀⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠆⣸⡇⠀⠤⠉⠥⢼⡏⠀⢠⡗⠁⢀⣿⡆⢠⣿⠀⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠫⠄⣿⠃⣠⡞⠙⡄⢿⠁⢀⠼⣇⣠⠎⠻⣖⣹⡯⠤⠍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⢂⣁⢠⡟⠈⢻⣀⡜⠀⢈⠓⠉⢀⣈⠀⠖⠉⣠⠟⠀⠠⠒⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠒⠋⢀⠄⠀⣉⠀⠀⢒⡰⠖⠒⠂⠠⢀⠒⡁⢴⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⣤⠶⡄⠀⠀⠀⠀⠈⠉⣉⢃⠠⠡⠀⠰⠇⡘⢉⠁⠠⢀⠀⣀⠉⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⣼⠋⠔⢋⢝⣠⠶⠂⠀⣀⢘⣘⠈⠄⠀⣀⣈⡀⠀⠀⠀⣀⡀⠤⢊⠠⠊⡴⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣼⠃⠀⢈⣡⣾⢃⠒⠡⢄⠀⠀⠀⠀⠀⠀⢫⡅⠃⠀⠀⠤⠄⠒⢈⡥⣤⡀⠹⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠒⠒⢹⡿⢁⣼⠃⢨⢆⣤⢀⡘⠀⢑⡒⢺⡟⢉⡁⣡⣤⢲⡆⢸⡇⢸⣧⠘⠢⠟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⠀⠺⠡⠚⠁⡾⢃⣼⠇⠀⢿⡄⢸⡇⠈⣿⠈⣿⠈⣇⠸⢧⡼⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠈⠓⠈⠿⠔⠃⣠⡿⠸⣇⠜⠿⠀⠛⠀⠉⠁⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠟⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡀⠀⠀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡴⠁⣠⠞⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⢀⡞⠁⢀⡤⠊⢀⣀⠀⠀⣀
⠀⠀⢀⠀⠤⠀⠀⠀⡾⢁⠀⡶⠀⠀⠀⣠⠆⠠⠂⢀⡞⠁⠀⢀⢴⠟⠒⠈⠁⠀⢠⡾⠁⠀⢠⠏
⠠⠊⠀⠀⠀⠀⠀⠸⠗⢁⡾⠁⠀⠀⠸⠇⠀⠀⠀⡾⠀⠀⠔⢁⠏⠀⠀⠀⠀⠀⠛⠀⠀⢰⡟
⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠂⢀⡴⠋⢁⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⠀⢀⣠⡾⠕⠂⠀⣰⠋⣀⠔⠃⠀⣠⡀⠈⣀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⠁⢰⠋⡑⠊⠉⢡⠏⠀⠀⠀⡾⠉⠁⢀⠤⢂⡞⠋⢠⡾⠋
⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠈⠀⠀⠀⢀⡏⠀⠀⠀⢸⠁⠀⠀⠀⢀⠈⠀⢰⠏
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣠⠏
⠀⠀⠠⠀⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⢉⣶⣫⣥⣬⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⣫⣭⣿⣮⢄⢻⣿⣿⢣⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣻⣷⢿⣣⠬⠙⣸⡇⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⢽⡗⠁⠛⣅⠈⠰⡆⠠⠈⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⠀⠀⢣⣀⠰⢠⠷⠤⠈⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⠃⠀⠀⠊⠙⠛⣫⠄⢀⠀⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⣌⣀⣀⣀⣀⣀⣤⣤⣤⣾⣿⡿⠿⣙⣶⣒⣶⣦⣄⣀⣀⣀⣀⣀⣀⣠⡤⣦⣤⠞⠉⡴⣧⠄⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣵⣇⣃⡾⡜⡜⣩⢏⠫⡹⡙⢉⠃⣄⣦⡾⠛⢶⣒⣲⡾⣏⠉⠉⠉⠉⠁⠙⣯⣧⣿⡀⠈⠀⠾⡻⠊
⠀⠀⠀⠀⠀⠀⣠⢾⠟⣡⣾⢋⣿⢿⠛⠛⠻⠾⠶⠷⢷⡞⠻⣯⡈⢧⡀⠈⠻⣶⠾⣿⢀⡠⠔⠋⠀⢀⣿⠕⣿⠁⠉⠉
⠀⠀⠀⠀⠀⢀⣧⡎⣸⢁⠂⡞⡟⢸⡇⠀⠀⠀⠀⠀⠀⢻⡌⠛⣣⡀⢳⡀⠀⠘⢿⡟⠛⠚⠛⠛⠋⠉⠛⠛⠋
⠀⠀⠀⠀⠀⢸⣿⣴⣿⣏⣼⡶⢡⣻⠃⠀⠀⠀⠀⠀⠀⠀⢻⡘⠿⠟⠀⢳⡀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⡞⠁⠀⠈⠙⢯⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣼⣿⠄⢳⣀⣀⣨⣿⣦⣤⡀
⠀⠀⠀⠀⢰⡇⠀⠀⣀⣤⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⡬⠿⠒⠛⢻⡏⢹⡿⡄⢸⣧
⠀⠀⠀⠀⠀⢳⡄⠀⠉⠀⠊⠙⡿⡳⣄⠀⣀⢀⣠⡤⠖⢿⣯⠁⠹⣆⢠⣿⣷⠈⢷⢸⡇⠹⣼⢹⡆
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣠⢾⢓⣹⠟⠩⣽⠋⡟⣦⠀⢸⠈⢳⡀⢹⡄⠉⠉⣀⣸⣾⣷⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣼⢿⢡⡴⡝⣶⢻⡇⠈⠳⣼⣄⣤⣿⣾⣿⣾⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢹⠙⢾⠋⣿⠋⢙⣾⣧⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⣄⣈⣷⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⢰⠖⠺⢿⣿⣿⡿⠋⠸⣿⣿⡿⠟⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⢻⡄⠀⢠⡞⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣦⣄⣀⡾⠁⠀⠈⣇⣠⣤⣶⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣼⣿⣿⡟⠛⠃⠀⠀⠀⠉⢹⣿⣿⣿⣦⣤⣤⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⢠⡖⡄
⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣡⠒⣦⠀⠀⣤⠖⠢⣴⡆⠀⣶⠀⡴⢦⠀⢠⠔⢶⡄⠀⠀⠀⠀⢠⠖⠒⢤⡶
⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⣿⠀⣸⡇⠀⠀⣿⠀⢀⣿⠀⢇⣸⢀⣟⠴⠋⠀⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⣟⡰⠻⣧⣀⡰⣿⣀⠞⣿⠀⣨⠛⠉⣿⣄⣀⡴⠁⠀⠀⠀⣿⣄⣠⢾⣇⡼⠁
⠀⠀⠀⠀⠀⢀⣘⠃⠀⠀⢉⠀⠀⢨⡍⢀⣌⠁⢀⣨⡉⠁⠀⣀⣬⠉⠁⠀⠀⠀⠀⢀⣌⠉⣡⠀⠉
⠀⠀⠀⠀⡏⡌⠿⣷⣄⣼⡿⠃⠀⣿⠃⣼⡅⠀⠀⠻⣿⣧⣴⣿⠟⡀⠀⠀⠀⠀⠀⣾⡁⢸⡷
⠀⠀⠀⠀⣿⠀⢤⡀⢟⣥⠤⣄⢸⡿⠀⣿⠃⢀⡄⠀⣤⠸⠋⠀⢀⡄⠀⣠⡤⣄⠀⣿⠁⢸⡇⠀⣤⠀⣤
⠀⠀⠀⠀⣿⠀⢸⠃⣼⠙⢄⣿⣸⡇⢀⣿⠀⣸⡇⢀⣿⢠⠀⠀⠸⡇⣸⡇⢧⣸⣤⣿⠀⣼⡀⢰⡇⠀⣿⢀
⠀⠀⠀⠀⠟⠀⠻⢎⠈⠣⠴⠋⠀⠳⠊⠹⠖⠙⠧⢊⣿⠁⠀⠀⢨⡟⠀⠳⠤⠋⠀⠻⠎⠘⠗⠉⠷⠎⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣏⡁⠒⠀⠀⠛⠂⠀⢠⡆⠀⠠⣆⡟⢠⡆⢠⣩⠇⠐⠓⠒⠒⠚⠟⠒⠒⠒⠚⠀⣎⡿
⠀⠀⠀⠀⡤⢲⡄⣿⡠⢲⡄⠺⡦⢲⠀⢰⠀⠀⣷⣀⠀⢸⡗⠀⣶⠐⢦⡠⢲⡄⢀⡴⠂⣴⠀⠰⣇⡀
⠀⠀⠀⢸⡇⠀⢀⣿⠁⢸⡇⡐⢠⡇⠠⢿⠀⡐⡠⠙⣷⢸⡇⢀⣿⠀⣸⠀⢸⠇⣼⡇⠀⣿⠀⣌⠄⠙⡇
⠀⠀⠀⠀⠛⠖⠁⠟⠀⠘⠋⠀⠘⠓⠁⠘⠚⠀⠓⠄⠋⠘⠗⠁⠛⠀⠛⠀⠘⠊⠈⠳⠊⠙⠊⠈⠢⠐⠁