Peanut Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠁⠀⠁⣶⢨⣤⣌⠢⠙⢢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠘⠁⢰⠁⠀⢀⡟⠈⠙⡟⠃⠀⣶⡶⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠆⢠⠎⢙⠃⣤⣬⡅⡤⣄⢀⣀⠀⠈⢂⣀⡉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⠠⠀⣁⣂⡈⠇⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢳⢀⣯⣅⠁⠒⠀⠱⠀⠄⠐⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠋⠀⢩⣍⣐⡃⠺⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢃⠘⠒⠂⡀⠀⠀⢈⣿⠉⠀⠀⠠⠂⠉⠋⣦⢸⠋⠉⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡀⢻⠀⠀⢤⠀⠀⢁⠄⠀⠂⠂⠀⠀⢤⣤⡄⠀⣥⢿⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣶⠛⠂⣀⣀⡀⠘⠀⠀⢀⠀⢀⡤⣤⣄⠁⣰⠛⡿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢷⣼⣿⡆⢹⠈⠋⢰⠉⠀⠀⠀⡀⠀⠈⠱⢀⢬⣇⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢁⠀⠀⡷⠿⠀⡀⠀⠀⠀⡀⣀⡠⣤⠘⡤⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠰⡶⠀⠇⠀⠀⠁⠀⠀⠈⠁⠀⠀⠂⢸⡟⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠰⠀⠀⢀⡀⣤⢰⠒⠂⠒⠂⠘⣂⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠀⠈⠀⠀⠀⠀⠈⠀⢠⠈⠲⠄⠠⠀⠈⠟⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠀⠀⠀⠔⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣴⡄⢠⣴⢶⡄⢸⠛⠏⠃⠹⠞⣠⣤⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⡇⣼⡟⠹⠃⡼⠟⠚⡇⢀⣀⣀⡀⠐⠟⠉⠈⠦⢰⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡄⣨⣴⣶⢀⣶⣤⣀⡃⠀⠉⠉⠁⢰⡾⠛⠻⠆⠀⢁⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣮⠀⡟⠀⠈⠸⠃⠋⠀⠁⣰⠆⠿⡇⠀⣁⣀⠀⠁⢀⠚⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢧⡈⠓⢶⣇⠀⣟⡛⠓⡃⢈⠀⢸⡇⠀⣁⣀⠀⢀⠀⠀⠤⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢹⡇⠈⢫⠠⣽⣄⢄⡁⠖⡆⠰⡆⠀⠉⠉⠀⡿⠋⠹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⣳⠘⣏⣧⡟⠻⣼⠃⣠⡽⢬⠃⣶⣶⠀⣼⣻⡿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡅⣀⡘⣿⢳⡄⣿⡷⡏⢀⣼⠐⠋⠟⣰⢦⣍⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣍⠺⣿⣿⣷⡄⣽⣶⠀⣴⡀⠘⠃⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣛⠻⠀⣿⡏⡼⠛⠁⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠤⠘⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠠⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠔⠀⠂⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⣤⣤⣤⢤⣤⠴⡶⢺⠋⠁⣔⣄⡤⡞⠠⠝⢤⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠍⠀⠈⠦⠈⢨⠤⠴⡒⢒⣒⢲⠞⢫⠉⠁⢹⣈⣤⡤⠴⢛⠖⢂⣿
⠀⠀⠀⠀⠀⠀⠀⢠⢾⠁⣀⡥⢔⡒⠋⠹⠀⠲⠀⣄⣌⢠⠶⡬⠴⢶⡺⠋⠉⠅⠠⠀⠀⢜⡀⣱⠏
⠀⠀⠀⠀⠀⠀⢠⡟⠀⡫⠥⠊⠀⠀⠂⢠⠔⠺⡉⠁⡔⣁⣄⡡⠤⣾⣊⣤⣭⢴⣤⡜⣋⡭⠞⠁
⠀⠀⠀⠀⠀⠀⣾⠑⢫⠀⢔⡁⢤⠤⢀⣢⠶⢓⡋⠋⠀⠉⢸⡵⠊⠉⠀⠀⠈⠀⠀⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠹⡎⠀⣀⠁⡠⠆⠀⢐⠀⣀⣠⠥⢖⣒⣰⠋⠀⠀⠀⠀⣀⣠⠴⠂⠀⢸⡇⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⠢⠀⠶⡷⠾⢏⣡⡤⠶⠛⢹⠏⠀⣀⠴⠚⠉⠁⠀⠀⠀⣠⣿⢁⡴⠒⠋⠉⠉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠛⠉⠁⠀⠀⠀⣟⣀⠀⠀⠀⠀⠀⢀⣠⡴⢛⡵⣻⠋⠀⢀⠤⠴⠖⠒⠒⠋⠉⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣞⣻⣭⠴⠞⠋⠐⢿⣄⡀⠀⠀⠀⠀⢀⣠⠴⢚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣛⣫⣭⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⡉⢁⠄⡀⠀⣀⠉⣑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡗⠀⠠⠁⠂⠀⠀⠀⢢⠁⠈⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠓⠀⠂⢀⠀⠀⠀⠰⠀⣄⠄⠐⠄⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠉⢢⠀⠉⢉⠉⠁⢀⠄⢠⠀⠂⠐⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠁⠀⠀⠆⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⡆⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠘⠤⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠤⠄⠀⡀⡉⠀⠀⠀⠀⠀⡀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠸⠀⠁⠘⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠄⠐⠀⢀⠀⢀⠠⠀⠀⢆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠐⠢⡀⠠⠀⠠⠄⠀⡈⢄⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠐⠂⠠⠂⠸⡀⠀⠀⡠⠀⠀⠀⢸⢆⠀⠄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠈⠁⠢⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠐⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠰⠄⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡔⠒⠀⠀⡀⠀⠤⠄⠈⣀⠀⠀⡁⠉⢅⠀⠰⠒⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⠤⠀⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⠀⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡄⠐⠂⠀⠤⠀⠠⡀⠀⠤⢄⠀⡐⢁⠅⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣑⠐⠃⢄⠀⠄⠀⠁⠀⠜⠀⢈⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⠤⠤⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⡀⠀⠉⠙⠲⠤⣄⡀⠉⠑⠦⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢤⢼⣈⣙⠒⠤⠤⠆⡀⠀⠈⠉⠒⠤⠤⣀⣀⡐⠀⠀⠈⢉⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⡡⠔⠀⠐⠆⠀⢤⣈⠑⠖⠤⣄⠉⠐⠂⠠⢀⠀⠄⠀⢉⠛⠓⠲⠤⣀⠀⠘⢏⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣴⠷⠒⠒⠒⠒⠦⢄⣘⠀⠉⠐⠖⠌⠉⠉⢟⢓⡲⠬⣔⡠⢅⠀⠀⠀⢀⠈⠑⣆⢸⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠉⠢⣄⠊⠀⠀⠀⠆⠀⠉⠁⢋⠐⠒⠒⠒⠢⢄⡈⠑⠠⡙⢦⡈⠑⠒⠤⠤⢄⢨⣾⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢧⡀⠌⠑⢦⡤⠞⠂⠉⠉⠅⠉⠈⠉⠒⠾⣄⠀⠈⣳⣄⣈⣤⣹⣄⢀⣀⣀⠤⠚⢹⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣕⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⡋⠭⠐⠒⠒⠂⠀⠉⠑⠦⡀⠂⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⢍⡳⢀⠀⣀⡀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠤⠤⠤⠿⠷⢤⣀⠀⢀⠀⣀⣀⣀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠤⠶⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠒⠒⣆⠐⡖⠒⠒⡆⠀⢐⣶⡄⠀⠀⢲⢦⡀⠐⡖⠀⣶⠂⠀⢲⠂⠴⠒⣶⠒⠆⢠⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠚⠁⠀⡏⠙⢀⡄⢀⡾⠦⢿⡄⠀⢸⠀⠙⢦⡇⠀⢻⡀⠀⣸⠀⠀⠀⣿⠀⠀⢬⡉⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠉⠁⠉⠁⠀⠈⠉⠀⠉⠁⠀⠀⠁⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⠁⠁⠉⠀⠁⠁⠀⠀⠀⠀⠉⠈⠈⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢖⠩⠭⠭⠀⠠⠀⢠⣴⣒⠯⠛⣛⣛⡓
⠀⠀⠀⡼⠀⣡⠂⡄⡀⣠⢤⢀⢄⡄⡞⠀⠀⠀⠀⠀⠀⠉⠠⢒⣐⣓⢀⣀⣀⣰⣚⡎⠊⠉⡉
⠀⠀⠀⠁⠀⠈⠈⠁⠁⠁⠈⠈⠉⠁⠁⠀⠀⠀⠀⠀⣀⠒⠷⠷⢦⣧⣷⣷⣶⡶⡚⠙⡉⣀⣁⣀⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡌⠃⠀⠀⠀⠈⠙⠋⠉⠉⠁⠓⠒⠦⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠳⢄⠀⠀⠀⠀⠀⡸⠛⠂⠀⠀⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣬⣉⣐⠦⣏⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣂⡠⣶⣖⣚⡩⠎
⠀⠀⠀⠠⠎⠀⠀⠉⠒⠀⠐⠁⠀⠈⠑⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣑
⠀⠀⠀⠀⠑⠊⠉⠉⠒⢤⠂⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⢀⡤⡤⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠠⠜⠁⠀⠀⠀⣸⢁⠂⠀⠀⠀⡀⢸⡄
⠀⠀⠀⠀⠐⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠈⠀⠐⢀⠆⠄⢀⠔⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⣀⠜⢡⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⡡⠊⢀⠄⠀⢀⣁⡴⢋⠄⠐⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⢠⠁⢠⠃⠀⢀⢞⣾⢣⠏⠀⠀⠀⢰⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡆⠸⡀⡪⢠⣴⣭⠞⠋⣞⠀⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣤⣐⡠⠊⠉⠀⠀⠀⠙⠦⠤⠔⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠠⠠⠀⠀⠤⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⠻⠓⢉⠀⠰⣄⠀⠀⣠⣾⢷⣘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢹⣿⢆⠀⠰⠁⠀⠀⠀⡙⠈⢩⣴⣿⢟⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣟⡹⣀⠰⠇⠀⠀⣴⠛⠀⣫⣶⡂⠈⢉⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠶⡟⠟⢛⣈⠁⡞⣭⣀⠀⡄⡄⠁⠐⣱⠈⢠⣶⣗⣀⣩⢿⡟
⠀⠀⠀⠀⠀⠀⢀⠀⢐⣿⣇⡰⠜⠃⣚⣀⢰⡶⣖⠿⣴⡦⣰⣿⢤⣀⢀⠁⣄⢰⣾⣿⣎⣿⣿⣿⣷⡔⠁⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⡠⠂⢱⠷⢚⡘⢵⡖⠉⠀⠛⢘⣃⢠⡵⣦⠻⢄⣣⡙⠁⣴⣷⡼⢟⣯⣿⣿⣿⣿⣿⠿⠋⢀⠤⠒⠉⣁⡀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⣰⠊⡷⠀⠀⣦⣀⠐⠀⢙⣭⢰⡄⠻⠉⡧⠁⡼⢧⠿⣙⣧⡘⣿⣿⡟⠹⠿⠛⠛⠉⠉⠀⢠⡔⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⢆
⠀⣼⣿⡁⢴⣂⠄⠀⣤⠂⠉⠊⢣⡀⢿⣂⠠⣶⣧⠁⣨⡄⢿⢉⣥⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠲⢷⡔⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⢸⣈⣷⣿⣆⣶⠀⠀⠈⠀⠂⣈⡀⢸⣟⣫⠇⢉⣴⡖⣹⣟⡰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⣓⠉⣓⢐⠀⢤⣈⣁⣀⣐⡶⡶⣞⣿
⣿⣿⣟⣷⣽⡛⣉⣄⠒⠘⣹⣉⣱⠈⢙⣥⣶⡆⠓⣦⣴⣿⡧⠄⠁⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠛⠃⠬⣹⣳⣾⣾⣿⡿⣿⠿⠟⠁
⢿⣿⣷⣽⣿⣽⡿⣿⣿⣿⣦⣤⣴⣟⡙⠿⠿⠿⠾⢻⣟⡋⠀⠀⣴⠞⣋⣤⣴⡷⠤⠦⠄⠀⠀⠀⠀⠉⠀⠠⡀⠀⠀⠀⠀⠈⠉⠉⠉
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢚⣉⣀⡄⢀⠀⡀⠀⠀⠀⠈⠑⠚⢴⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠈⠻⠿⣿⣹⣿⣿⣟⣵⠏⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠄
⠀⠀⠀⠀⠀⠀⠉⠉⢻⣅⣠⡀⣀⠀⠀⡀⡀⠀⢀⢀⠀⠀⡠⠀⠐⠁⡐⠁⠀⡀⠀⠀⠀⡊⣀⣀⣤⣮⡥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣵⡟⠀⠨⣚⠐⢿⡭⣣⠊⠴⠖⠐⠾⣿⠲⣿⡷⠺⣿⠿⠿⠊⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣟⡛⣿⣿⢶⡿⠿⠓⠚⠋





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠃⣴⢃⡀
⠀⠀⠀⠀⠀⠁⡀⠘⣇⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠵⣄⠃⣪⢁
⠀⠀⠀⠀⠀⠀⣰⣦⡈⠃⠁⠠⠀⠂⠀⠀⠀⠀⠀⠀⢩⣛⣷⡄⣳⢂⠘⠀⠀⠀⢀⣠⡤⠀⠶⢤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⢀⣀⢰⡄⠀⠈⠉⠻⠆⠛⠙⠳⠶⢷⣾⢶⡷⠠⠄⢈⠁⢁⠐⢚⣻⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⡀⣹⠗⣠⣤⡐⠛⠙⠟⠰⠛⠓⣦⠀⠤⢬⡀⠐⠒⠶⠉⡤⠶⡶⠉⣴⢿⣄⡷⠀⠀⠀⠀⡀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢻⡏⣠⡥⠌⠒⠛⢻⡖⠚⠛⣷⡦⢠⣶⣶⣶⠰⠾⠛⠿⣂⣠⣶⢟⣀⢿⣵⣿⣶⣈⠨⢤⡍⣤⣄⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣧⣵⡶⢦⣍⠙⠻⠄⢢⣄⠻⠋⠭⠀⠲⠎⢽⣶⣿⣿⣿⣏⣵⣿⣫⣤⣿⣿⣃⣬⣤⣀⢤⣀⣩⣤⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⡛⠶⠦⠴⢿⠷⣿⣿⠀⣤⠶⠶⠈⣙⠛⢰⡝⢿⣿⣿⣟⣯⣶⣿⣿⣯⣉⣉⣬⣭⠰⢾⡍⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠋⠉⠉⠉⠉⠛⠶⣶⣶⣿⣿⡏⢰⣷⣾⣷⣿⣽⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡶⠿⠿⠧⣿⣷⣮⡯⠟⠋
⠀⠀⠀⠀⠰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢟⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣨⡭⠽⠿⠛⠛⠫⠤⣀
⠀⠀⠀⠈⢧⣝⠢⢄⣀⣀⠀⠀⠀⢀⣀⣄⣀⣤⣶⣿⢿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣅⣀⠀⠀⠀⠀⠀⠀⠈⣷⣤
⠀⠀⠀⠀⠘⡼⣿⣧⣭⣭⣷⣶⣾⣿⣿⣟⣛⣿⣿⣧⣿⣿⣭⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⠛⢿⣦⣄⢀⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢮⣿⡿⢿⣽⠯⣭⠔⠛⣛⡥⠛⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠃⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡸⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⣀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⡀⠀⡀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡸⠯⠧⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠹⠟⠪⠽⠋⠛⠤⠏⠃⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡸⢾⠔⠚⠃⠁⠒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠙⠦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⢠⣤⠞⡛⠁⠁⠀⠀⠀⣀⢀⠇
⠀⠀⠀⠀⠀⠀⠲⠤⠛⠉⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠴⠖⠉⠁⠀⢀⡀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢⣀⡀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠁⠀⠀⠀⠈⠙⠉⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⠲⠤⣄⣀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠳⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⠩⠀⠁⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠘⢦⡁⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠈⠛⢷⣂⠔⡦⠠⣀⣠⣀⣄⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠈⡀⠀⠤⣤⣀⡤⠜⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠳⣤⡠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⡂⢀⡝⠀⠀⠀⠐⠂⠀⠀⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠰⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠬⠴⠃⠀⠀⠀⠀⠀⠤⠀⠦⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠙⠀⠀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠂⡸⢀⠊⠉⠆⠀⡗⠢⠘⠂⠪⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡎⠀⢀⠁⠀⠀⠀⠐⢄⠈⠀⠈⡀⡄⠀⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣉⡁⠀⠢⣀⣀⣀⠘⠀⠓⠒⠀⠉⢉⡀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡌⠀⠈⡆⠀⠀⠤⠤⠀⠀⠖⠀⡆⠘⠁⠈⠄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠀⡆⠀⠀⢰⠀⠁⠀⠃⠠⠀⢁⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠢⠀⠁⢃⠀⠀⡀⢠⡀⡐⠀⠣⠤⠊⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡀⢄⠀⠀⢈⡉⠁⠀⠀⠀⠀⠀⡀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠁⠀⠉⠑⠀⠊⢀⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣈⠀⠀⠈⠒⠀⠒⠀⠂⠀⠈⠃⠂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠑⠀⠉⠀⠉⠑⠀⠂⠈⠆⠄⢢⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠃⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣈⠁⠒⠊⠀⢣⡀⢀⡀⠴⠀⡀⠀⢀⡝⠤⠐⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠂⠀⠈⠐⡄⠀⡤⠤⠤⢄⡀⠀⡀⠀⠀⠀⠔⠀⠀⢀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠦⠀⢀⣀⡀⠀⡁⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⢀⠀⠀⡀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡤⠤⠀⢀⡀⠀⢈⣐⠀⠒⠀⠁⠈⠒⠒⢒⠊⠀⢠⠤⠄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⡆⠀⠈⠁⠀⢱⠀⡄⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⣠⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠁⠀⠈⠀⠑⠀⠀⠠⠤⠆⠀⠄⠠⠄⠂⢀⠭⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠒⡉⠉⢢⠐⠂⠁⠐⠄⡠⠂⠒⡄⠀⣂⠠⢂⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣑⠊⠐⠤⠤⠔⠀⠤⠀⠔⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠲⠶⠶⠦⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠶⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⠽⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣇⠃⠀⢀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣘⠀⢼⠟⡡⠤⠤⣤⠀⠬⠻⣶⣶⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⣚⠛⠊⣩⠄⣰⠋⣠⢄⠀⠈⢧⠀⢀⠄⠉⠘⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣡⠄⠀⠈⠉⠀⡴⠃⠀⡏⠸⣿⣾⠃⠀⢸⠀⠀⣉⠓⠀⠸⡀⠀⡀⠤⣤⠙⣦⠰⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠊⣡⠆⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠃⢀⣠⣤⣤⣀⠋⠀⠀⠈⠀⠀⠀⡇⠘⢧⡀⠈⣧⣀⣉⡉⠙⡆⣠⠤⢤⡀
⠀⠀⠀⠀⠀⣰⠁⡀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠁⠐⠉⢀⣠⣄⠈⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⣡⠀⠶⠝⡋⠳⠀⣿⠃⣠⠞⠁
⠀⠀⠀⠀⢠⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠁⡀⠀⠈⠀⣄⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣧⠀⠐⠉⠈⠉⠀⣡⠞
⠀⠀⠀⠀⠈⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠂⠀⠀⠀⠀⠀⢉⢛⠓⠖⠀⠀⠀⢰⡏⠀⠀⠀⠈⢳⠀⣤⠤⠶⠞⠁
⠀⠀⠀⠀⠀⠘⣦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠊⠀⠀⠀⠸⣆⠚⠦⠀⠀⠀⣿⠀⠀⠀⠀⠀⡝⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣉⡒⠀⠀⠐⢒⣁⣼⡇⠀⠀⠀⠀⠀⠠⣌⡛⣁⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⢁⣸⠇⡈⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠹⡄⣒⠢⠤⣤⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⢖⣛⣯⠭⣶⠆⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠅⠀⠀⢠⠈⠉⠛⠲⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣌⠣⣄⣀⢰⡏⠘⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⡀⠀⠀⢀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡛⠦⢍⡀⠐⢰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢍⡹⠂⠀⢹⠠⠈⠀⠀⠀⡀⠀⠀⠀⠐⠰⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠓⣾⠀⠀⢠⡇⠠⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠴⠿⠀⠀⣿⠁⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⠤⠻⣦⠠⠀⢄⠀⠀⠁⣈⠀⠁⠀⢤⣤⡿⠁⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⡦⢤⠀⠄⠠⠀⣒⣴⢿⡋⣼⠀⢚⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠤⠞⠀⡟⢒⡚⠛⠉⠁⠀⣵⣼⠤⠾⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣤⣀⣠⡽⣦⠁⠀⠀⠀⢠⣯⣍⠻⡶⣦⣎⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠊⢢⣩⡦⣽⡕⠈⣉⢠⡀⠀⠀⠀⠑⠾⢳⣤⡍⠉⠑⣀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⠬⠈⣹⡭⡭⠴⠖⣋⡴⠇⠀⠀⠀⠀⠀⠀⠉⠛⠥⢬⡭⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠶⠀⠐⠐⠂⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⢶⠚⠉⡅⣄⣀⡴⢃⡐⢂⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⠋⠙⠛⡄⠂⢉⣉⡡⠬⠥⠤⢥⠼⢒⠒⠉⠛⡄⢉⣀⣠⠼⡯⠄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢐⣀⠤⠴⠒⡆⠠⠬⠂⠀⡂⢉⣡⣑⣠⡬⠤⠶⠚⢛⢩⠁⠀⡈⠇⠙⣽⠁
⠀⠀⠀⠀⠀⠀⠀⣼⢁⠷⢚⡩⠂⠉⠀⠄⣁⡠⡴⠒⠋⡩⠃⡠⠁⣀⣸⠽⠄⣐⣡⣄⣀⡦⢖⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢰⡟⠼⠈⢀⡴⠀⠈⡀⠠⣁⣴⠥⢤⠖⠒⠊⢙⣫⠴⠚⠋⠉⠙⠋⠉⠓⢾⡋⠁
⠀⠀⠀⠀⠀⠀⢸⡥⠒⠇⠔⠉⣈⠉⠄⡂⠉⠀⢸⣊⣀⠤⢬⠞⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠻⣌⠒⢂⠈⢁⣴⣠⣴⠔⠚⢋⣡⡴⢶⡏⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⣰⡇⠀⣀⡤⠴⠒⠒⠒⠲⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣬⣭⣥⠧⠶⠛⠉⠀⠀⡞⠀⠀⠚⠁⠀⠀⠀⠀⢀⣤⢞⣽⡵⠋⠁⠀⢀⣀⣀⣀⡠⠤⠂⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣤⣤⣀⣠⣤⠴⢞⣫⡴⠋⣼⠁⠀⠐⠊⠉⠁⠀⠀⠀⣀⡤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠛⠉⠁⠀⠀⠉⠻⣦⣤⣄⣤⣤⠤⠖⣛⣭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⡄⣀
⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠳⡀
⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠠⢤⣀⣀⡀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠑⠒⠤⠄⣀⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⡠⠤⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠙⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⠎
⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⠀⠀⡰⠁⠀⠀⠀⠂⠀⡰⠋⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠤⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑
⠀⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⢄⠘⢄
⠀⠈⢦⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢘⠀⠀⠉⠒⠠⠔⠊
⠀⠀⠀⠙⠢⠤⠤⠋⠀⢀⠔⠒⠂⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⡄⠀⠀⠀⠀⣠⠎⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠳⠄⠤⠒⠊⢠⠔⠉⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⡶⠛⠉⠉⠉⠉⠉⠉⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠦⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠂⠠⢄⡀⠙⠒⠶⢤⣤⣤⡀⢀⣀⠀⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⠀⠀⠄⠀⣀⠀⠈⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠐⠒⠒⠢⠬⡉⠐⠋⠉⠒⠒⠄⠀⠀⠀⠄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠽⠿⣶⣷⣖⣶⣀⣤⡤⢤⣤⣀⠀⠀⠀⠦⢀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⢀⡾⠋⠀⠈⠀⠀⠀⠀⠀⠀⠙⠳⣄⡲⠄⣀⠉⠂⠀⠀⠀⠀⠀⡀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢆⠁⠀⠀⠀⣲⣾⣿⣅⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣬⣀⣀⠀⠀⠀⣠⣀⣤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣤⠖⠒⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠙⢷⣄⣀⣤⠄⠠⠞⠋⠉⣠⠿⠋⠉⠙⠉⣉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⢁⣠⠤⠤⠖⣫⠕⠒⠒⠀⠈⠉⠉⠀⠀⠈⠁⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡡⠚⠁⠀⠀⢀⡴⠃⠀⣀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠉⠛⡛⠓⢤⣀⣀⢀⡀⣠⠴⠺⠏⡠⠊⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣀⣀⣈⡉⠉⠉⠀⣀⠴⠊⠁⡠⠐⠐⠒⠒⠀⠠⣀⠈⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠉⠁⠀⢀⡞⠄⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⠙⠒⠶⠤⠤⠤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⢀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⢸⠘⢹⠁⡇⡞⢸⢠⡇⡎⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠇⠀⠀⢐⡃⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠲⠆⠀⢀⣀⣀⠀⠀⠀⠒⠛⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢰⡄⠀⠀⠘⠿⠟
⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠐⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠰⠀⠀⠀⠀⢀⠀⡴⠴⢦⡖⣖⢲⢒⡆⢲⠂⣰⣴⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠐⠒⠒⠒⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠈⠀⠓⠓⠚⠀⠁⠘⠒⠓⠘⠀⠉⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡤⠀⡀
⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢰⣶⣜⡆⠀⠀⠀⣦⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⢿⣿⡿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢐⡀⣂⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⣠⣭⣄⠀⠀⠀⠀⠀⠈⣙⣋⠉⠹⡄⠀⠀⠀⣠⡄⠀⠿⠂⠀⣤⣀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠸⠿⠇⠿⠿
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢿⣿⣿⠿⠀⠁⠀⠀⠀⠈⠁⠰⣶⠀⠀⠉⠉⢶⡦⠀⠀⠀⠸⣿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠻⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⡾⠃⠀⠀⠀⣰⡟⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠘⣷⡀⠀⠀⠀⠻⣦⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣿⠁⠠⣿⣉⣻⡇⠀⠀⣿⣋⣹⡧⠀⢹⡇⠀⠀⠀⠀⠈⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣦⠀⠀⣿⡄⠀⠙⠻⠛⠁⠀⠀⠙⠻⠛⠁⠀⣼⡇⠀⢀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠸⣷⡀⠀⠀⣤⡀⠀⠀⣠⡄⠀⠀⣰⡿⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠈⠛⠛⠛⠋⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⣿⠓⠀⠉⠛⠿⠶⠶⠶⠾⠟⠋⠀⠐⢻⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠿⠀⠀⠀⣤⣀⠀⠀⠀⢀⣤⡄⠀⠀⠸⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣤⣤⣤⣤⣤⣬⣽⣷⣦⣶⣿⣭⣤⣤⣤⣤⣤⣄⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⣦⣼⠿⣧⣤⡿⢿⣤⣼⠿⣧⣤⡿⢿⣤⣾⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⡿⠷⠶⠾⠿⠶⠶⠿⠷⠶⠾⠿⠶⠶⠿⣿⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⡾⢻⣷⠟⠻⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⣠⡾⠟⠁⠀⢘⣿⣀⠀⠀⠙⠿⣦⡀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣿⠿⠋⠀⠀⣀⣴⠟⠋⠛⢷⣄⡀⠀⠈⠻⢿⣇⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⠛⠁⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠙⠻⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣶⣶⣶⠆





⣿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣟⣿⣟⣛⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠚⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠛⠀⣿⡁⢘⣀⣀⡤⠢⡀
⠀⠀⠀⣀⠤⠤⠄⣀⠀⠀⠀⡰⠊⠀⢀⡤⠤⢄⡀⠈⣧⠀⠀⠀⠀⠀⡖⠲⣄⠇⠀⣸⣆⢀⢧⡏⠈⠀⠸⠁⡜
⠀⠀⡼⠁⠀⠀⠀⠀⠉⠲⠎⠀⢀⡔⠁⠀⠀⠀⢻⠀⢸⠀⠀⠀⣠⡉⠣⡈⠻⡅⠀⢩⢿⣏⠀⠛⡄⠀⠀⢰
⠀⢰⡇⠀⡔⠉⠙⠓⠦⡄⠀⢠⠯⡀⠀⠀⠀⠀⡸⠀⢸⠀⠀⢮⡈⠿⡆⠀⠀⠀⠀⠀⠜⢿⠀⠀⠃⠀⠀⠈⡇
⠀⠈⡇⠀⠱⡀⠀⠀⠀⢇⠀⠊⠀⡃⠀⠀⠀⠀⠇⠀⣼⠀⠀⠀⠈⠢⣄⠀⢀⠠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠹⡀⠀⠱⡀⠀⠀⣨⠂⠀⡰⠦⣀⠀⠀⡸⠀⢠⡇⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠙⣄⠀⠙⣤⠞⠁⢀⡞⢦⠀⠈⠑⢶⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠈⠣⣀⠀⠀⢠⡎⠀⠀⠑⣤⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠹⠤⢖⠁⠈⠓⠒⠊⠀⠀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⡤⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣀⡠⠴⠶⠊⡉⠉⠉⠩⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⣠⠔⠚⠉⠉⡉⠉⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⣹⠓⠒⠒⠂⠒⠒⠂⠂⠒⠒⠒⠒⠀⠒⠒⠀⠀⠀⢧⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠸⡇⠀⠀⠀⠀⠑⠁⠀⠈⠐⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄
⠀⠀⡠⠏⠀⠉⠈⠁⠁⠀⠀⠂⠀⠀⠀⠔⢎⠐⠂⠁⠀⠀⠘⢲⠀⠀⢳⡄⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⣿
⠀⠈⡷⠈⠓⠀⠀⠄⠄⠀⠀⠄⠂⠄⠀⠠⠐⠄⡀⠂⠀⡢⣤⡼⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠉⢻⡐⠒⠉⠑⠠⠔⠀⠄⢀⣀⠖⠒⠠⠴⠐⠐⠊⣠⠎⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠙⠒⠦⠤⢦⣄⣠⣤⣀⣀⣠⣀⣠⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠊⠉⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⢁⡌⠀⠀⠀⠀⠀⠀⣈⡶⢀⠀⡀⠀⠀⠀⠀⠀⠰⣩⢹⡑⡒⠀⠀⠀⠀⠀⠀⢀⠀⣩⠏
⠀⠰⠀⠤⠀⠰⠌⠰⠀⠀⠀⠀⠸⠁⢀⠀⠈⠥⠀⠀⠀⠀⠀⠰⡃⢱⣢⢠⠀⠀⠀⠀⠀⠀⠉⠙⠚⠉⠅⠀⠀⠀⠀⠀⠴⣤⠚⠕
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠻⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠊

⠀⠀⠖⠒⢒⠒⠒⠆⠀⠀⠀⠀⠀⢀⠠⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡄
⠀⠀⠀⠂⠤⢤⠀⠀⠀⠀⠀⠀⢀⠚⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⣔⠙⢄⡙⠈⠀⠀⠀⠀⡱⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢠⠪⣩⠷⢱
⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠘⠉⣉⡉⠙⠀⠀⠀⠀⠀⢠⡐⢆⠱⠄⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⠙⢬⠀⠁
⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠚⠒⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠠⠒⠢⡈⠂⠀⠀⠀⠀⠐⣁⠄⡄⠡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⠀⠀⠀⠀⠞⠀⣀⢀⣀⠐⠷⠀⠀⠀⠀⠠⡮⡖⠿⠶⢄
⠀⠀⠈⢂⡂⡂⡊⠁⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⢾⢠⠤⠘⠀⠀⠀⠀⠀⠈⠀⢤⠤⡄⠂⠀⠀⠀⠀⠨⣀⠅⠀⠀⠀⡠
⠀⠀⠀⠨⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡸⠜⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠈⣄⠀⡠⠊
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢱⠊⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⢰⠦⠭⢴⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡱⠀⠀⠀⠀⠀⠘⠚⠛⠚⡃⠀⠀⠀⠀⠀⠐⠛⠄⠎⠈⠆
⠀⠈⠅⠈⠁⠉⠉⠆⠀⠀⠀⠀⠀⠠⠀⠀⠴⠀⠀⠀⠀⠀⠀⡀⠊⢥⡤⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠂
⠀⠀⢾⡦⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⡁⠀⡁⠀⠀⠀⠀⠀⠈⠢⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⡉⠉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡾⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⣭⣵⣶⣄⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡇⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠃⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⣠⣴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠁⠀⠀⠘⢿⣷⠀⡀⠀⠀⢀⠀⠀⣀⠄⢀⣿⠿⠛⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡎⢀⡤⠀⠀⠀⠀⠛⠻⣿⣿⣯⣷⣶⣾⣽⣬⣿⣿⣿⣿⠢⠄⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⠂⠀⠀⠀⠀⠀⠀⠀⠘⣉⣉⣁⣀⣤⣤⡤⢤⢤⡀⠀⠀⣀⣀⣀⡀⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠳⡻⢦⣴⣄⡠⢤⣖⣐⠾⠿⠷⠮⠿⠿⠿⠿⠿⠾⠶⢛⣛⣋⣩⣥⣴⠶⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⡟⠛⠿⣿⡿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠿⠛⠳⠟⠀⣾⣿⣿⣷⡄⢿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣭⠿⠺⣿⣿⠏⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⠔⠊⢹⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⢀⣀⢀⡜⠁⡰⠃⠀⠀⢸⠀⣠⠀⡰⠊⠉⠲⣄
⣴⡖⠤⠋⠈⠋⠀⠰⡁⠀⠀⠀⣸⡤⠄⠠⢇⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠓⠊⠉⡆⢀⡠⠤⣈⢧⠀⢼⡡⠤⠄⠒⢶⣸⢶⡖⣒⡇⠀⣀⣀⠤⠤⠤⠔⠲⠤⢄⡀⠀⠀⠀⠀⢾⡵⠒⣷⣄⣤⣄⣀⡀
⠀⠀⠀⠀⠉⠁⠀⣀⣈⣯⣷⠀⠉⠓⠒⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠸⡅
⠀⠀⠀⠀⠀⢀⣸⡁⠠⠶⠮⠁⠀⠀⢀⡀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡔⠛⢤⠀⠀⡟⠲⡁
⠀⠀⠀⠀⠀⠈⢧⢈⣲⠶⠒⢢⠀⠈⠙⡧⣄⠀⠀⠀⠀⠉⠂⠄⢀⡀⠀⠄⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢱⠸⠊⠀⠀⠈⡯⣉⣱
⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⢀⡜⢣⠀⠀⠹⡜⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⠤⢤⣤⣀⠠⠄⣶⠤⠒⠁⣀⠷⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠑⢤⣣⣀⡀⠈⠃⠀⠙⠂⠀⠀⣀⣀⣀⣀⡤⢄⣈⢻⠉⠓⠤⢀⠀⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡝⠀⠙⠢⠤⣄⣈⣉⠉⠉⠉⠁⠀⠀⡆⠀⠀⠉⠳⠝⠂⠀⠃⠉⠛⣢⣄⡀⠀⢀⣀⢠⣤⠤⠒⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠂⠃⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⠀⠤⠋⠁⠀⡠⠊⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⠌⡒⢄⠄⠀⢀⡞⠁⠀⣀⠄⣠⣞⠾⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡛⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⠞⠛⠂⠤⢾⣴⠊⢉⣼⡶⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢦⣕⡢⢄⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠑⠻⣁⠀⣀⡠⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠉⠓⠮⣕⣢⢄⣠⢎⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⠀⠀⢀⣀⠜⣹⠙⠓⠦⠭⣕⣢⣤⣄⣀⣀⣠⡯⠛⠉⡷⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠤⠖⣊⠭⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⢹⠀⠀⠀⡰⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠦⠒⣹⠁⠀⠀⣘⠤⠢⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠻⠔⣒⡺⠅⢴⣉⠦⢶⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⣀⡸⠀⠀⠀⠀⠀⠀⠀⢎⡀⡱⠀⢀⣄
⠀⠀⠀⠀⠀⠀⡃⠈⡄⠀⠖⠲⠀⠀⢀⠴⡄⠀⠀⢠⠀⠄⠀⡌⠀⡂
⠀⠀⠀⠀⠀⠀⡭⢭⠀⠀⠀⢸⠀⠀⠨⣀⠸⠀⠀⠐⠀⠀⠀⢨⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢰⠀⢦⠀⠀⠸⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠊⠉⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠠⠒⠒⠀⢸⠉⠉⢹⠀⢘⠉⠉⠙⠀⠒⠂⢆⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠸⠀⠀⠈⠉⠁⠀⢐⠀⡇⠈⠢⡀⠀⠀⢀⣤⣤⣒⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠷⢀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸⠀⣨⠀⠀⠀⠀⠀⠀⠘⠒⠃⢀⠴⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠂⡞⠅
⠀⠀⠀⡂⠀⠁⠒⠀⠤⠤⠀⣀⣀⣀⣈⣉⣁⣀⣀⣀⡀⠠⠤⠄⠐⠊⠁⠀⡇⠀⠀⠰⠆⠀⠀⠀⠤⠤⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠐⠒⡏⠄
⠀⠀⠀⣉⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢈⠀⠀⠀⢐⠒⠂⠀⠠⠤⠤⠤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⠀⠈⠉⠒⠠⠤⢀⣈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈⢉⣀⠠⠤⠒⠈⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠁⡏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⠤⠄⠄⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆
⠀⠀⠀⠈⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠒⠒⠒⠒⠒⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣄⠤⢀⡤⠠⢄⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⢒⡠⠶⠺⣦⠴⠦⣴⠳⠶⢄⠀⠩⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⡠⠊⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠑⣄⠈⠢⡱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀
⠀⠀⠀⢠⠃⡔⠁⠀⢀⠃⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠑⡘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢀⠆⡜⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠐⡈⠆⠀⠀⠰⡁⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢁⠇
⠀⠀⠎⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠐⡈⠄⠀⠀⠋⢲⡐⠢⠤⠬⣉⣉⠈⠉⠀⠁⣉⣀⣀⡉⣁⠠⠀⢐⡴⠙⠆
⠀⠈⡶⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡀⠀⠀⠰⡆⠀⠀⠁⠦⠌⣁⠐⠂⠀⠄⠀⠠⠨⠤⠀⠀⠠⠀⠀⠒⣈⣁⣰⠋
⠀⢰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠈⠒⠤⡉⢈⡁⠀⠐⠒⠀⠀⠀⠈⠉⢉⣀⣁⠤⠒⠁
⠀⠈⠒⠀⠄⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⠂⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠉⠂⠤⢀⣀⠠⠔⠊⠁⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⡽⠛⠋⠛⠛⠓⠶⢤⣄⣀⢀⣀⣠⣤⠶⠶⠶⢦⣄⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡏⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣰⣦⠀⠀⠙⢦⠀⠀⠀⠙⢷⣄⣀⠤⠤⢤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡿⠀⠀⠀⢸⣾⡿⠀⠀⠀⣄⢠⡄⠀⠀⠈⠛⠛⠀⠀⠀⠈⢷⣄⢀⡤⣾⡁⢠⣤⡄⠛⠉⢀⣠⡍⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⡯⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠿⠗⢈⣥⡄⢀⠾⠶⠀⠾⠿⠀⠰⠿⠉⢢⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠞⠃⠀⣀⣠⣤⣤⣤⣴⠶⠦⢤⣄⠀⠀⠨⣧⠀⡼⠁⠰⠶⠆⢡⣗⠀⠶⡶⢀⣴⡌⠛⠓⠰⣿⠀⢳
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⣡⡴⠚⠛⠉⠉⠙⠛⠲⢬⣳⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡟⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⢷⡀⢸⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀
⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⢀⣀⠈⠃⠘⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢸⡇⠀⣾⠀⠀⠚⠛⠉⠀⠀⠀⠹⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣶⠒⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠁
⠀⠀⠀⠀⣧⠀⡟⠀⠀⠀⠀⠀⠀⠛⠳⠆⠘⠿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠨⡆⠘⠤⠊⠉⠓⠤⠤⢤⡀⠀⠀⠀⣠⠖⠦⣀⠀⠀⡰⠋⢸
⠀⠀⠀⠀⠸⡆⢿⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠛⠷⠦⣤⣤⣤⣤⠤⠶⠋⠁⠀⡀⣣⠀⠀⠀⠀⠀⣠⣀⠀⢧⡀⢀⡴⠃⢀⣄⡀⠉⠉⠀⠀⡎
⠀⠀⠀⠀⠀⢹⡜⣆⠀⠀⠀⠀⠀⠈⠻⠂⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠛⡿⣿⠀⠀⢦⠀⠘⢷⡿⠀⠀⢌⡤⠀⠀⢿⡿⠇⠀⢰⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⣴⠇⠀⠀⠀⠘⠷⠀⠀⢸⠇⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠙⠲⠶⢤⣄⠀⠀⠀⠀⠀⠉⠀⠀⠈⠻⣆⢀⣀⡀⢀⡟⠀⠀⢹⡀⣈⣄⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠙⠾⠤⣴⠚⠺⠏⠉⠉⢧⠀⠸⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣝⣓⣲⠒⠚⠋⠁⠙⣦⣀⠀⢀⣠⠾⢦⣀⣀⣀⡴⠛⠒⠒⠀⠤⠤⠤⠀⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣄⠀⠀⠀⢀⣾⠏⢀⡴⠀⢀⣤⠆⠀⢀⣤⠀⠀⢺⠻⠷⣧⣖⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⢸⡿⢀⠀⢀⣾⠏⠀⣾⠁⠀⣾⠟⠁⠀⣾⠃⠀⠀⠀⡄⠀⠀⠀⡸⡩⢵⡆
⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠈⠛⠁⠀⢸⡟⠁⢸⡟⠀⠀⠻⠤⠀⠀⠛⠀⠀⠀⠀⢀⡀⠀⢠⡁⠱⠞⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣤⠘⡇⠀⢸⡇⠀⣴⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣦
⠀⠀⠀⠀⠀⢠⣬⣾⠛⡟⢻⠉⠈⡆⠀⠙⠀⠀⠉⢰⣿⡏⡰⠁⠀⣰⡄⠀⣠⣞⠂⠀⣴⡶⠆⠀⢸⣿
⠀⠀⠀⠀⠨⡀⠙⢧⢳⡘⣸⠀⢰⠀⠰⠂⠀⠀⠀⣼⣿⠋⠀⡵⠀⣿⠇⢰⡿⠁⠀⢼⡟⣠⠇⠀⢸⡿
⠀⠀⠀⠀⢀⡈⠑⠒⠧⣵⣿⣰⠏⠀⠀⠀⠀⠀⠀⢿⣿⠠⠚⠁⠀⠿⠀⠀⠛⠂⠀⠸⠷⠃⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠉⠀⠐⢁⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⠿⠿⠿⢿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠐⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣍⣁⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣔
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠋⠀⠁⠀⠂⠀⠀⠁⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⠟⠁⠀⣜⠐⢶⣶⡄⠀⠀⠰⠿⠛⠀⠇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⡀⠀⠰⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠄⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈⣷⣉⠛⣛⣿⣿⠿⠱⠿⣿⣍⣉⣤⣴⣶⣶⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠠⠄⢻⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⠏⢻⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠈⢿⠿⠷⠀⠀⠀⠀⠐⠛⠛⠿⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠸⣦⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣀⡀⢻⣧⢹⡇⣽⣏⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣾⠏⣁⡼⠘⠁⠘⠀⣾⢉⡇⣼⠉⡇⣠⡤⡀⣴⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠉⢀⣴⣳⡄⣸⣇⣚⣡⡟⠚⣱⡿⠤⢳⡟⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣹⠛⣻⠃⠀⢸⡏⠉⠙⢧⠴⠋⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢀⡠⠋⠛⠁⢀⡿⠀⠀⣾⠀⣴⠶⠦⢄⣀⢀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠚⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠳⡄⢸⣿⠿⢷⠀⣿⠛⠿⠀⢸⣿⡇⠀⣿⠃⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣅⢸⣿⣶⡾⠀⣿⢶⠀⠀⣿⢹⣧⠀⣿⠶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⡿⢸⣿⠈⣿⠀⣿⣤⣶⢰⣿⠻⣿⡤⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣳⣶⣾⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡄⠀⠀⠀⢠⡾⣻⠏⣿⢻⣇
⠀⠀⠀⠀⢀⣸⢃⣿⠀⣿⠦⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⢏⠹⡇⡹⡆⠋⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠋⠸⠟⠀⣴⣿⣿⠛⢿⣿⣦⡀⠀⠀⠀⠀⡄⡆⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⡟⠀⠈⢻⣿⣿⣦⡀⠀⢀⡡⠐⠊⠁⠀⠀⢀⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣷⠀⠀⣀⣹⣿⣿⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⠀⣠⣄⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⡄⠀⠀⣀⠀⠀⢸⣿⣿⠿⢐⣇⣈⡄⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⢿⣿⣿⠦⣀⠀⢀⣠⠞⣿⡿⠀⠘⠉⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠛⠉⠁⠀⠀⠀⠃⠀⡀⠠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⣿⠀⠠⠄⠀⠄⠄⠤⠂⠈⠀⠀⠀⠑⣄⢚⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⡋
⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣇⡀
⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠋⠘
⣿⣶⠀⡀⢀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠀⣠⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠳⠆⣶⡟⣦⣾⣿⡛⢰⣿⡛⠃⣿⣟⠓⢸⣿⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠆⢿⣧⡟⢹⣿⠁⢸⣿⠉⠀⣿⣯⣄⢸⣿⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⣶⣄⣀⣀⣀⣀⣀⣀⠀⠖⢆⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡧⢀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⡒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡁⠈⠀⠀⠀⠀⠀⠀⠀⡓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠅⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠂⠀⢄⡀⠀⠀⣀⣀⢠⠤⢖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠄⠀⠄⠀⠀⠀⠐⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠆⠁⠀⠀⠀⠀⠀⢈⠖⠓⠄⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⡅⠀⠀⠀⠀⠀⢈⠀⢀⣠⢒⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⢨⣭⣭⣥⢠⣤⣤⣤⠀⢠⣭⡍⢩⣤⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣿⢸⣿⣷⡿⢸⣿⡷⠄⠀⣿⣿⣧⢸⣿⣿⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⡴⡆⠰⣊⡥⠎⠀⠀⠀⠀⠀⠀⢀⣴⡟⠛⠃⣀⠈⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣤⡄
⠀⠀⠀⠀⠀⡀⣇⠣⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢀⣤⠾⠉⠻⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣟⣻⡿⢾⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣵⣁⣼⠀⠀⠀⠀⠀⠀⠀⣭⣤⣤⣥⣤⣤⣤⣤⣤⡍⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣷⣽⣛⣿⣥
⠀⠀⠀⢀⣼⣿⣉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣤⣤⣤⣤⡀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣟⣯⣿⠉
⠀⠀⢀⣺⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠙⠛⠛⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣄⣈⣙⣿⡇
⠀⠀⠈⠉⠙⠷⠿⢿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠾⢯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⡴⠛⠻⠋⢓⣦⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠠⠀⠠⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⣋⣭⣴⣾⣿⣿⠄
⠀⠀⠀⣾⠛⠀⣶⢀⣨⣭⡇⠀⠀⠀⠀⠀⠀⠘⠳⠤⣄⡀⠀⠀⠀⢀⡴⣚⠁⠀⠀⠀⠀⠀⣴⣭⣶⣾⠿⠟⠋⠁⠈⠹⡏
⠀⠀⠀⠻⣾⠂⣴⡏⢥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠰⠿⣶⣍⡲⠤⢞⣭⣾⣿⡄⠀⠀⠀⠀⢺⣿⣿⠁⠀⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠙⠳⠾⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢯⣻⠿⣛⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠻⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠰⢿⣶⣤⣉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢲⣄⣿⢰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡈⠛⠁⠀⠀⠀⠀⠀⠀⠰⡖⢾⠸⡇⣿⢸⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣷⣶⣶⡄
⠀⠀⠀⣿⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣬⣶⣷⣷⣾⣧⣬⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⠀⠀⡟
⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣾⣿⣦⣶⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⠟⢻⡇
⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⣠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠀⠐⠆⠀⠀⠀⢐⠁⠀⠈⣡⠕⠀⠀⠀⠸⢏⣙⡆⠀⠀⠀⠀⠀⢠⡆⠤⠀⠀⢤⠀⠀⠀⢀⡠⠜⠿⢦
⠀⠀⣈⠙⠓⣾⣛⣷⠀⢰⣿⡿⢿⣂⣸⡄⠀⠀⡀⠀⠀⠀⣸⣄⠀⠀⠠⣷⣦⣽⣷⢆⣰⡆⠀⠀⠀⣾⡟⠒⠚⠈⢰
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠰⢸⢸⣿⢯⡇⠀⠃⠀⠀⠹⠿⠀⠀⠻⠆⢄⡤⠀⢸⡷⣦⡄⠀⣼
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠊⠁⠀⠐⠀⠀⢀⣀⡀⠀⢠⣤⣤⡤⠀⢸⣄⣈⡁⠀⣈
⠀⠀⠀⠀⢀⢀⠀⠤⢀⡢⠀⠀⠀⢠⣾⣛⣛⡿⠞⠀⠀⠀⠀⠀⠀⠀⠤⡅⠈⠧⠺⠖⠶⠶⠶⠖⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣟⡶⣶⢤⣌⡀⠀⠀⠐⠀⠤⢍⣙⣷⠀⠀⠠⠔⠀⠀⣤⣶⣢⠀⠀⠀⠀⠀⢀⣚⣁⠚⠻⢶⢂⣰⠄
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⡟⠀⠀⠯⣉⡓⠢⢤⣙⠀⠀⠁⠀⠀⠀⡠⣾⡏⠀⠀⠀⣄⡀⣉⣉⠉⢀⢠⠼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠑⠺⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠙⠂⠐
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⢀⡀⢀⠀⡔⠀⠢⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⢰⠄⢰⠂⢀⠆⠀⢲⠀⣀⠀⠀⠔⠒⠒⡄⠀⣀⠀⠀⡠⠄⠤⡀
⠘⠁⠃⠀⠀⠁⠀⠀⠀⠄⠘⠀⠀⠑⠂⣤⡈⢿⣵⣮⠣⡈⣄⠾⠲⣤⣘⡠⢃⣀⠀⠀⠀⠀⠘⠨⠁⠀⠈⠀⠀⠀⠸⠀⠀⠀⠉
⠀⠤⢄⠀⠆⠉⠁⠀⠀⠀⢀⠀⠰⠃⠀⢻⣝⣶⣇⣉⢦⢋⣤⣶⣶⣄⣈⡶⣋⠏⣄⠀⠴⠤⠀⠔⠀⠀⠈⢢⠠⠄⠀⠂⠈⠁⠂
⠀⠤⠄⠀⠀⢂⠀⠘⠁⠀⠀⠀⠠⡔⢂⢦⣽⣿⣿⣄⣶⠸⣿⣟⠛⠛⣇⡶⠧⠾⣥⣄⣀⠀⠀⡀⢐⠈⠉⠀⠀⠀⠀⠉⡀⠀⠁
⠀⠀⣠⠴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠙⠣⠿⢿⠛⠛⣏⣉⠭⣿⣶⣾⠟⠃⣸⠒⢾⣿⣿⣿⣷⠄⠀⠀⠱⣠⣶⣶⣾⣿⣳⣶⣤⡀
⢠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣛⣀⡤⠞⣹⠉⡸⣧⢴⣇⣴⡦⠻⣎⢙⠉⠙⠈⠛⢯⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡽
⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⠁⠐⠃⠚⠅⡾⢳⡈⠁⠈⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣄⠀⠀⠀⠀⢠⠞⠀⠀⠙⣄⠀⠀⠀⠀⢠⣴⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⢦⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠸⡻⠟⠋⠹⡄⡴⠁⠀⠀⠀⠀⠀⠀⠈⢧⢀⠟⠉⠛⠛⡏⠉⠛⠛⠛⠛⠛⠋⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣀⣳⡀⠀⡇⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠄⡀⠀⠲⣭⣯
⠠⣶⣦⢠⣤⣄⢀⣄⡀⠙⠿⠋⢀⡀⣧⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⢾⠁⠀⠀⠀⡏
⠀⢹⠇⠂⠻⠃⠘⠿⠃⠒⠚⠒⢻⠟⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⣇⣀⣀⣠⣤⣤⠴⢻⠲⠤⠒⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠀⠐⠀⠐⠒
⢠⣀⣀⣄⡄⣀⢠⣀⣀⣀⣤⣤⠤⠖⣺⡆⠀⢨⡴⣖⣋⠉⠉⠉⠉⠉⠉⣓⣲⢤⢰⠀⠀⣼⠆⣄⡀⡀⣀⣀⣀⠸⠴⡇⠀⠤⠤
⣼⣿⣿⠿⠿⠟⠛⣋⡉⠀⠢⠃⠫⣯⢽⢳⠀⡿⢸⣏⡛⠻⠿⠿⠿⠿⠛⣋⣿⡜⣿⠀⢠⣿⠈⣐⡪⣳⠐⢚⡀⢀⠐⠀⢀⠊⢰
⢀⢢⢤⠤⣷⡉⠉⢤⠐⣾⢫⡶⡂⢠⢸⡘⣷⠇⢸⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⡇⢻⡄⡼⢸⢰⢢⠢⠄⠡⠠⣤⠳⣞⣀⡸⠱⣅
⠐⢽⡉⢡⣈⡟⣉⣉⣇⣼⠐⠀⠅⣀⠘⣷⡇⠀⠘⠿⢿⣧⣶⣤⣦⣼⣿⣿⡿⠁⠀⢻⡇⣾⢀⠝⢁⡂⣸⡀⠨⠤⠏⠋⣠⣀⣤
⠰⣄⡈⠣⡜⡷⣨⠃⡦⢤⠼⠲⠠⠁⠄⣟⠧⣴⣶⣾⡿⠿⠿⠿⠿⠿⠿⣿⣷⣶⡦⠞⢡⡇⡜⠋⢯⢔⡹⠈⠞⠆⢒⠫⣥⡽⠥
⠀⡁⢈⠀⢿⢻⡁⡈⢤⡾⣤⢺⡜⡼⠀⡜⢦⡀⠉⢪⡻⠭⠭⠭⠭⠭⠭⢋⡞⠁⠀⣠⠏⠄⢧⠆⣸⣁⡄⠁⡘⠧⣾⠤⢃⠰⢰
⠀⡧⢸⠎⠉⢸⡈⢣⡘⠿⠛⡯⡠⠃⡂⠹⣄⠳⢄⡀⠳⣄⣀⣀⣀⣀⣠⠞⠀⡠⢚⡁⠐⣞⡎⢉⠓⢴⠘⣒⢡⣥⡌⣢⢌⠄⢛
⠀⠎⡆⢼⠫⣳⠙⡼⣗⠓⢊⡅⡀⠼⣡⠀⡏⠳⣄⠉⠓⠦⣍⠉⣉⠭⠖⠒⠚⠱⡱⠀⠆⢻⠘⢤⡾⠀⡣⣠⠸⣍⡆⠣⡜⢢⠐
⠈⡄⡱⠼⣥⡥⡜⢫⣘⢾⠄⣹⠁⡄⠀⡴⡁⠸⡈⣉⠙⢲⢬⡛⢁⡴⡞⠛⡩⢠⠁⣶⠀⣟⢉⡌⠩⢹⢴⠈⢏⢸⠰⣃⡨⢶⢸
⠀⠻⠆⠲⠑⠃⠣⠇⠋⠖⠈⠻⠄⠫⠁⠠⠅⠸⠰⠇⠎⠀⠰⠟⠻⠴⠁⠘⠓⠚⠷⠠⠆⠨⠉⠃⠰⠚⠖⠖⠉⠾⠰⠡⠰⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡶⠶⢿⡟⠛⠛⠉⢻⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢿⠛⠋⠉⠹⣇⠀⠀⠈⣧⣀⣠⣤⣼⡷⠾⠿⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠟⠛⢿⡁⠀⠀⠘⡇⠀⣀⣠⣿⡶⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⢀⣤⣴⡶⢿⡟⠋⠁⠹⡆⠀⠀⢘⣧⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠸⣿⠀⠀⠈⢧⠀⣀⣠⣿⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠶⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠹⣧⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠌⠁⠈⠻⠀⠀⠀⣀⣠⣤⠴⠖⠛⢿⣆
⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠈⢿⡆
⢰⡟⢹⣧⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣾⡇⠀⣿⡆⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⣿⠀⠀⠸⣷⠀⠀⢻⣧⠀⠀⠀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⣿⡀⠀⠀⢿⡆⠀⠀⢻⣶⠚⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⢻⡇⠀⠀⠘⣷⠀⠀⠈⢿⡄⠀⣠⡾⢁⡾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⢸⣧⠀⠀⠀⢻⡆⠀⠀⠘⣷⡀⠉⢠⡟⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⣿⡀⠀⠀⠘⣷⠀⠀⠀⢹⣧⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣠⣶⠆⠀⢿⡆
⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢿⣤⡷⠀⢿⣤⣀⠀⠘⣿⡀
⠀⠀⣿⡆⠀⠀⠘⣿⡀⠀⠀⠈⣿⡀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠈⣿⣷⣄⠀⠉⠹⣷⠀⢹⣧
⠀⠀⠸⣷⠀⠀⠀⢹⣇⠀⠀⠀⠸⣷⠀⠀⠻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣦⡀⠀⣿⡀⠀⠀⠀⠘⣿⠙⠃⠀⠘⠋⠀⠀⢿⡆
⠀⠀⠀⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⢻⣇⠀⠀⠀⠉⠻⢶⣄⡀⠀⡀⣀⣄⡀⠀⢰⡟⠀⠀⣿⣧⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠘⣿⡀⠀⠀⠸⣷⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠙⢿⡌⣿⡟⠙⢷⡄⠘⢷⣤⣴⡿⠙⠃⠀⠀⠀⠀⠀⢀⣠⡤⠶⠂⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢹⣇⠀⠀⠀⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷⡀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣿⡀⠀⠀⠀⢹⣇⠀⠀⢀⣀⣀⣸⡟⠀⠉⠁⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⢰⡆⠀⣰⠀⣀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠈⠙⠛⠋⠀⠀⢀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⠀⣿⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢻⣆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⢿⡄⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠘⣷⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠹⣧⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢻⣇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡆⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⣿⡀⠀⠀⢿⡆⠀⠀⣀⣠⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠸⣧⠀⠀⠸⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣇⠀⠀⣿⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⢿⡟⠋⠉⣷⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⣿⡄⠀⢻⡇⠀⠈⠳⣄⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠻⣏⠉⠀⠀⠈⣷⣠⣴⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢸⣷⠀⢸⡇⠀⠘⠳⢮⡻⠆⠀⠀⠀⢀⣠⣤⣴⣶⠟⠛⠉⠙⣧⠀⠀⢀⣹⣦⣴⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⢿⡇⣾⡇⠀⠀⠀⢀⣀⣤⣴⠶⢿⡟⠋⠉⠀⠸⣇⠀⠀⣀⣼⣶⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣁⣤⣶⡾⠛⢻⡅⠀⠀⠀⢻⡄⠀⣀⣤⣿⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉⠁⠘⣧⠀⢀⣻⣤⣤⣴⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⣶⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢲⠁⠐⠋⠀⣀⡀⠉⢷⠉⡴⢟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⣎⣀⢠⠔⠀⠀⠀⠀⡀⠀⠀⢁⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠓⠉⠎⡉⠣⠀⡀⣤⠔⠒⠉⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠘⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠚⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠰⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⣴⡶⠟⠋⠉⠉⠳⡄⠀⠀⣸⣁⣁⣼⣁⣋⣀⣀⣤⡴⠞⠋⠁⣄⠀⣀⡀⠀⠀⣠⠚⢏⡧⠀⠀⠀⡇
⠀⣰⣿⠏⠀⠀⠀⢰⣏⡦⠃⠔⠉⢹⣄⠀⢻⡏⠉⠉⢉⡴⣶⠄⢰⠀⢀⡞⢁⡼⠀⡼⠁⠀⠀⡴⠂⠀⣼⠇
⢸⣿⡏⠀⠀⠀⠀⢀⣼⣾⣶⣤⡁⠀⠻⣦⠈⢿⡆⠀⣿⣠⠏⢀⡏⠀⢸⡖⠉⢀⡼⠁⠀⠀⠀⠘⠒⠛⡟⣤
⣿⣿⡇⠀⠀⠀⠀⣿⡏⠈⠀⠘⡇⠀⠀⠘⣇⠘⣷⠠⠛⠧⠶⠛⠀⠀⠁⠙⠒⠋⠁⠀⣴⠂⢰⣃⠷⣄⢷⠾⠤⠤⠞
⢻⣿⣿⡄⠀⠀⠀⢿⣧⣀⣀⡴⠃⠀⠀⠀⣿⠀⡏⠀⠀⣠⠴⠒⣶⣦⠀⣤⠊⠓⣸⠀⠹⠦⠂⠉
⠀⠙⢿⣿⣶⣤⣀⡀⠉⠉⠉⠀⠀⠀⠀⣰⠃⡜⠀⣠⠊⠁⣠⣴⠟⠋⣰⠃
⠀⠀⠀⠈⠙⠻⠿⢿⣿⣶⣶⣶⣤⣄⠀⠃⠰⠁⡼⠁⠀⠀⣉⣿⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⡆⢈⠐⣠⠶⠚⠛⠉⠉⠁
⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄
⠀⠀⠰⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠿⠿⠛⢻⣿⠿⡛⠛⣻⣿⣿⣿⣀⣤⣤⣤⣤⡀
⠀⠀⠀⢻⡿⣿⣿⡿⠛⠻⠿⠷⠶⠶⠖⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⠟⠛⠉⠛⣿⣿⡆
⠀⠀⠀⠈⢧⢹⣿⣗⠀⣴⣿⣷⣦⣠⣴⣾⣿⣷⡄⠀⠈⣸⣿⣿⠁⠀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠈⣦⢹⣿⡂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣾⣿⠇⣠⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠹⣧⡹⣿⣌⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⢴⣿⣿⡿⠟⠉
⠀⠀⠀⢀⣀⣤⣷⡹⡾⢿⣦⡀⠀⠙⠏⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀⣀⣀⡀
⠀⣠⣾⣿⣿⣿⣿⣿⣮⣋⡻⣷⣤⣤⣀⣠⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⢸⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠹⠿⣿⣿⣿⣿⡇
⠙⢿⣿⣿⣆⠀⠈⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠛⠛⠋⠭⠗⠒⠀⢀⣠⣽⣿⣿⣿⠃
⠀⠀⠉⠛⠿⢿⣿⣶⣶⣶⣶⣤⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠑⠒⢒⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⣀⣀⣤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣇⢸⣻⣿⡇⠙⢶⡀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠈⣏⠟⠓⠲⣾⣿⣷⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⡀⢐⡶⢿⡗⢠⡄⠀⠙⢻⡟⣉⣉⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣨⣃⡈⠙⠊⢱⠀⢠⡄⢀⡬⡟⢿⡟⠷⠀⠀⢠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠬⢭⣀⠀⠀⢢⠀⠀⣈⣿⡟⡮⢁⣄⠐⣜⣳⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⢽⣛⡟⠡⠴⠷⣾⣿⣿⣎⠝⠋⠀⢀⡜⠿⢽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣾⣧⣞⠉⠀⢤⢞⠀⠀⠈⢉⣀⡤⡄⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠈⠋⠤⠴⠿⠿⢟⢵⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣽⣿⣷⣦⠀⢀⡀⠀⣀⠜⠫⠄⠂⢈⣷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⡯⢾⡟⠉⠀⠀⡐⢈⢂⣾⣿⣮⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠙⢳⣸⠃⣍⣷⣤⣤⠾⠛⠁⠈⣻⠟⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠟⠛⠋⠉⠀⠀⠀⠀⠼⠣⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠀⠰⠄⠀⠀⠀⠀⠈⠻⣿⠿⠀⠐⠾⣻⢓⣧⠀⠀⠀⢠⠤⢀⠀⠀⠀⠀⣀⠒⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⡀⠰⠦⠐⠓⠸⠃⠶⢰⠦⠒⠘⠛⢶⣶⣿⡄⡀⡍⡉⡁⠰⠃⠀⠀⠀⣴⣦⡤⠀⠀⠙⣉⣿⣿⠏⠁
⠠⢊⣠⠀⠀⠀⠤⠀⠆⠐⠂⠛⡀⠛⢠⣮⣤⠆⠀⠀⠀⠈⢹⠇⠆⠻⠃⠓⠀⠀⠀⠀⠀⣿⡟⠁⠀⠠⠾⠟⠛⠁
⠀⠈⠀⠀⠰⢠⡄⠰⢂⠐⠃⣈⠁⠶⠂⣈⠙⠀⠀⠀⠀⠀⣾⠀⠀⣀⣀⠀⣵⣦⡤⣴⢶⣿⠈⠠⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⡄⠗⠈⢁⣄⠋⡀⠒⠀⠉⣀⠉⠁⢠⡤⠚⠽⣏⣻⠟⣡⣼⣿⣿⣿⡇⣓⠿⡻⠆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠋⡀⠛⣀⠁⠘⠋⣠⣏⣭⣽⢛⣛⠭⠥⢲⣿⠿⣿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠛⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣩⠔⠚⠓⠢⣍⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡥⠒⠉⢀⣠⣼⣦⣄⡀⠉⠲⢌⡙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⣈⠳⢤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⠴⢋⡠⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⣌⡙⠿⣿⣿⣿⡿⠟⢉⠤⠒⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠉⠒⠤⣉⣡⠔⠊⠁⠀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⣧⣠⣄⡀⠀⢸⠀⠀⠀⢠⠿⢄⡀⠙⠲⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⠀⠳⢄⡈⠑⡶⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⠃⢸⠀⠀⠀⠀⠀⣀⣘⠀⢁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢿⡿⣿⣶⣿⠿⣶⣄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⠟⠁⠀⢸⠀⠀⠀⢠⠛⢅⣉⠀⢸⠀⣿
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣛⣻⣿⡿⢟⣿⣻⢿⣿⣟⣿⡿⣷⣤⣀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⢄⡉⠀⠸⠀⣿⣶⣤⣄⡀
⠀⠀⠀⢰⣿⡿⣷⣾⣯⣿⣿⣯⡺⠿⠿⠿⢿⣪⣿⣿⣾⣟⣿⣿⢿⡆⠀⠉⠓⠦⣄⡀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿⣷⣿⣾⣿⣿⠿⠋⠁
⠀⠀⠀⢸⣿⣿⣷⣭⣻⢿⣭⣿⢿⣷⣾⣶⢿⣿⣭⣿⠿⣻⣽⣾⣿⣷⠀⠀⠀⠀⠀⠙⠳⢤⣸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⢸⡏⠻⣿⣿⣿⣷⣯⣛⠿⣿⣟⣻⡿⢟⣫⣷⣿⣿⡿⠿⠋⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡿⠟⠋⠁⠈⠁
⠀⠀⠀⠘⠳⣄⡀⠉⠙⠻⢿⣿⣿⣾⡍⣽⣾⣿⡿⠛⠁⠀⠀⣀⣤⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠙⠻⢿⣧⡿⠟⠁⠀⢀⣠⣴⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⢸⠀⣀⣤⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⢀⠀⣀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠤⠤⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⣶⣰⣦⠀⠀⠀⠀⠀⠀⢐⠀⠄⢂⠈⢀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⣠⠐
⠀⠀⢀⣠⣤⣴⣶⡆⠀⠸⠀⠈⠹⠀⠀⣠⠀⠐⣥⣤⣤⡄⣤⡄⠀⡂⠀⣀⠄⠁⠀⠀⠣⠀⠀⠠⠰⠀⠀⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠐⡐⠈
⠀⢸⡿⢟⡿⣱⣼⡇⠀⠠⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠁⠀⠀⠀⠄⠀⠀⣠⣴⠀⡄⣐⡥⠤⠄⣀⣤⠀⠆⠐⢀⣀⠐⠓⠒
⠀⢸⡷⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⣻⠀⠃⠀⠁⠈⡛⠛⠁⠠⠀⠀⢿⢸⠠⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠸⠂⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣹⡴⠛⠁⠀⠀⠀⠀⠙⠃⠄⠈⠀⠀⠈⠈⠉⠀⠀⠁⢰
⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣞⣁⣀⣺⣆⠀⡅⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡿⠋⢀⡄⠀⠀⠀⢄⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠈⠀⢼
⠀⠸⢯⣿⣿⣽⠻⠇⠀⠀⣾⠙⡋⣩⡇⣜⡷⠀⠀⠀⠠⡰⠖⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠺
⠀⠈⠂⠤⠠⠄⠐⠁⠀⢀⠈⠒⠻⠟⠛⠛⠁⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣄⠐⠑⠄⠀⠐⠐⠁⠀⠀⠐⠀⠀⠀⢐⡹⢄⠀⠀⢘⠀⠀⠀⠀⠀⢰
⠀⠀⢀⡀⠀⠀⠒⠨⠊⠀⠁⠂⠀⠀⠀⠐⠈⠀⠈⠐⠀⠀⠀⠐⠊⠀⠀⠀⠈⠁⠐⠓⠈⠀⠀⠐⠊⠁⠂⠢⠀⠀⡐⢃⡄⠀⠐⠀⠀⡀⠀⠀⠄
⠀⠀⠈⠉⠀⠀⠄⠲⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠄⠀⠀⡀⠀⠀⠈⠄⠂⠀⢞⣘⠀⢈⠒⡆
⠀⠀⠃⠂⠀⠀⡀⣀⡤⠖⠉⠀⠀⠀⢸⡿⠛⠛⡃⠀⠀⠀⠀⠀⠀⣷⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠰⠾⠃⠁⠀⠀⢀⡀⠠⠤⠄⠠⠄⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠃⠀⠀⠀⢸⣧⣀⠘⠓⠒⠰⠆⠂⠲⠂⠙⠀⠈⣹⠃⠀⠀⠀⠀⠀⠀⠀⡰⢂⣀⠀⢰⡀⠀⢀⠀⠀⠀⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣏⠉⣀⣄⣀⣀⣀⣀⣀⣈⣙⣀⣀⣘⠃⠀⠀⠀⠀⠀⠀⠀⠑⣆⡠⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⣜⢁⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠆⠀⢀⡁⠀⠐⠉⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⣾⡶⡎⠁⢸⠀⠀⠨⠀⠒⠀⠀⢒⣀⣠⣴⣶⣖⡒⠂⠒⠆⠠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⠀⠀⠀⠀⠤⠤
⠀⠀⠄⢀⠀⠀⢾⡏⠀⠐⠁⠀⠀⢜⠀⣠⠶⠿⠟⢋⡙⢫⣼⠰⢜⡆⠀⡁⠀⠀⠀⠀⢰⠰⣴⠀⡄⢀⠅⢸⡇⣇⡿⠀⣼⡟⠁
⠀⠀⡀⠀⠀⠉⠉⡀⢀⣀⠀⢀⠀⠀⠀⢧⣛⣣⣦⣦⣵⣷⣶⠿⠋⠀⠀⡇⠤⠠⠤⠠⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠄⡈⠀⠉⠀⠀⠀⠀⠀⠀⣼⠂⠐⠀⠈⠉⠛⠛⠋⠉⠁⠰⣯⣩⡿⠀⡆⡠⠀⠀⠐⠀⣀⡀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠐⢠⠤⡄
⠀⢈⣈⣁⣀⣀⣈⣉⣉⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣰⠺⡄⠅⢔⠐⠊⡀⡆⠀⠀⠀⢀⠀⠀⠀⠈⠄⠣⠀⠰⠂⠃
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⣄⠔⢨⡅⠖⡄⠀⡆⠔⠀⠑⡆⢦⠀⠣⡀⠁⠀⠀⠀⠈⠁⡐⢀⠠⠀⠈⠀⠈⠁⠂⠀⣠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠉⠀⠀⠁⠁⠀⠁⠁⠂⠐⠉⠉⠀⠀⠈⠢⠄⠀⠀⠔⠊⠀⠀⠀⠁⠒⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡈⠐⠁⡀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢰⣀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⣀⣤⣤⣀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⠿⡿⣷⡄⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸⣿⣥⣭⣿⢈
⠀⠀⠀⠀⠓⠲⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⣶⣷⣿⣇⡀⠀⠀⠀⠈⠀⢠⣤⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠠⠀⡀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠠⠀⠐⠄⠀⠀⠀⠀⠴
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠃⠀⠀⠂⠀⠄⠀⠐⠁⠀⠈⠉⠀⠒⠈⠀⠀⠀⠀⠈⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠉⠀⠀⢰⡆⠀⠀⠈⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⢾⣄⠀⠀⠀⠸⠇⠀⠀⠀⢠⡶⠀⠀⠁⠀⠀⣿⡄⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣠⣿⡟⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠘⠛⠛⠀⠀⠀⠘⠛⠛⠛⠛⢿⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣴⡟⠀⠀⠀⢨⡅⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣤⡄⠀⠀⣤⣶⣦⣴⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣤⣤⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢠⠞⢉⢤⡈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢠⡏⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⢀⠉⠀⠀⠀⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣠⡄⢰⣅⢀⡀⠀⢀⠙⠀⠀⠀⣠⠀⠀⠀⠀⠂⢹⠃⢀⡾⠁⠀⠛⠍⠀⠀⣀⣷
⠀⠀⠀⠠⢀⡸⠀⡠⠆⡠⠼⠿⠨⠦⣤⣄⡙⠲⣼⡄⠀⠂⣤⣤⣿⠶⠯⠴⠿⣿⠶⢤⣤⣤⣭⠟
⠀⠀⠀⠀⠙⠀⠀⠇⣀⠃⢀⣨⣤⡶⠶⣿⣿⣷⡘⣿⣆⣼⡿⠛⠉⠐⠀⠈⡀⢈⣳⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⡸⠋⠀⠁⡀⣀⡀⠈⢿⣿⣾⣿⢏⣴⠶⠛⠛⠓⢒⡀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠻⠆⡮⠚⢿⡰⣶⠀⠙⣿⣿⡟⢀⣠⠘⡄⠁⢈⣉⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠋⡀⠉⠁⠂⠀⢘⣿⠇⠐⠂⠁⠀⠀⠉⠘⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡿⣹⡆⠀⠉⠀⠈⠀⢨⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠄⣸⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠟⡁⠀⣼⠞⣧⡤⢸⣦⠀⣳⡶⠶⠀⣬⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⡸⡝⠀⣈⣵⡄⠈⢬⠃⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠘⣤⠀⠀⠁⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⠟⠉⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣾⣿⠻⡆⠘⢿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⡿⠋⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⢱⣿⠿⠁⠀⠁⠀⠀⠻⣿
⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢸⣿⣿⣿⣿⣇⣾⣿⣿⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⢠⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡿⣿⣎⣿⣿⣿⣾⣿⡟⣸⣿⣿⣿⣿⠃⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡟⠻⡟⠀⠀⠀⠀⠀⡀⣤⡀⠠
⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣴⠏⠀⠀⠠⠂⠀⢀⣤⣠⣴⠞⣽⣿⣿⡏⠀⣴⡇⠀⠀⠀⠀⠀⡇⢹⡇
⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢠⡿⠃⠀⠀⠀⣠⣴⣾⣿⣿⣿⣣⣾⣿⣿⣿⠀⣼⣿⣧⣤⠀⠀⠀⠀⠁⢸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡆⡀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡿⣧⠃⠀⠀⠀⠸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⣼⣿⣿⣿⡿⢨⣿⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣧⠟⠀⠀⠀⡀⠀⠁
⣿⣿⣿⣿⣿⣿⣻⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣯⣾⣿⣿⣿⣿⡟⠁⢸⡞⣿⣿⣿⣿⣧⠀⠀⢠⣇
⣿⣿⣟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠿⣿⠟⠀⣿⣿⣿⡿⣿⠛⣿⣧⡄⠀⢇⠈⠻⢿⡇⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡟⠀⣠⢿⣿⣿⣿⣿⠀⠈⠻⣷⡀⠘⠆⠀⢸⣷⡀⠘⠀⠀⢻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠇⠀⡇⠈⣿⣿⣿⢹⡆⠀⠀⠹⣧⠀⠀⠀⢸⣿⣷⡤⠀⠀⠈⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣾⣿⣯⠇⠀⠀⠀⠙⡆⠀⠀⠀⢿⣿⣧⣇⠀⠀⢹⡆
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⠃⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⠀⠀⠀⠀⢰⡄⠀⠀⠈⢻⡿⣿⡀⠀⢼⠁
⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠟⠁⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠳⠀⠀⠀⠘⣇⣿⣧⠀⢸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣾⣿⡟⢸⣷⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣷⣀⠀⣀⣤⣴⣄⣀⣤⣴⣿⣿⠀⠸⡇⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⡗⠀⠀⣿⠟⠿⠛⠛⠻⠿⠿⠛⠛⠛⠉⠁⠀⢸⣿⡟⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⠸⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣟⠋⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⢦⣀⣀⣀⣀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⣰⡌⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡟⣿⣿⣿⡿⣟⡿⠛
⣿⣿⣿⣿⣷⡜⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⢿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⠂⣠⣤⣾⣿⣿⣿⣿⣿⠇⠿⣿⠿⠚⠉
⣿⣿⣿⣿⣿⣿⣞⢷⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⡖
⣿⣿⣿⣿⣿⣿⣿⣯⠻⣆⠈⠛⠿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣉⣉⣭⣿⣿⣿⣿⣿⠿⠟⠫⠐⠋⠁⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣷⣦⡀⠀⠉⠲⠬⣝⣛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⢣⠃⠀⠀⢀⣸⣿⣿⣿⠟
⠀⠀⠀⠀⠀⡇⡇⠀⡌⠀⠀⣛⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠃⢰⠀⠀⠀⠸⣿⣿⡗⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣽⡄
⠄⠀⠀⠀⠀⢻⡀⢰⠀⠀⠀⠀⣻⣿⣿⣄⠀⠀⠀⣿⣦⡀⡀⡀⣾⡟⠀⠀⣠⣼⣿⣿⣧
⣧⠀⠀⠀⠀⠀⢳⡀⢆⠀⢀⣶⣿⣿⣿⣿⣤⣤⣤⣻⣿⡿⣷⣿⣿⣅⣶⣿⣿⡟⣿⣿⢯⢃⡀
⣿⣧⡀⠀⠀⠀⠀⠙⢌⢲⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⡿⡌⠛⢸⣿⡿⠉⠙⠜⢋⣵⣿⣿⣷
⣿⣿⣷⣶⣦⣄⣀⢀⣼⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣾⣤⣼⠿⢤⣤⡴⣚⠛⢛⣛⡿⠟
⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠅⠛⠀⠀⠈⣿⣿⣯⣿⠿⣿⣿⠁⠀⠀⠉⢅
⠀⠀⠀⠀⠅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⡀⠀⣠⣿⣿⣟⢃⣶⣤⣭⣔⢦⣄⠀⠀⠱⡀
⠀⠀⢠⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⢫⣿⣿⣿⢿⣿⣷⡄⠀⠐⡀
⠀⠀⢼⢷⣿⣿⣿⣿⣿⣿⡿⠙⠛⠉⠙⣿⣿⣿⣿⣿⣟⣿⣿⣿⣦⣾⣿⣿⢹⣿⣿⣿⠛⠀⠀⠱⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⠉⠻⢧⣅⣈⣿⣿⣤⣿⣿⠃⠀⢀⣴⣶⣿⠇
⠀⢠⠷⣿⣿⣻⣿⣿⠟⡃⠀⠀⠀⠀⠀⡿⠛⠃⣥⣿⣧⡄⠀⠀⡀⢰⣼⣿⣿⣿⣹⣾⣟⠞⣻⡿⡏
⠀⠀⢠⠟⢿⣿⣿⣧⣦⢉⠁⢀⠆⢸⣾⣃⠀⠀⠉⠿⠏⠁⠀⣼⠇⣸⣿⣿⣿⣿⣶⠁⠈⠉⠁⠀⡁
⠀⢰⣧⣦⣶⣿⣿⣻⠇⠘⠐⣿⠀⠀⢻⣿⢷⢦⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠋⣠⡖⠀⠀⠀⠀⠀⠃
⠀⢰⣿⣿⣿⣿⣿⡁⠀⣆⢤⠉⠀⠠⣾⣿⣅⣁⢡⠀⠀⢀⣤⣆⢀⣙⠋⠉⠀⠁⠀⠀⠀⠀⠀⠰
⠀⠈⠇⣿⣹⣿⣿⣿⣦⡘⣤⡀⠀⣼⣊⣿⣝⠈⠳⠀⠀⣿⡻⣿⠇⠀⠀⠀⠠⣀⢠⣀⠀⠀⢠⠁
⠀⠀⠀⢻⣷⣿⣿⣿⣿⣿⢛⣿⠛⠿⣿⣿⣿⣆⠀⠀⠐⣿⡿⠯⠀⠢⠀⠀⠀⢽⣿⣿⣷⣶⣧⣤⣀⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠆⢤⡤⢘⠻⣷⣄⡀⠀⠀⠙⣷⢂⠀⠈⠢⡀⠀⠀⢋⠟⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⢿⢿⠿⣿⣫⣿⣿⣿⣿⣆⣿⣿⣾⣿⣿⣦⣈⢿⣿⣿⣆⡀⠀⠀⡡⠖⡁⠀⠀⠈⠈⠙⢿⣿
⠀⠀⠀⠀⢸⣆⡴⣷⡿⣿⣿⣿⣟⢿⣿⣿⡿⣿⡝⡿⣿⣿⣿⣿⣿⣿⣶⡶⠉⠀⠈⢊⠲⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠟⢰⢻⢹⢻⢉⣎⡾⢿⣿⣿⠻⢿⡿⡸⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢃⠙⣆
⠀⢤⠄⠀⠀⠀⠘⡆⡸⣼⠞⠋⠀⢠⢏⡿⠀⠀⠙⣧⡼⠏⠉⠀⠈⠹⣿⣿⡇⠀⠀⠀⠘⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢼⠃⠀⠀⠀⢸⠞⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢰⠀⢠⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣿⣿⣯⡅⠀⠀⠂⠀⡌⡞

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠒⠈⠉⠁⢀⣈⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠿⠋⣉⣭⠶⠛⣋⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⠉⠛⢛⠟⠛⠭⢠⡄
⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⣢⣀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠓⠒⠦⢤⣄⡀
⠀⠀⢀⠴⠊⠉⠀⢔⣮⡅⠻⢮⣿⣿⣿⡶⢤⣤⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣌⣬⣵⢦⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣭⠵⠶⠛⠋⣉⣉⣿⠿⠿⢿⣯⣯⣷⣒⣶⣧⣄⣀⣀⣿⠛⠉⠁
⠀⠀⠈⠢⢄⡀⠀⠈⠐⠀⠀⢴⣿⠿⠖⠒⠛⣩⣽⣛⡥⠴⠟⠛⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠘⠇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠤⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡀⠀⢀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡃⢻⡋⣿⣖⢒⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣩⠿⣧⡼⠻⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣞⢙⣶⡋⣳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣤⠿⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡉⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠤⠀⠰⠶⠴⢿⠛⠋⠙⠂⠋⠀⠀⠀⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠣⠆⠀⠀⠀⠀⠠⢀⣰⠒⠛⠃⠀⠀⠀⠔⠒⠀⠚⠀⣠⣄⣬⠀⠀⢂⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣹⠇⠀⠀⠚⣿⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠛⠆⢿⣷⠀⠀⢀⡀⠜⠳⢄⣀⡴⠖⠲⣄⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠠⠏⢠⣦⡄⠀⠀⠈⠀⠻⠿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣻⣍⣁⠀⠀⠀⠀⢀⣰⡆⠠⠆⠀⠀⠀⣤⣀⡀⠈⠉⠉⠠⣴⠐⠀⠠⣤⡤⠖⠒⠚⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠉⠈⢡⠉⠀⠀⠀⠀⠈⠁⣾⠤⠀⢠⡖⠛⠉⠛⠀⣁⣀⠀⠀⠁⠈⣷⣶⡏⠀⠀⠀⠀⠀⠙⡷
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢻⣶⣾⠋⠀⠀⠀⠠⣾⡥⠄⣤⠈⡴⢄⠀⠀⠀⠈⢃⡹⠂⢀⡸⠇⢀⠀⠚⢿⣿⠛⠀⢀⡸⠛⢀⣠⣴⣿⠐⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠋⣸⣆⠀⠀⠀⣤⠃⠘⣷⡘⠧⠀⠀⢦⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⣦⡟⠁⠀⠈⠁⣭⣤⣌⣀⠀⠀⠚⡂
⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⢀⣄⣈⣉⠇⠠⠾⡇⢠⡄⠘⠁⡈⠃⠀⠐⠊⠁⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠘⠛⠀⠀⠻⣄⠀⠀⠀⠀⠈⣹⣙⠉⠀⠐⡀⠉⠲⠶
⡀⣀⣰⣆⠀⠀⠀⠀⠁⠈⠿⢧⣄⠀⠀⠀⠀⠀⠀⣻⢾⡇⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠘⢻⠀⠀⠀⠀⠀⢳⣤⡄⣸⣷⠶⠖⠂⠈⠛⢀⣾⣿⣦⠀⠀⢀⡀
⠀⠀⠙⠟⠀⢀⠀⠀⠈⠀⠀⠀⣹⡄⠀⠀⠀⠀⢀⠣⠈⠁⠘⠲⣄⠙⣿⣶⠶⠖⠲⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⣾⠃⠀⠈⢙⠀⠀⠀⠀⢢⡈⠻⠛⠁⠀⠀⣼⡇
⠀⠀⠀⢦⣤⠾⣳⠴⢀⡀⠀⠀⠉⠁⠂⠐⠆⠀⠀⠐⠀⠀⣀⣼⣿⡄⠀⠀⠀⠀⠀⢰⡿⠰⢀⣠⣄⡄⠂⠐⠂⠛⢃⣉⠀⠈⠁⡟⠀⠀⣤⡄⠸⠻⠇⢠⡔⠉
⠀⠀⠀⠸⡇⠀⠀⠀⠘⠁⠀⡀⠀⠰⠓⠀⠀⣀⢠⠀⢤⣠⡈⢉⣿⣥⡀⠀⡀⠐⣦⠈⠀⠀⠀⢹⣿⣤⡀⠀⠀⢰⣦⠙⢶⡌⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣇⠀⠀⠂⠀⠄⣀⣽⠿⠇⠀⢰⣾⡟⢣⠀⠀⠉⠛⢀⣄⡙⠟⠈⢀⣸⣿⡇⠀⣠⣀⣠⣷⣄⢡⡀⣤⡈⠛⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠛⢇⣸⠀⠀⠀⠀⠸⣿⣇⠀⠀⢿⣿⡄⠀⠀⠉⠹⠾⠿⠛⡛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⠣⢀⣠⣿⣄⡀⠘⠀⠀⠀⠈⡃⢀⠶⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠙⣻⡀⢀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠔⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡁⠀⡉⠠⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣗⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣿⠀⠀⣀⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⡃⠀⠀⠠⠀⠈⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣰⢦
⠀⠀⠀⠰⠀⠂⠀⠀⠐⠀⠄⢠⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢇⠀⠉⢀⣇
⠀⠀⠀⠀⢣⠀⢰⠉⠂⠚⠀⠀⠃⠔⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠉⠉⠁⠈⠣⡀
⠀⠀⠀⠀⠀⢆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⡴⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢔⠞⠝⠀⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠃⡌⠀⠀⠣⡈⠁⠒⢽⢄⡠⡀⣀⡀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⣤⠁⠀⠃⠀⡇⠀⠀⠀⠘⡄⠀⠀⠣⢕⠁⡇⠓⢖⠊⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠈⠩⠀⡸⠆⣀⢃⠀⠐⣄⠀⠀⢀⣄⣀⠴⣗⢤⠭⠑⢆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠬⠉⡾⠥⢓⣄⡠⠢⣉⠔⠫⣉⠜⢅⠔⢀⣀⢴⡤⠵⢤⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⢹⠒⠆⠨⠇⠀⢠⠀⠀⡄⠀⠰⠀⢠⡡⠔⠈⠉⠀⠀⠀⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡆⠘⡀⠸⠀⠈⡀⠀⠄⠀⡄⢀⠊⠀⢀⠀⢠⠦⣔⡑⠤⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣘⠀⢀⡀⢸⡤⠓⠠⣇⠀⠃⠀⠀⠀⠇⡆⠠⠀⡀⠱⡋⠀⠀⠀⡈⠃⠀⢀⡀⢐
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠀⠈⠂⠀⠁⠀⠀⢸⡀⠐⠀⠀⡐⠀⣧⠲⠠⢄⠀⠈⠙⠉⠁⠀⠀⡠⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠇⣀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠓⠊⠑⠤⠊⠉⠈⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⠒⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠠⠀⠐⢄⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠑
⠀⠀⠰⠀⠀⠀⠀⠈⠀⠆⠂⠀⡂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠰⢀⢀⢀⡀⠀⡔⠓⣀⠰⠃⠀⠀⠈⠀⢀⡈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈
⠀⠀⠀⠀⢀⠄⠀⠂⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢱⠠⢍⠉⡠⡀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⡉⠀⠀⠑⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠐⠒⠑⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠤⠠⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠓⠒⠶⠼⠧⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠡⡀⠀⠀⠀⠠⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠀⠀⠀⠘⠄⠁⠁
⠀⠀⠀⠨⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⡌⢐⠨⡟
⠀⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠻⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⢿⣄⠀⠀⠀⠀⠀⡉⢠⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠈⢻⣦⠀⠀⠀⡰⠁⣾⠃⠀⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⢀⡠⠀⠈⢿⡄⠀⢻⣧⠀⢰⠇⣸⡏⠀⢸⣿⠀⠀⠀⢂⠄⠉
⠀⠀⠀⠀⠻⣿⣛⠛⠻⠷⢶⣤⣄⡒⠉⠲⣄⠘⣿⡀⡄⢻⣆⠈⢰⡿⢀⠆⣼⡇⠀⣠⠔⠁⠀⣀⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠈⠉⠻⢷⣤⡈⠳⣼⣧⠰⠈⣿⣧⣿⢁⡞⣠⡿⢀⠜⣁⣤⡶⠟⠋⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠠⣀⠉⠻⣦⡙⣿⡆⠃⢸⣿⡇⠎⢠⣿⣷⡷⠟⢋⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡙⢦⡈⠻⣿⣷⣿⣿⣿⣿⣶⣿⠟⢋⡠⠖⣁⣴⠿⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⢲⣿⣿⠏⣁⠉⠻⣿⣿⡎⣁⣤⣾⠿⠥⠖⠚⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠒⢂⣴⣿⣿⣿⡏⢀⣭⠖⢀⣿⣿⣿⠿⠿⠿⠶⠶⠶⠶⢶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠁⠀⢀⣤⣾⠟⠋⡩⣿⣿⣷⣤⣥⣤⣾⣿⡿⠉⠈⠛⠒⠀⠀⠂⠀⠀⠀⠀⣉⣉⣛⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣶⠿⠋⠔⣪⣵⠞⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣤⡶⠛⠉⢀⣴⣿⢃⠏⣸⣿⣿⢰⠀⢿⣿⣌⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠞⠋⠁⠀⠀⡠⠊⣼⡏⡎⢰⡟⢸⣿⡀⠆⠸⣿⢻⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⢀⠜⠁⢰⡿⡘⢠⡿⠀⡟⢻⣧⠘⡀⢿⡄⢿⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠑⠀⠀⣾⠃⢡⡿⠁⢠⠇⠈⣿⣆⠀⢸⡇⠸⣷⠀⠀⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⡿⢠⡿⠁⠀⡞⠀⠀⠘⣿⡄⢸⡇⠀⣿⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣾⠁⠀⠰⠃⠀⠀⠀⠹⣿⣸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠃⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⡇⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢷⢀⣿⣡⠞⠫⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢸⣿⡿⠋⠆⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣸⣿⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣧⡾⠋
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀
⠀⢈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠓⡀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠈⠑⠂⠁⠀⠈⠂⠀⢀
⠀⠀⠀⣄⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠐⠈⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠦⠀⠀⠈⣐⠁
⠀⠀⠀⣏⠀⠟⠀⢠⢨⡁⠀⠀⠀⠈⠒⠁⠀⠀⠈⡈⠀⠀⠘⡐⢂⠀⠀⠐⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢎
⠀⠀⠀⠀⠓⠀⠀⠀⠓⠉⠢⡀⠀⠀⠈⠀⠀⠀⠠⠦⠄⢀⣨⠠⠴⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⡆⠀⠀⠀⠀⠸⠆⣄⠀⠀⡀⠀⢀⠀⠀⠤⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣶⡄⢀⣒⣼⡓
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠰⠿⠀⢈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⡁⠄⠀⠀⠀⠀⢅⠁⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⣄⠉⠡⠋⠘⠌
⠀⠀⠀⠀⠉⠂⠂⠚⠀⠀⠀⠀⠊⠀⠰⠈⡄⠀⠀⠀⠀⠉⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⡅⠀⠠⣶⠆⠀⠢⠤⠀⠀⠀⠀⡐⠁⠀⠀⠐⠂⠠⠀⢀⠁⠀⢀⡀⠀⠀⠐⠄⠐⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠂⠀⠀⠠⠚⡔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠊⠁⠀⠀⡀⠀⠀⠀⠀⠇⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⢆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡐⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠐⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠢⡈⠢⡡⠀⠀⠀⠠⣹⠓⠂⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠱⠄⠀⠀⠀⠀⡅⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⢠⠀⠠⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢖⣈⠶⢌⠀⠀⠀⠈⠂
⠀⠀⠀⣂⡠⠐⠀⠃⢀⠚⠀⠀⠀⠀⠀⢈⠂⠒⠁⠀⠀⠀⢈⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⣀
⠀⠀⠈⠚⠢⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⢀⠘⠂⠀⠀⠐⠀⣈⡭⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⢐⣢⡄⠀⠀⠀⠐⠀⢠
⢀⠀⠀⠀⣙⡀⠈⠀⠀⠀⠂⠀⠀⠀⠃⠀⠈⠀⠁⠀⠀⠀⠀⢚⡩⣥⡶⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⣒⡀
⠙⠛⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠀⠀⢀⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣉⠀⠐⠤⢐⡀⢠⡆⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡿⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠉⠛⠓⠲⠾⠭⠦⠀⠀⠘⠤⢄⣀⣀⡇
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⢀
⠀⠀⠘⠀⠀⢈⡁⠀⠩⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣟⣿⣿⡂⠀⢦
⠀⠀⠁⠀⠸⠋⠙⢛⠛⢤⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠘⠛⠉⠁⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣮⣆⣠⠤⡎⠀⢀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⢃
⠀⠄⠀⡇⠀⠀⠀⠈⢉⢲⠄⠀⠒⠠⠰⠖⠁⠀⠀⠀⠀⣠⠀⡀⠀⠄⠀⢀⠀⠀⠀⠐⡀⢸⠀⠀⠒⠀⠈⠆
⠀⠀⠀⣷⣀⣀⣀⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠢⢌⣉⠙⠰⠂⠦⢤⡀⠀⠀⠉⢺⠀⠀⠀⠀⠀⠀⣀
⠀⠠⣀⡍⠠⠄⣀⣉⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠱⠂⠀⠉⢕⣒⡒⠡⢬⠀⠀⠀⠀⠱⠶⠶⠶⠒⠛⠉
⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠴⠬⣄⣉⣡⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣤⣤⣄⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⣾⣿⣿⣿⣿⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣞⢦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⡟⣭⡿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢸⣿⡇⣿⡇⣿⢱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢿⠇⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢞⡇⠀⠀⣿⠇
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⣿⣿⣿⣦⡀
⣿⣟⠀⣸⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣶⣷⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤
⠀⢨⣿⣿⢟⢿⣿⣧⠀⠀⠀⣰⣞⡛⣳⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠶⢤⠁⠆⠰⠆
⠀⠸⣿⣯⠈⠠⣿⡗⠀⠀⢠⡟⠛⠁⠙⠛⡇⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢿⣤⣬⣇⠁⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⢶⢆⣶⣶⣇⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠤⠤⠤⠆⠀⠀⠂⠀⠉⠉⠈⠉⠈⠀⠀⠀⠠⠄⠀⠤⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠻⡿⠿⠃
⠀⠀⠀⠀⢀⢀⠀⠀⣈⠥⠀⠀⠰⣠⡆⣴⢰⣴⢰⠀⣤⣤⢀⡆⣦⢰⠀⣆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠐⠻⠳⠀⠀⠉⠁⠀⠀⠈⠁⠀⠈⠈⠈⡈⡀⣁⡈⡀⡅⠀⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⡄
⠀⠀⢠⡀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿⡶⣾⣏
⠀⠀⠀⠁⠈⠁⠁⠀⠀⣶⡄⠀⠀⢠⣶⠀⠀⣀⣻⠟⢉⠙⢿⣃⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣿⠙⢹⣿
⠀⠀⠀⠏⠀⢒⣛⠀⠀⠘⡇⠀⠀⢸⠇⠀⠀⣭⣿⠀⠀⠀⢈⣯⡅⠀⠀⠀⠈⢹⣿⠀⠀⠀⠀⠀⣿⠀⢸⡟
⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢹⡷⣶⣶⣿⡍⠁⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⢸⣶⣾
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣍⠀⠀⠀⠀⠶⠖⠀⣬⣿⡄⠘⠿⠗⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡰⢂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢆⠉⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⡎
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣦⣎⡀⠀⠀⣀⡘⢣⣤⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣼⠀⣷⣦⣤⣤
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⣷⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⢡⠀⢠⢺⣿⣿⣿⣿⣿⣿⡿⠐⣄
⠀⠀⠀⣴⣿⣿⣯⡅⣿⣿⣿⣿⡁⣿⣿⡟⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⡀⠠⡞⠀⣿⣿⣿⣿⣿⣿⡇⠀⠘⡆
⠀⠀⠀⠛⠛⠛⠋⣱⢿⠛⠫⠋⡁⠙⠟⠃⡀⠤⠒⠀⠀⠞⠒⠒⠒⠒⠳⡀⢀⣴⠙⣿⣿⣿⣿⠿⠛⠂⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠈⢃⠀⠈⠂⠤⠤⠤⢀⣤⣦⣤⣤⣄⣀⠀⠤⠤⢃⠿⡿⠛⠧⡄⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡟⡇⠀⠀⣧⠀⠀⠀⠀⣁⣼⣿⣟⠃⠀⠀⠀⠀⢰⠃⢠⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⡇⠀⠀⢹⠀⠀⠀⢸⣿⣿⣿⣿⠀⢀⠀⠀⢠⠏⢀⡇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⣧⠀⠀⢸⡆⠀⠀⠈⢹⣿⣿⣿⣿⣿⣀⠀⡾⠀⡞⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⢻⠀⠀⠀⣇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⠁⣼⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠸⣄⣀⣀⣿⠀⠀⣶⠟⢻⣿⣿⣿⣿⣽⡇⢠⠇⠀⣰⠃
⠀⠀⠀⠀⠀⢀⣿⣶⠂⠋⠀⠀⠀⣯⣿⣄⠀⠈⢿⣶⣿⣿⣷⣿⣿⣿⣅⣙⠄⡀⠃
⠀⠀⠀⠀⠰⠟⠉⠻⠀⠀⠀⠀⠀⠛⠈⠛⠷⠀⠈⠉⠁⠈⠉⠉⠉⠂⠐⠢⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⣿⣥⠽⠬⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠻⢶⣴⠿⢿⣄⠀⠀⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣶⣦⣶⡞⠁⠀⠀⢈⣷⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠖⠋⠉⠻⢿⣧⣬⣁⣠⣼⣿⠁⢀⣀⣸⡃
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠴⠉⠩⠭⢌⢻⣿⣿⡿⢿⡉⢉⣿⣃
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠒⠖⠃⠀⠀⠀⠀⠀⠁⣗⣀⣶⡆⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣸⠂⠀⠀⠀⠀⠀⠠⣿⠅⣿⠇⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠤⠤⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣆⠀⠀⠀⠀⠀⢀⣽⣸⡟⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⣤⠴⢒⣾⡷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣤⡙⣿⣿⣤⣤⣀⣴⣿⣿⣿⣵⠿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠋⠁⠒⠻⡿⠿⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⣿⣿⣿⣿⣿⣿⠿⠛⠑⠉⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⣄⡀⠀⣾⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⡗⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣗⢶⡖⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣴⣷⡄⢛⣿⣿⣿⣖⣦⣼⣀⡀⠀⠀⢹⠀⠀⠀⣥⣾⡗⠆⠀⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠿⢟⠛⠉⣉⣤⣶⣛⣻⡿⣿⠿⢿⣿⣿⣶⣦⣤⡏⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠎⣸⢀⣆⠠⣤⣀⡀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⣀⠙⠉⠁⠀⠐⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⣴⣯⣀⢨⣦⢈⣁⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢿⣖⠲⣶⡤⣀⡈⠛⠛⣩⣟⣛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠺⠾⢇⣀⣿⣶⡙⢦⠛⣿⡶⢆⠉⠉⠁⠀⡈⠳⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠁⠀⠀⠀⠀⠀⠀⠙⢀⣬⣏⣆⣀⡠⠥⣦⠷⣦⡄⢠⠀⠀⢽⡇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣁⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣨⣟⣁⡙⣿⣳⢶⣿⢻⠘⠀⠀⢸⡇⠠⡅⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘⠿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣭⣿⠛⠿⢾⣿⣦⣭⡿⢀⡁⣰⣿⣿⣿⣧⣌⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣂⣾⣿⣿⡶⠶⣞⣿⠷⠉⢙⣲⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠈⠀⠸⠿⣓⡲⠶⠶⠾⠟⠻⠉⠉⢠⣶⡿⠿⠷⠞⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠄⣀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⢿⡾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡃⡼⠃⠀⠀⠀⠀⣴⣶⣶⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢤⠀⠀⠀⠀⠈⢃⣀⣀⡸⢱⣀⠤⠙⠛⠛⠛⠿⣿⣿⡿⠃⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⢠⣄⣀⣠⠊⠁⠀⠐⢁⠜⢣⠀⢸⣏⣶⣤⡀⠘⣿⣿⣷⡄⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠈⠒⢤⠤⠀⠠⠀⠘⠀⢀⠀⠆⢠⣉⡙⠻⠛⢹⡏⠉⠉⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⢏⠤⠒⠚⢄⠀⠢⠴⢶⡊⠁⠀⢰⠀⡏⢙⡀⠀⠠⡀⠀⠀⣴⠟⣻⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠱⣁⣀⢶⣾⠂⢣⡀⠀⠸⣨⠗⠈⠙⠚⠀⠛⠳⡦⡁⠇⠀⠠⠵⣾⣿⣝⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⡇⠛⠿⣤⣽⣿⣿⣇⣀⣰⠁⠀⣀⣀⠀⠠⢆⡀⠀⠙⣄⠀⠀⠀⠈⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢠⣀⡇⠀⠒⢃⠜⠋⢡⣂⡄⠀⣉⠲⠄⠋⢀⣠⣴⠀⣀⠤⡀⠉⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡡⠨⢳⡀⠀⡏⠀⠀⢨⡽⢗⠻⠀⠀⡎⠁⡪⠽⠋⠰⠥⡀⡨⢰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠰⡅⡀⡇⠙⠂⠖⠂⠘⠁⢀⣎⠀⣀⠔⠋⠉⠑⠢⣾⠼⣀⣈⢣⠸⣌⠆⡀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠳⢌⣘⡦⡄⣠⡀⠀⣤⠈⠈⢶⠁⠠⡄⣠⣶⣴⠈⡞⠀⡏⡆⣠⠃⠊⠐⠂⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠕⠠⢊⠼⢿⠀⠉⣀⣀⣄⠀⠀⠸⠀⠀⢀⠁⢀⡀⠀⢰⠊⠀⠀⢹⠍⠉⡓⣎⠔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠡⡐⠆⠆⠀⠻⠽⠟⠀⠀⠀⡆⠧⡸⠀⠿⠃⠀⠸⠀⠀⠇⢸⠈⢑⠈⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⠖⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⣶⣶⣶⣿⡖⠒⠒⠚⠧⠁⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠈⠛⠟⠛⠁⠀⠀⣠⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣶⣤⣀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢀⣀⡀⠀⠀⠀⣰⣶⣶⣦⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠊⡉⠙⠢⣄
⠀⠀⠀⠀⠀⢀⠔⠚⠉⠁⢀⠀⠂⢈⠀⢠⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⢰⠁⠀⠆⠀⠂⠀⠠⠄⠈⠀⠀⢀⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠃
⠀⠀⠀⠀⢇⠀⠄⠀⠠⠆⠀⠄⠀⠰⠂⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣩⣯⡢⡀
⠀⠀⠀⠀⠘⡆⠀⠆⠀⠀⠀⠠⠄⢀⡤⢤⡀⠀⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠊⣹⡇⠀⠙⠀⢀⡇
⠀⠀⠀⠀⠀⢸⡀⠠⠀⡠⠤⣀⢀⡼⠀⠀⠱⡀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠛⠦⠔⠤⠎⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠁⠠⠄⠈⢀⠁⠀⠂⠀⠘⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⢆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⣀⣴⢶⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⢴⠞⡽⠁⣿⡀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠊⡴⠃⡜⠀⠀⢷⠘⠦⢼⡀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡞⠀⠸⠁⠀⠀⠈⠢⡀⠀⠈⠑⢦⡷⣤⠖⡆⢀⣤⡀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠁⠀⢸⠀⠀⠇⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⣈⡱⠃⢸⠤⠷⣆⠒⠛⣣⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣀⠤⠴⡞⠉⠉⣿⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⢅⠑⠂⠺⣄⢀⣈⣳⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⡄⢠⠃⠑⠦⠤⠧⣀⠀⢘⣦⣀⠀⣀⡤⠛⠒⠒⠋⢹⠎⠳⣏⠉⠉⠳⢄⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠵⠐⠸⠿⠭⢍⡲⢄⣠⠖⠲⡄⡨⠛⢦⣀⡤⠒⢦⡰⠒⢄⣀⠴⣦⡤⠶⠳⣖⢢⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠂⡴⠚⢳⠤⣤⡈⣈⣣⠀⠀⢨⠀⠀⠀⡍⠀⠀⢠⠀⠀⢸⠁⣀⠷⠛⠊⠉⢉⠉⡉⠉⢑⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡀⠀⡆⠀⢹⡄⠀⠘⡄⠀⠀⡇⠀⠀⣾⠀⠀⡾⠊⢁⠀⠁⠂⠀⠀⢀⡤⡀⠀⠀⠠⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢇⠀⢹⠀⠀⢧⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡞⠁⠤⠀⠄⣀⣀⣎⣓⡋⢀⣉⡒⣄⠐⠀⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡞⠀⠀⠀⣀⣘⣄⡤⠓⠢⢜⡄⠀⢸⠀⠀⠀⠀⢀⠃⡸⠀⡄⠠⠀⠀⢧⠊⠁⠀⠀⠀⠀⢉⠇⢘⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⠹⠷⠉⠉⠻⡀⠀⠙⠂⠀⠀⠈⣷⠀⠀⡆⠀⠠⠀⢸⠀⣇⢀⡀⠀⣈⠀⠆⡙⠒⡦⠐⠒⠚⡁⠐⠀⢠⠏⠙⢲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠗⠒⠲⠶⠶⠶⠒⠒⠒⠚⢳⡘⠊⠈⢦⠀⢀⣀⡀⠂⠈⣠⣀⣀⠖⠊⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⡴⢥⣀⡀⢀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠑⠉⠀⠙⠢⠞⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⣀⣀⡠⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


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

⠀⠀⢴⣦⢠⠀⠀⠀⡐⠀⠀⢀⠀⠀⢴⣿⡆⠀⠈⠀⠐⠩⠐⡔⢀⡂⠁⢀⠀⠀⠀⠁⠀⠀⠈⠂⣶⡆
⠀⠀⠈⠁⠠⠂⠀⠀⠠⠀⠀⠀⠤⡂⠈⠉⠀⠀⠄⠀⠀⠁⠊⠀⠀⠄⠀⢀⠀⠀⠄⠂⠀⠀⢠⠀⠀⢀
⠀⠀⢂⠀⢰⠀⠂⠂⠀⡀⡄⠀⠀⠀⠀⠠⠐⠤⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠱⠼⠀⠀⠄⡀⠃⡠⠆
⠀⠀⠠⡑⢠⣔⠩⠁⡠⠉⠤⠀⢀⡶⠋⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠙⣆⠐⢙⢂⠣⠈⡠⠾⠮⠐⢀
⠀⠀⢁⠖⢁⠠⠑⠀⠀⠒⢀⣠⣼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣦⣄⠁⠀⠐⠀⠁⠄⠘⠂
⠀⠀⢂⢀⠈⠀⠠⠀⠀⠐⣿⣿⡿⠿⣿⢿⣿⢿⣿⡿⣿⣿⢾⢿⣿⣿⠿⢿⣿⡿⠃⠠⠌⠂⢀⣀⠢
⠀⠀⠀⠠⣾⡧⠀⠀⠀⠂⠀⢸⣿⣽⣿⣸⣿⣸⣿⡇⣇⣿⣼⣏⣿⣿⣯⣿⡇⢀⠀⢀⠀⢀⠻⠼⠀⠉
⠀⠀⠄⠒⢄⢐⡁⠀⡀⠘⠀⠘⣿⣿⣤⣿⠿⠿⠿⠶⠿⠿⠿⠿⣧⣠⣿⣿⡇⢨⠀⠄⠁⠀⠆⠔⠉⠑
⠀⠀⠑⠒⠀⠈⠀⡀⠤⠔⠀⠀⣿⣿⣿⣿⣥⣤⣤⣤⣴⣤⣤⣬⣿⣿⣿⣿⠀⠀⠑⡂⠠⠉⠄⠀⣁⡁
⠀⠀⢈⠝⢀⠀⠈⠀⠂⢈⠄⠀⣿⡟⣴⡿⣴⣧⠃⣿⣿⣲⣾⣴⣾⢩⣽⣿⠀⠠⠑⡂⠀⠁⠀⡄⡑⡄
⠀⠀⠄⢈⠄⠀⠀⠰⣿⡦⠀⠀⢸⣇⣿⣿⢻⡟⡇⣿⡯⣿⡏⣿⡟⣿⣿⡇⠀⡀⢾⡽⠂⠀⢀⠒⡄⠐
⠀⠀⠀⠀⢈⠠⠐⠀⢈⠀⡀⠀⢸⣿⣶⡾⣷⣾⣿⣿⣿⣿⣷⡾⣷⣿⣿⠇⠀⠀⠀⠀⠀⠠⣂⠄⠀⠠
⠀⠀⢀⡾⠀⠅⠄⠐⠡⠂⡀⠀⠈⣿⡿⢡⣿⣦⣿⣧⣼⢧⣼⢫⣿⣿⣿⠀⠀⠦⠐⠀⠂⠁⢐⠀⢇⣄
⠀⠀⠑⢥⢈⠥⡄⠁⠀⠄⡀⠄⠀⣿⣇⣾⣿⢧⣿⣻⣧⣵⣏⣾⡻⣿⡟⠀⠀⣒⡂⠀⢀⡰⠠⠀⢶⣂
⠀⠀⠑⢃⠠⡔⠄⠁⠐⠁⠀⡀⠀⢻⣩⣿⣿⣾⣿⣿⣿⣷⣿⣿⡿⢿⠇⠀⣄⡢⠈⠂⠀⢀⣢⠀⣍⠈
⠀⠀⠈⡁⠀⠀⡀⡀⠀⣤⣲⡄⠀⢸⣿⣿⣿⣟⣿⣿⣿⣷⣿⣿⣿⡾⠀⡀⢰⣾⡦⠀⣠⢥⠈⠀⣈⠁
⠀⠀⢈⣤⣀⠀⡈⡭⠅⠈⠉⠀⢀⠀⠛⣛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠁⠀⠁⠀⠉⠀⠨⢭⢄⠀⣔⣦⡀
⠀⠀⠀⠛⠁⠀⠁⠀⢀⠈⢇⠄⠈⡀⢄⠄⡁⠀⣾⣷⠄⠀⠀⠇⠀⠅⡸⠀⢀⠪⠉⡆⡠⠀⠀⠈⠛
⠀⠀⠈⠀⡈⠀⠀⠀⠠⣅⠤⠂⣰⢈⡂⠚⢓⠠⠀⠀⠐⠠⢲⡛⠒⢚⠁⠆⠡⠍⠩⠔⠈⡀⠀⠁⠈⠁
⠀⠀⠈⠐⠁⠀⠀⠀⠐⠒⠂⠀⠂⠀⠘⠀⠘⠊⠀⠀⠈⠈⠒⠁⠘⠈⠀⠒⠘⠒⠒⠂⠁⠀⠘⠀⠂⠁

⠀⠀⠀⠈⠆⠀⠀⠃⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣦⣤⣤⣴⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡀⣢⣉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢹⣿⣿⣿⣿⢿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢠⣆⢢⣲⣶⣠⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⣜⣶⣿⢿⠎⠑⡛⢽⣿⣟⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⡔⠃
⡀⠀⠀⠀⠀⢠⣟⡫⠇⠈⡀⠀⡇⠈⠈⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⡀
⢿⠆⠀⠀⠀⣞⣛⣒⠀⠂⡆⠀⡇⠀⢈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠤⠤⠤
⣾⡆⠀⠀⠀⠴⣖⣚⠀⠀⠹⡿⠇⠀⠈⣙⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⢂⢀⡀⠀⠀⠀⠀⠀⠀⣾⣤⣦⣄⠀⢠
⣿⡇⠀⠀⠀⠈⠟⣶⣧⠀⡀⣐⣀⣀⢠⣻⡦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠒⠻
⡻⠃⠀⠀⠀⠀⠘⠻⣻⣿⣿⣿⣴⣷⣿⠏⠛⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⠀⠒⠒⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣤⣶⣦⠠⣶⣶⣶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⣄⡀⡀⡄
⠀⠀⠰⠖⠂⠀⠀⠀⠒⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠼⠍⠉⢼⢗⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⣀⡿⣿⣿⡂
⠀⠀⠀⠀⠈⠡⠻⠓⡈⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠀⠀⠀⠤⣯⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⣤⣼⣿⢚⣛⡁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢲⡞⠂
⠀⠀⠀⠘⡀⢸⠀⠐⠀⡰⠁⠈⠀⠀⠀⠀⠀⡴⢧⡖⠀⠀⠐⠊⠀⠈⠹⣮⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⠠⠀⢠⣥⡀⠄⢰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⣿⡷⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣿⣿⣤⣾⣆
⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⡿⢿⠿⡿⢿⣿⣧⣶⣦
⠀⠀⠀⠈⠁⠙⣿⣿⡅⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠀⡆⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢀⠠⠀⠛⣿⠃⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⡇⠀⠃⠆⠸⣿⣿⣿⠗
⠀⠀⠀⢸⠛⠰⣶⣶⡆⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠂⠈⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⢷⠇⠀⣿⣿⣿⡶

⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠸⠄⠤⠀⠠⠄⠼⠀⠀⠘⠈⠠⢄⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⡇⠀⠀⠀⠠⠐⡈⠄⡐⠣⡀⠀⣔⠂⠉⠉⠉⠉⠉⠉⠁⠐⡄⠧⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⣀⣤⣤⣴⠀⠀⠀⠀⠀⢻⣄⡀⢘⠀⠠⢌⣁⣀⣄⢈⣡⡀⠀⠆⠀⠀⡤⠉⠀⠀⠸⣁⠀⠐⡄⢨⠉⠁⠐⠒⠒⠒⠂⠉⠉⠁⡇⠀⠀⠄⠤⢠⠘
⠀⢰⡾⣿⢿⠏⣯⣽⠀⠀⢠⢀⠈⠀⠀⠉⠙⠀⠁⠈⠉⠉⠉⠈⠉⠀⡀⡇⠀⠛⠀⠀⠀⢄⠀⠀⠀⢀⡄⠀⠀⡠⣊⣀⣀⠁⣢⠀⢰⠀⠇⠀⠀⠴⠮⠅
⠀⢸⣧⣏⡾⠾⠛⠛⠀⠀⠈⠈⢉⣉⣁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠠⠀⠀⠀⠀⣠⣾⡟⣧⠀⠀⡏⠇⠰⠮⠿⠟⠀⡄⠀⣰⡏⣇⣐⣒⡂
⠀⠘⢋⡁⠀⠠⠀⠀⠀⠀⢎⡁⠀⠀⠀⠀⠀⢈⡃⠀⡏⠉⡍⠨⡅⠨⠀⠀⠀⠀⠀⠀⠀⢰⠾⡿⣤⠟⠋⠀⡃⠃⠀⢿⣿⣀⠀⢁⠁⠀⡇⠿⠏⠁⠠⠄
⠀⠀⠀⠍⠁⠀⠄⠀⠀⠀⠀⠀⣤⠬⡉⣩⡅⠀⠁⢠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣻⠟⠁⠀⠀⠀⢠⠈⠨⠀⠀⠥⠌⡘⠀⠀⡇⢀⠀⠐⠤
⠀⢰⡦⣤⣤⣤⣤⣴⠀⠀⢀⣴⣷⣷⣿⡿⣻⣦⠁⢸⠀⠄⠀⣀⣠⢰⣆⠀⠀⡄⠀⠀⠀⠘⠁⠠⠚⠆⠀⠀⠀⠑⠠⠀⠀⠠⠐⠁⠀⠀⡇⠄⠀⠀⠀⠀⡁
⠀⠘⡛⠛⠚⠓⠒⡹⠀⠀⠘⢿⣸⣖⣾⣷⣯⡟⠃⠘⠀⠀⠱⠋⠁⠀⢸⠀⠀⡇⠀⣀⠀⠀⠀⠃⣠⠀⡀⠀⢀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠈⠉⠉⠁⢀⣀⡀⠠⡀⠉⠉⠉⠉⠁⢀⠆⠀⡄⡃⠀⠀⠀⠀⡸⠀⠀⠷⠁⣀⠑⣀⢀⠩⠐⠈⠀⢀⢠⡀⠀⠀⢸⠖⡓⠄⠀⢰⠅⠀⠀⠀⠀⠀⢽
⠀⠀⢠⣄⡀⠄⠚⠁⡚⠀⠀⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠄⠂⠉⠀⠀⠀⠘⠀⠀⢤⡭⢞⠀⢈⡉⣀⠤⣀⠀⠀⠊
⠀⠀⡄⠀⢀⠤⠔⡊⢓⢠⢤⡄⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠣⠀⠁⠐⠀⢀⣠⡄⡂⠀⠀⠒⠉⠀⠸⠥⣇⠀⣨⢹⠆
⠀⠀⠏⠐⠐⠄⠄⠠⣴⠶⠃⡀⠀⠀⠀⢸⣿⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⣿⡇⠀⠀⠀⠄⠉⠀⠀⠸⠛⠓⠁⠇⠀⠀⠀⠀⠠⠠⠄⠀⠈⠄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠈⡇⠀⠀⠀⢸⣿⣄⠈⠛⠒⠒⠖⠂⠐⠒⠂⠙⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡖⢣⢠⠄⠸⡤⠀⣀⣀⡀⠀⢀⣀⣀⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⣏⠈⢀⣤⣀⡀⣄⣀⣀⣀⣈⣹⣀⣀⣈⠃⠀⠀⠀⡇⠀⠀⠀⠀⣐⣇⡠⠀⠀⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣠⡛⢀⠄⡄⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢤⣈⠀⣀⢁⡠⠖⠉⠀⠀⠈⠲⣀⠀⠀⠃⠀⠃⡠⠊
⠀⠀⠀⠀⠀⠀⢰⣿⣥⡟⠁⡇⠀⠀⢰⠀⠒⠀⠀⠒⠀⣀⣀⣀⣐⡒⠂⠀⠐⡄⢀⢀⣀⣀⣀⣀⣀⣀⣉⣁⣀⢀⣀⢀⢀⠀⠀⡀⢁⣀⣁⢀⣁⢀⣀⣀⢤
⠀⠀⣀⠀⠀⠀⢨⣿⢏⡠⠔⠃⠀⠀⡸⠀⢀⣬⣴⡾⡿⠛⠿⣫⡏⢥⢱⡄⠀⡇⠀⠀⠀⠀⠀⡄⣄⣔⢰⠠⢠⠀⢰⡆⣆⢲⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⠀⠀⠨⠀⣾⢰⢷⢠⣠⣛⣰⣭⣽⡶⠞⠁⠀⡇⣀⢀⣀⡀⢀⠃⠈⠃⠘⠀⠛⠀⠘⠃⠉⠋⢠⣿⡏⠀⠀⠈⠀⠀⠀⣀⣀
⠀⣐⠩⠅⠱⠎⠀⠉⠀⠉⠉⠉⣰⠀⡨⠀⠘⠳⠿⠿⠿⠿⠛⠋⣽⣶⢖⣦⠀⡇⠀⠀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⡀
⠀⠠⠼⠤⠤⠤⠤⠤⠼⠥⠬⠼⠏⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠛⠛⠃⠂⠃⡈⢥⣤⡃⠾⢚⡭⣤⢦⢱⡀⠀⠀⠀⠀⢤⠀⠀⠀⡏⣹⠑⠄⣹⣸⡆
⠀⢰⠒⠒⠒⡒⠒⠒⣒⠒⠒⠒⢶⠀⠀⢀⢀⠤⠤⣀⡀⠀⢀⡀⢀⠤⢄⡀⡀⠈⡇⠚⠭⠹⢩⠭⠢⠭⠘⢸⠁⠀⢀⠠⠔⡠⠤⢀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⢿⢩⡘⠃⠬⣸⠀⢸⣨⣅⠀⢀⠇⠽⠀⠈⠢⣀⠀⠀⠀⠀⣀⠔⠁⡖⠊⠄⣀⠀⠀⠀⠨⠀⡐⠛⠁⠈⠈⠛⢂
⠀⠀⠀⠀⠀⠒⡆⣲⠖⠀⠀⠀⢸⠀⠀⣤⣀⡀⠁⡀⠀⠀⠀⠀⠈⠉⠁⠀⣤⡄⠀⢀⡈⠡⠭⠭⠍⢁⠀⠀⠁⠀⠀⠉⠀⠀⡀⠀⠀⡇⠈⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠤⠀⠁⠤⠐⠀⠀⠸⠀⠀⠃⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂⠀⢸⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠃⣠⢶⠶⣶⣄⢰
⠀⠀⠀⠀⡀⠀⠠⡀⠠⢀⠀⠀⠀⠀⠀⠇⠀⢀⣾⣿⠻⢛⡿⢻⢻⣿⡆⠀⠀⠄⠀⢸⠀⠒⡄⡈⠁⠸⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⡆⠻⢷⣶⡶⠿⢸
⠀⢠⠀⠀⠉⠉⢦⣈⠴⠊⠀⠀⢰⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠧⠄⠀⡅⠀⢸⠀⠀⣴⣶⠂⢰⠀⠀⠀⠠⠀⠸⠀⠀⠀⢘⠀⡇⠀⠀⠀⠀⠀⠸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠰⡇⠀⢸⠀⠠⠄⢤⠀⢸⠀⠀⣀⠐⠀⠐⠀⢀⠠⠘⠀⢣⠀⠀⠀⠀⠀⡜
⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠃⠀⠈⠐⠂⠠⠀⠒⠈⠀⠀⠈⠉⠀⠛⠈⠁⠀⠀⠀⠀⠉⠀⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣃⠀⠀⠀⠀⠀⠙⠋⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠘⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠙⠀⢀⠈⠁⠀⠺⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢛⢫⡀
⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⢀⡀⠀⠀⠀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠉⠁⠛⠑⢯
⣶⣼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⡶⠖⠒⠀⠀⠀⠸⠆⢀⡀⠤⠀⠒⠐⠒⠂⠠⢸⠁
⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⠇⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣍⣩⡆⠀⠀⠀⠀⠀⠴⡀⠣⡀⢠⡄⠀⠀⠀⢴⡄⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠠⣀⣤⡀⠀⠀⠀⠸
⠉⠀⠀⠀⢀⠀⢀⡀⠈⠅⠀⠀⢀⠀⢠⠼⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠋⠁⠀⠀⠀⢀⡀⢐
⠀⠀⠐⠇⢀⡠⠀⠀⠀⠀⢀⡀⠛⠛⠛⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣸⢒⣶⠶⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡀⡠⠀⠠⢰⡀⣴⠶⠶⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠪⠟⠷⢆⣤⠦⣀⣤⠂⠀⢦
⠀⢀⣤⠀⠀⠀⠓⠀⢤⠀⣌⡁⠀⠀⢊⣡⡍⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣴⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⣄⠀⠀⡀
⠀⠈⠙⣄⢀⠀⠈⠁⠀⠀⡏⠉⠀⠀⠨⠉⠹⠶⣤⣿⣤⣴⠆⠠⠲⢲⠚⠧⠤⠤⢀⣀⠀⣿⢀⢀⡄⣀⡀⠢⣠⡏
⠀⠀⠀⠍⣧⢀⠀⡈⠁⣁⣁⠀⠀⠀⠀⠀⠁⠀⠈⡈⠁⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⢈⡧⠒⠻⠙⣷⠉⠻⣏⠑⠂
⠀⠀⢠⠆⠁⠘⠉⠉⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠡⡀⠀⢈⠁⡈⠐⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡟⢿⡄⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⢾⠋⠩
⠀⠀⠀⠈⠉⠀⠀⢉⠖⠤⠀⢃⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⠋⠀⠀⠹⡄⠀⠀⢀⠶⠦⠐⡀
⠀⠀⠀⠀⠀⠙⠀⠀⢟⣿⠶⣾⡄⠀⠰⡖⠋⢹⠀⢀⣴⠁⣠⡄⢀⡀⢰⡀⢠⠿⠀⠂⡐⠉⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢠⠒⠒⠉⣿⣾⡟⢼⡧⠤⠧⠀⠺⣤⠟⠁⠚⠛⣣⠾⠿⠈⠛⠋⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣴⣤⠈
⡀⣀⣠⠀⠀⣤⡄⠀⠀⠙⠛⠻⠦⠄⠰⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠛⠷⠚⠀⠀⠀⠀⠀⠸⠋⠠⠤⠀⠂
⠅⠈⠀⠂⠀⠼⠤⠊⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠖⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⠂
⠀⣶⠄⠁⠀⣀⣥⠰⠃⠀⠈⢡⠀⠌⠀⠀⠀⠀⢀⣀⢀⢀⣠⣴⠶⢶⡀⢀⡀⠀⠀⠀⠀⠀⠰⠀⠶⠂⠀⠀⠀⠀⡀⠀⠀⠓
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉