White rice Emojis & Symbols

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⠶⠾⠛⠓⢶⣤⠴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣤⠾⠁⠈⠑⠚⠉⠁⠀⠀⠀⠀⠈⠉⠳⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⡤⠀⣀⡀⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⠟⠈⠁⠊⠙⠁⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠈⠻⠖⠲⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡤⢾⣃⡴⠊⠁⠀⠀⠀⡀⠀⠀⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠉⠀⠀⠿⣄
⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⢀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠤⠴⠛⠋⠙⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⢀⣠⣼⠇⠀⠀⠤⠏⠀⠀⠀⠀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣇
⠀⣠⠞⠉⡤⠛⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣄⣀⠀⠀⠈⡷⢦⡀
⣼⠃⠀⣴⠃⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⢹
⡟⠣⡀⠘⢦⡐⠘⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⠂⠀⣀⣀⡖⠋⠀⠀⣠⠴⠋⢀⣠⠟
⡗⠀⠉⠳⣤⣈⠛⠲⠦⣤⣀⡂⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢊⣉⣠⣤⠴⠞⠋⣁⣤⠖⠋⠁⢸
⣿⢤⡀⠀⠀⠉⠙⠳⠦⣤⣉⡉⠛⠛⠒⠲⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠚⠛⠉⢉⣀⣤⡴⠞⠋⠁⠀⠀⠀⢀⣼
⢸⡄⠉⠳⢤⣀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠖⠚⠛⠋⠉⠉⠀⠀⠀⠀⣀⣠⠴⠚⢉⡏
⠀⣷⢀⡭⠳⡌⢙⣲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣶⣯⣉⢘⡍⣷⣼⠁
⠀⠸⣦⡓⠚⠁⣨⠍⣷⠠⠬⣍⠙⢓⣒⠲⠦⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⣒⡚⠋⡭⠗⢦⠀⢡⣖⡼⢈⣻⣿⠃
⠀⠀⢻⡉⠓⠦⣍⣉⠁⢰⣯⠾⠀⣭⠍⣧⠀⢚⡋⢳⡄⠰⠖⠓⣦⠀⠰⢛⡛⣦⠀⣫⡍⢹⠀⠰⣯⠼⣁⣠⠽⠚⠉⢠⠏
⠀⠀⠀⢻⡄⠀⠀⠈⠙⠓⠲⠤⣤⣙⣛⠁⠀⠿⡭⠾⠁⠐⣯⣥⠾⠀⠀⢯⣥⠞⠀⣙⣒⣫⠤⠖⠚⠉⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠷⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠚⠋⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠻⣛⡋⠉⠉⣈⡅⠈⠉⠍⠍⣉⠀⠻⠿⠛⢿⣦⣤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠋⢥⠄⣶⢦⣥⠴⠛⠂⠠⠶⠄⣴⢦⡈⢉⠓⠶⢶⡄⢀⢀⣉⠙⠛⠻⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠟⠁⢰⠆⡄⠿⣋⠀⢴⠄⠘⢋⣀⣀⠀⢉⡀⠘⠛⠃⠀⠀⠀⠋⠘⠉⠻⢦⡌⠣⠄⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢩⡄⢡⠚⢫⠍⠠⠤⠿⢹⡦⠠⡤⠀⠨⢭⡉⠀⠈⢡⠄⠀⠴⠒⠛⠋⢳⠄⠘⠓⢤⠄⠓⠰⠦⠰⠆⠿⣦⣄
⠀⠀⠀⢰⣶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⢶⣶
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣴⣶⡾⠟⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣀⣀⣴⣾⡟⠉⣉⣛⠁⠀⢠⢤⢉⣉⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠛⢛⣁⡴⢂⡄⠙⠩⢴⡶⠀⠋⡀⠈⣥⣌⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠶⠿⠋⠁⣠⡴⠈⠉⠀⠘⠟⠀⠔⠦⠤⠔⠙⠁⠀⠀⠿⣤⣤⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠈⠛⣀⣾⡏⠉⠐⠟⠁⣘⡉⠱⣾⣶⠞⠂⠞⠛⠻⣇⣀⠟⠀⠙⠦⠀⠘⢿⣦⣶⡄
⠀⠀⠀⠀⠀⠀⣴⡶⠿⢩⠶⠚⠉⠠⠶⠖⠀⠀⠛⠛⠉⠠⠦⣍⡀⠰⠶⠃⠀⠈⠙⠃⠀⠀⠊⠛⠀⠰⡦⠹⣿⡆
⠀⠀⠀⢠⣶⣶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⢿⣿⣶⣶⡄
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠾⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣈⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣉⣩⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠻⠶⢏⠁⠀⠈⢿⣤⡴⠶⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠻⣣⠀⠀⡐⠃⠀⠀⠠⢶⠆⠀⠀⠀⠉⠽⠉⣙⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⠀⠀⡴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠾⠋⠁⠀⠀⠐⠀⠀⠀⡠⠀⠀⢠⡖⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠏⠀⠀⢘⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⢰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠚⠀⠀⢠⠟⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⣠⢄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣼⢧⣄
⠀⠀⠀⠀⠀⠀⣠⠞⢉⡾⠁⠈⡤⠀⠀⠀⠓⠂⠀⠀⠀⠀⠁⠀⠀⠀⠘⠧⠀⠀⠀⡀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠙⣧
⠀⠀⠀⠀⠀⢸⣇⠀⢸⣇⠦⠄⠉⠀⠀⢶⣁⠀⠀⠀⢰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢰⣿⡇
⠀⠀⠀⠀⠀⢸⠛⢦⡀⠙⠷⣤⡀⠀⢠⠄⠀⢠⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡾⠃⣠⠟⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠙⠳⣦⣈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠋⠀⠀⣴⠶⠾⠋⣠⡾⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠉⠓⠶⣤⣙⡳⠞⠛⠿⠶⢶⣴⣤⣭⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠞⠓⠚⣁⣤⠶⠋⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⢤⣤⣀⣀⣀⣉⣉⣉⣉⣉⣉⣁⣀⣤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠉⠛⠲⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠶⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣁⣀⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣤⣤⣤⣀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠾⢋⡉⠍⣉⡀⢖⡀⢙⠉⠥⣈⣛⠉⠳⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⡾⠀⡄⡩⠾⠉⣭⠀⢆⡈⠁⠋⠁⠶⠆⠈⠐⠒⠳⢦⡀⢍⠻⢧⣄⡀
⠀⠀⠀⠀⠀⢠⣤⠟⠡⠉⠘⠏⠁⠶⠋⠇⢠⠀⠈⣍⠁⠉⡄⠀⠖⠒⠋⣆⠘⠂⠄⠀⠲⠐⠘⠷⣄
⠀⠀⠘⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢛⡿
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠳⣄⣤⠤⠖⣦⢤⡶⣆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠚⠶⠞⠓⠛⠀⢀⡤⠀⠀⠀⢤⣦⠀⣬⡛⠹⠷⠺⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⡞⣻⠿⠀⠀⠀⠀⣠⠆⠀⠘⠟⢡⣾⡆⠄⠁⠀⠛⠃⠐⠀⠀⠈⡁⠻⠦⣤⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣭⣷⢿⣿⠀⠀⠀⠀⢠⣒⢦⠉⠁⠀⠿⠓⠊⠈⠁⠀⠀⢀⣄⠊⠑⠪⠇⢸⣿⡄⣤⡀⠀⠉⠙⢦⣤⣀
⠀⠀⠀⠀⠀⣠⠞⣁⣴⣾⣏⠉⠀⢀⠀⡆⠀⠀⠀⡈⠁⠀⠠⡖⠀⠀⠀⢾⠱⠦⠜⠋⠈⠀⢤⢶⡀⠀⠀⠀⠐⢁⡤⣦⠀⠀⠉⣯⡙⠦⡀
⠀⠀⠀⠀⣼⠁⣸⠏⠛⠉⠁⠀⠀⠀⣸⡏⠂⠀⠀⠟⠂⠶⠰⢻⠆⣤⣰⣤⠀⠀⠀⠀⣰⡄⠀⠈⠀⠀⢠⣤⠀⠀⠈⡑⠆⠘⠁⠉⢿⣦⠘⡆
⠀⠀⠀⢰⡇⢸⣿⠄⠠⣖⡂⠀⠀⡘⠈⠀⠸⠓⠀⠰⠃⢀⠿⠳⢾⠁⢨⡄⢀⣤⠠⠐⠃⠇⠀⠀⢠⣰⠾⠊⠁⠀⠈⠙⠐⠀⠀⠀⢨⣿⡇⢿
⠀⠀⠀⠀⣧⠈⢿⣷⡆⠈⢩⠲⣆⣉⡀⠀⢶⠦⠤⠞⠉⠀⠀⠀⣤⠀⢈⣥⡻⢖⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠂⠀⠀⣠⠟⢀⣼⠁
⠀⠀⠀⠀⢻⡀⠦⡙⠿⣦⣤⡀⠷⠁⠀⠀⠠⣄⠀⠺⠅⠀⠀⠀⠀⢚⡛⠘⣧⣶⠭⠘⠙⣃⠀⣴⢳⠀⠀⠀⡄⢹⠦⠆⢶⣤⣤⠾⢋⡀⢺⣿
⠀⠀⠀⠀⠘⣇⠀⠉⠲⢄⡉⠻⢶⣤⣄⣀⡉⠒⠂⠀⡄⠰⣤⣤⡷⣆⠈⡿⣝⠻⢷⣴⡙⠾⠇⣀⠠⡼⠙⣦⣀⣤⡴⠶⣛⣩⡴⠞⠁⠀⢸⡿
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠢⠬⢙⣛⣛⠛⠷⠶⠶⢦⣤⣤⣥⣤⣧⣤⣤⣴⣦⣤⣥⣤⠾⠿⠶⢚⣛⣩⣭⠶⠞⠛⠉⠁⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠓⠒⠶⠶⠶⠶⠦⠤⠤⠴⠶⠶⠒⠚⠛⠋⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠛⠛⠉⠁



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

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣰⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⣦⡀⣾⢱⣿⡿⣿⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⡛⣿⣿⡟⣿⢣⣿⣿⣿⣳⢺⠇⠀⢀⣠⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣟⡛⢇⢻⣿⠛⢚⣿⣡⡿⠶⠚⠉⠀⠀⡀⠀⠉⠉⠓⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠓⠲⠾⣿⣾⣦⠿⠦⠾⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠓⠲⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⢉⣉⣙⡿⠟⠁⠀⠀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠠⠉⣛⡿⠍⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⡖⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠄⠀⠀⠀⠀⠁⣀⣀⣀⣴⠾⠁⠀⠀⢀⣠⠴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠲⠶⠤⣤⡖⠚⠉⠉⠉⠉⠉⠁⠀⠀⣀⣠⡴⢒⡩⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⠴⠖⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠙⠙⠛⠛⠛⠒⠚⠒⠚⠒⠓⠻⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢾⡁⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣔⣠⡤⠤⣤⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠴⠦⣤⣤⣤⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣉⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢾⡉⠛⠚⠋⠉⠙⢦⡀⢠⡾⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⣡⠴⠋⠁
⠀⠀⠀⠀⠀⠀⣼⣋⠉⠉⠉⠋⠲⠀⠀⠀⠀⠀⠀⠀⣹⠏⣴⣯⣀⡀⠀⠀⠀⠀⣀⡴⠚⣉⡴⠞⠉
⠀⠀⣀⣴⣶⣿⣟⡎⠀⠀⠀⠀⠀⠀⠀⣴⠚⠂⢀⡼⢣⡾⠁⠀⠉⠙⣦⣠⠶⢋⣡⠖⠋⠁
⢠⣾⣿⣿⠻⡍⠚⠁⠀⢾⠉⠁⠀⠀⠀⠉⠀⣠⠟⣴⠏⠀⠀⣀⡤⠞⣩⣴⣾⣏
⣿⣿⣟⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡾⢃⣠⠴⣋⡥⢶⠋⠁⠀⢿⣿⣧
⢿⣿⠿⠅⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠈⠑⠟⠀⠈⠴⠚⠉⠀⠀⠀⠀⠀⢸⣿⣿
⠘⣿⣿⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠇
⠀⠘⣯⣻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠇⠀⠀⠀⠀⠀⣀⣠⣴⠞⢫⡟
⠀⠀⠈⢷⡩⣥⡈⠙⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠉⠁⠀⣠⠟
⠀⠀⠀⠀⠻⣦⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠈⠙⢾⣟⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠶⠤⣤⣤⣤⣤⣤⣤⠴⠶⣿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠒⠒⠀⠐⠒⠒⠒⠒⠒⠢⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢣
⠀⠀⠀⠀⠀⢸⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣸
⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠉⠒⠒⠒⠒⠋⠉⠑⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣒⠉⠁⠀⠊⠀⠴⠀⠀⠀⠀⢀⠀⠀⠀⠕⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⢀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⢤
⠀⠀⠀⠀⠀⡠⠖⡁⠠⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠈⠀⠀⠄⠀⠀⠄⠀⠈⠈⢧⡀
⠀⠀⡠⢒⣾⠃⠀⠀⠠⠀⠀⠈⠁⡀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠤⠀⠀⠄⡀⠀⠀⠀⠀⠀⢣⣀⣀
⠀⢸⢦⣙⢧⣀⡀⢠⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣗⡎⢙⡆
⠀⠘⣄⠈⠉⠒⠫⠭⠵⣖⣒⣲⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠖⢒⣒⣒⣊⠭⠕⠒⡹⠃
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⢄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⡖⠛⠿⣉⡭⠀⠀⠈⠛⠉⠙⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠛⠋⠐⠲⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠙⠛⠙⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠋⠔⠩⠤⠔⠳⡶⠦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⢉⡩⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠀⠀⠀⠠⠤⠤⠀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠉⠃⠋⠀⠀⠀⠀⠠⠒⠀⠀⠈⠁⠈⠳⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠦⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣰⠒⠊⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⣀⠴⠚⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠀⠀⠙⣦⣄
⠀⠀⠀⠀⢀⡼⠁⠀⡜⢀⠎⠀⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⣯⠈⢳⡀
⠀⠀⠀⠀⢸⢧⡀⠘⢇⠀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⠤⠀⠀⠀⣠⠤⠄⠀⠀⣀⡴⠃⢀⣼⡇
⠀⠀⠀⠀⢸⠀⠙⢦⣄⠙⠲⢤⣄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⣁⣀⣤⠶⠛⣁⣠⠴⠋⠁⡇
⠀⠀⠀⠀⢸⣄⠀⠀⠈⠙⠳⢦⣄⣉⠛⠳⠶⠦⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠴⠶⠚⠛⢋⣩⣤⠶⠛⠉⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠈⣏⠛⠦⣄⡀⠀⠀⠀⠉⠛⠛⠲⠶⣤⣤⣤⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣍⣥⣤⣤⣴⠶⠶⠶⠛⠋⠁⠀⠀⠀⢀⣀⡴⠞⣿
⠀⠀⠀⠀⠀⢻⡀⢐⡲⣝⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡚⠩⢖⢦⢠⡇
⠀⠀⠀⠀⠀⠘⣧⡻⠤⠟⢐⣛⢳⡌⣉⣗⠲⠶⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠶⢒⣾⣭⡁⢚⡥⢹⠆⠻⣾⡟
⠀⠀⠀⠀⠀⠀⢹⡟⠲⢤⣘⠓⠛⠡⣖⣨⠇⢘⣋⢳⠀⠠⠖⠶⡅⠈⡥⠿⢬⠉⢉⡼⠻⢤⠀⠰⣚⢳⡄⠈⣶⣨⠇⢈⣛⡭⠖⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠉⠓⠶⠭⣅⣀⡙⠶⠚⠀⢰⣛⣠⠇⠀⣶⣛⣸⠇⠀⢰⣋⣸⠃⠘⠧⣞⣁⡤⠽⠗⠊⠉⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠶⠤⠤⠤⠬⠭⠤⠤⠤⠤⠽⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠳⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠞⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⢀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠾⠛⠛⠉⢉⣁⣠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠋⣉⣠⣤⡤⠶⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠟⢛⣏⣛⣫⣟⢿⣧⣀⣠⡴⠞⣋⣥⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠇⡄⠻⠋⢏⡌⣡⡔⠂⡽⠉⢉⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⡘⢛⡛⠙⣐⣂⡤⠖⢋⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣒⣚⣛⣉⣉⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⠶⠶⠞⠛⠛⠻⠶⠶⠶⠛⢷⣴⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢛⡉⣠⣄⣋⡴⠦⠈⣥⡀⣤⣀⠚⠳⠤⢤⠀⠉⢙⠻⠶⢶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠞⠁⣴⢀⠲⣋⠀⠤⠀⠚⣀⣀⠀⣁⠀⠚⠟⠀⠀⠐⠃⠋⠳⢦⡐⠦⠙⠷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠤⠀⠘⠭⠁⠶⠞⠹⠶⠰⠆⠀⠥⠌⠀⠈⠤⠀⠰⠛⠛⠉⠧⠈⠋⠰⠄⠁⠲⠀⠂⠻⢶⡄
⠀⠀⠀⢺⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠂
⠀⠀⠀⠀⠻⣦⠒⠂⠒⠂⠐⠒⠀⠒⠂⠐⠒⠐⠒⠀⠒⠂⠀⠒⠀⠒⠒⠀⠒⠒⠀⠲⠂⠐⠒⠀⠒⠂⠐⠖⠐⠒⠀⢒⣾⠋
⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠟⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⢾⡉⠛⠛⠋⠉⠙⢦⡀⢀⡼⢋⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢋⣡⠶
⠀⠀⠀⠀⠀⠀⣼⣋⠉⠉⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⣹⡟⣡⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣉⡴⠞⠋⠁
⠀⠀⣠⡴⠞⢻⣟⡞⠀⠀⠀⠀⠀⠀⠀⣴⠚⠂⠀⣴⢏⡼⠋⠀⠈⠙⣦⣀⠀⠀⢀⣤⠶⢛⣡⠶⠛⠁
⢠⡾⣡⣴⠻⡭⠛⠁⠀⢾⠉⠁⠀⠀⠀⠉⠀⢀⡾⣡⡞⠁⠀⠀⠀⠀⣿⣬⡿⠞⣫⡴⠞⠉
⣿⢰⣟⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣴⠋⠀⠀⠀⢈⣷⠴⣛⣥⢶⠛⣷
⢿⣴⡿⠅⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⣀⡤⢞⣫⡵⠞⠉⠀⢸⠀⣿
⠘⣿⣿⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢭⠖⠋⠁⠀⠀⠀⠀⣨⣿⠏
⠀⠘⣧⣹⣳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠇⠀⠀⠀⠀⠀⣀⣠⡴⠞⢫⡟
⠀⠀⠘⢷⡩⣥⡀⠉⠛⠛⠶⠶⠶⣤⣤⣤⣤⣤⣤⠴⠶⠶⠛⠛⠉⠁⠀⣠⠟
⠀⠀⠀⠀⠻⣦⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠈⠙⢾⣟⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠶⠦⣤⣤⣤⣤⣤⣤⠴⠶⣿⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠀⠉⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠈⡌⢿⣦⣐⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⡿⣦⣤⠀⠀⠀⠀⠑⢦⡈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠈⣿⡷⣼⡟⠀⠄⠀⠀⠀⠱⣄⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡻⣶⡤⡿⣿⡟⠎⠉⢾⣷⣠⡀⠀⠀⠘⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⡿⠷⠶⣴⡌⠠⣅⠀⠀⠀⢹⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡆⠀⠀⠀⠋⠹⠶⢋⣀⣤⣤⡈⢳⠀⢉⣷⢧⡶⣺⣹⡿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣀⣴⣿⣷⣿⣆⡿⣦⡹⠿⣿⣧⢹⡿⠾⠛⠁⢀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠘⠀⠀⠀⠾⠟⠉⣸⠛⠛⠋⢰⣽⣯⠈⠋⠙⠋⠀⠀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣴⢆⡄⠘⠁⠀⠀⠀⠈⣿⡿⠀⠀⠀⢀⣀⡦⣀⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢦⡀⠀⠀⠟⣀⡀⠀⠀⠀⢀⡼⠛⠠⣄⠢⢴⣿⣿⣧⡿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⠀⠀⠐⣌⠻⢶⣤⣀⣘⠁⠀⠀⢀⣀⣨⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠸⣷⡀⠀⠉⠙⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠚⠉⠛⠉⠙⠛⠉⠳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⣀⠀⢀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⣀⡴⠚⠉⠉⠉⠀⠀⠀⠈⠉⠋⠙⢦⣤⣄⡀⠀⢀⣧⡀
⠀⠀⠀⠀⠀⢀⡴⣇⣀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⡀⢹⡀
⠀⠀⠀⠀⠀⢸⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀
⠀⠀⠀⠀⢠⠏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣆⠀⢀⡰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢸⣿⣿⣟⣻⡇⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣸⠛⠛⠓⠚⣇⣀⣠⠤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡾⠶⠭⣦⡀⢀⣜⣉⣠⡤⠴⢿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⡇⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠘⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⣼⣀⡤⠖⠚⣇⣸⡀⠀⠀⠀⠀⠀⢹⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠉⣩⡿⡄⠀⠀⠀⠀⠘⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⣇⠀⠀⠀⠀⣤⣶⣅⠀⠀⠀⠀⠀⢹⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⡖⠒⣛⣶⠒⠲⡖⣇⣀⣸⠷⢶⣶⣶⢤⣈⣇⡴⢻⢷
⠀⠀⠀⠀⡴⠒⠒⣲⡾⣭⣿⣿⠽⠋⠙⠤⠴⠃⠀⠉⠁⠀⢯⠀⣸⡇⠈⢿⡷⣿⠾⣷⡒⠒⠒⢦
⠀⠀⠀⣸⠃⣠⠞⠁⢠⣾⣷⣛⣦⡤⢖⣦⠀⠀⣠⣤⣄⠀⢈⣭⣭⣤⠖⢋⣴⡿⠓⡆⠙⢢⡀⠈⢧
⠀⠀⣰⠃⠀⢻⡀⠀⠘⢯⡙⠻⢭⣛⣛⣛⠓⠛⠓⠛⢋⣉⣉⣠⡤⠴⠚⣩⣾⣳⠋⠁⠀⣰⠃⠀⠘⣆
⠀⢠⠇⠀⠀⠀⠙⠲⢤⣀⡉⠓⠶⠤⣬⣉⣉⣉⣉⣉⣉⣉⣥⠤⠴⠒⠋⠁⠀⣉⣠⠴⠚⠁⠀⠀⠀⠸⡆
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠖⡡⠐⠒⠒⠠⡙⢦⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⡠⢂⠥⢂⠈⠌⢁⠠⠤⢀⠀⠀⠀⡀⠀⠀⠈⠂⢃⠀⢀⡀⢞⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡠⡪⢚⠕⠈⠀⠐⢊⡔⠂⠀⢨⡇⠢⠀⠀⠐⠄⠀⡀⠈⠀⠀⠹⡄⢣⠁⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠌⠔⠔⠑⠀⠀⠀⡀⠈⠂⢊⠔⠋⠈⠓⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠰⠀⠃⠳⡘⣆⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⡌⠀⠀⠀⠀⠀⠁⠀⠙⢄⡉⠀⠀⠀⠆⠀⠆⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠁⠀⠀⠀⠒
⠀⠀⠀⢁⠀⣤⠀⠛⣀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠙⠀⠘⠉⢼⣻⡆⠀⠀⠈⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⢼⠰⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢠⣻⠛⠀⠀⠀⠀⠀⠀⠒⢄⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠈
⠀⠀⢀⡀⠀⠄⠀⠀⠀⠈⠠⡄⠀⠇⣞⠄⠀⠂⠁⠀⠁⠐⢀⠀⠂⠐⠀⠆⠱⠠⠈⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⢄
⠀⠀⡜⠱⠀⢄⠀⠀⠀⠀⠀⠠⠖⠚⣿⢲⡦⢀⡄⢀⠄⠠⢂⠀⠀⠀⠀⡄⠃⠀⡀⠀⠀⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠉⢋⠉⠅⢀⠠⢊⠔⠁⠀⠀⠀⠀⢟⠀⠰⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⡈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⢒⣀⠠⠐⠈⠀⠀⢀⡀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠌
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⢿⠀⠇⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡆⠀⢀⠈⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠢⢤⠂⠐⢄⠀⠀⠀⠇⠄⠀⠀⠂⠃⠀⠘⠂⠃⠀⠛⠀⠀⠇⠀⠀⠀⠀⠀⢀⡤⣤⢤⡤⠄⣲⠶⡄⣀
⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠆⠀⠀⠀⠀⠀⠐⠐⠠⠒⠀⠔⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡀⠀⠀⠀⠈⠢⢬⣎⡢⠄
⠀⠀⢀⠄⠢⠎⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠈⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⣠⠎⠀⢢
⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠙⠲⣄⢸⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠊⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢂⡵⢶⠒⢦⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⡂⢡⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠰⠦⢴⣒⣐⠀⡠⠶⠆⠀⠄⠀⠀⡐⡀⣄⣘⠶⢞⡴⠀⠑⡄⠀⣠⠇
⠀⠀⠀⠀⠀⠘⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⣯⠍⠄⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠺⠀⠀⠏⠀⠀⠀⠈⡁⠀⠀⠀⡼⠜⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⢰⠄⠉⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⢄⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠛⠄⠀⢌⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⡼⠇⠀⠀⢀⡠⠒⠉⣀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠔⠒⠒⠶⠤⢀⠀⠄⠀⠀⠀⠀⠀⢸⠀⡏⠁⡇⠀⠠⠚⠁⠀⢀⠄⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠃⢀⠈⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠺⠄⡰⠃⡀⠰⠅⠒⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠂⠀⠀⠀⠚⡉⠂⠀⠀⠉⠉⢉⢩⡅⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⠆⠀⠀⠸⠿⠃⠀⠀⠀⠀⢱⡆⠃⣀⠔⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⢴⠊⠀⠐⠋⠉⢉⠍⣠⠞
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⢧⠀⢤⠤⠤⢀⡠⠄⠀⠀⠀⡀⠡⡼⢶⠶⠿⠭⠄⠒⠈⠁
⠀⠇⠀⠄⠋⠓⣦⢤⡀⠀⣠⣤⣷⡄⠻⠉⠹⠁⠀⠀⢀⡔⣀⣴⣿⣷⣤⣤⣀⡀
⠀⡄⠀⠀⠓⠀⡌⠀⢰⣾⣿⣿⡏⢹⡄⠒⠃⠀⣠⣴⡫⢕⡫⡾⠃⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠈⢦⡀⠈⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⢖⣋⠉⡀⠀⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣍⠽⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣷⡄
⡀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠟⠋⠨⠟⠛⠛⠛⠛⠛⠛⠛⠳⣬⣙⠿⠿⢿⡿⠟⠛⢷⣽⣿⣿⠟⠋⠉⠙⢄
⡇⠀⠀⠀⢠⢂⠴⠋⠀⢀⠤⠤⣀⣈⣀⣤⡀⡠⣤⣠⣤⣾⣿⣿⣷⣿⠛⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⠀⠙⠢⢄
⠱⠤⠤⠄⠊⠁⠀⠀⠀⢸⣿⣿⣿⠿⣿⠿⡿⢿⣿⣟⣿⣟⡁⠉⠉⠙⢼⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⢿⣿⣽⣿⣿⣿⣿⣟⣳⣆⠀⠀⢀⠊⠐⠤⠐⠀⠂⠉⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⢄⠀⠀⢼⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠿⠁⢈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠭⠭⠉⠭⠭⠽⠯⠥⠜⠂⠲⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⡿⠿⠿⢟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣀⡀⡀⠈⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⢻⠿⡤⠀⠀⠀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣑⡒⠊⢀⡀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡓⠀⠉⠀⠀⢀⣤⠂⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢶⠿⣿⣧⣀⣀⣠⣴⠟⠁⢀⠀⢸⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡍⠁⢀⡄⠀⠀⡎⠀⠈⣏⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠟⠀⠀⢀⠀⠀⠀⠀⡀⠸⠇⠀⠈⣧⣤⠈⠀⠀⢸⠃⠀⠀⣿⠀⠀⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡁⠀⠀⠀⠀⠀⠉⠀⠺⠁⠀⣾⠠⠞⣿⣿⠢⡀⠀⡌⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠋⠑⣄⠀⠀⠰⠀⠀⠀⡄⠀⠀⠐⠀⠀⢿⡄⢀⣿⣷⡀⠀⢰⠃⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠼⠃⠀⢀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡇⠀⡎⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⠂⠀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢰⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣄⠉⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣞⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⡼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⡰⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠰⠁⠀⠀⠀⠀⣧⠀⣀⣀⣤⣤⣄⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⡋⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣀⣠⡼⠟⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠸⠟⢠⡴⢀⣠⡄⠀⠀⢸⡇⠈⣿⣿⣿⡟⣼⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣉⣀⣀⣀⣿⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣿⣅⡉⠁⠀⠀⠀⡼⠧⠤⠬⠷⢤⡾⠿⠦⠴⠷⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢧⣀⡈⠓⠶⠶⠶⠶⠒⠀⠀⠀⠊⣉⣁⡤⣤⠤⠊⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠿⠿⠿⠿⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠐⠲⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠆⠸⣧⠀⢿⣆⠰⣷⡀⢾⣆⠐⣷⡀⢺⣦⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣸⡿⢀⣿⠇⢨⡿⠀⣼⡇⢠⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⣿⡁⢸⣏⠀⣿⡁⢸⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢹⣷⠀⣿⡆⢘⣿⠀⢻⡇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣾⠃⢰⡿⠁⣾⠏⢠⣿⠁⣼⡏
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣀⣿⣦⣘⣿⣄⣻⣧⣈⣿⣄⣹⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠴⠶⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣶⡾⠯⠭⠽⠷⠒⠒⠒⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠶⢾⠀⢸⠧⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠘⡀⢸⡇⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣀⣤⣴⣾⣟⣿⢹⣿⡷⢿⣷⢧⡤⡤⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣒⣭⡿⢛⣯⣽⣏⡙⠛⠛⠁⠨⢸⣉⣄⡘⢬⣻⣗⡤⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠣⣴⣿⣽⠋⢁⣄⠐⠤⣴⣮⢵⠿⠛⠒⠻⡟⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣲⢭⣒⣙⠾⡻⢭⡽⠿⢿⡿⠿⠿⢅⣻⣿⠿⣟⣯⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣭⣭⣵⣖⣛⣛⣻⣯⣭⣭⣷⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠪⠭⠭⠭⠭⠕⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠒⠶⠋⠙⠚⠉⠙⠚⠋⠙⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣠⠦⠤⠴⠞⠲⠶⠛⢦⣄⣠⢤⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠲⣄⡀⢀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡤⢿⣀⣰⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⠃⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⡄
⠀⠀⠀⠀⠀⢀⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡦⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣤⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣴⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⣼⢿⣿⣿⣯⡽⡇⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣟⠲⠾⡀⠀⠀⠀⣰⠷⠖⠛⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢹⠋⠙⠓⠻⢦⢀⡾⠧⠶⠶⠒⠋⠉⢿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡿⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣼⣇⣠⠴⠖⠛⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢋⣩⣇⡀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢈⣉⣼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣸⣇⣀⣀⣀⣀⣼⠋⠉⢳⣄⠀⢀⣀⡀⠀⠸⡆⢀⣤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⣇⣨⣭⡽⣏⠀⠈⣿⠙⠦⠤⠞⠉⣩⠟⠻⢯⠛⢶⣷⣞⢁⡟⢳⡀
⠀⠀⠀⠀⢠⡟⠉⠛⣉⡿⠿⣶⠿⣿⡖⠋⠀⠙⠒⠚⠃⠀⠀⠀⠀⠀⢻⣄⣀⡼⠀⠀⢹⠞⢻⣟⠻⢿⣝⠉⠉⠙⢧
⠀⠀⠀⢀⡞⠀⣠⠞⠁⠀⣴⣾⣿⣉⣧⣤⠴⢛⣧⠀⠀⣠⣤⣤⣄⠀⠀⣠⣴⢤⣤⠟⢋⣠⣿⠟⢒⡆⠈⠳⡄⠀⠘⣇
⠀⠀⠀⡾⠁⠀⢿⡀⠀⠀⠻⣍⠛⠯⣝⣓⡛⠻⠿⠶⠾⠿⠒⠚⠛⠛⠛⢁⣀⣠⡤⠖⢋⣴⡛⣶⠋⠁⠀⢀⡿⠀⠀⠸⣆
⠀⠀⣼⠁⠀⠀⠀⠛⢦⣄⡀⠈⠓⠦⣤⣉⣉⠛⠛⠓⠒⠒⠒⠒⠛⠛⠛⢉⣉⣤⠴⠞⠋⠀⠙⠛⠀⣠⡴⠛⠀⠀⠀⠀⠹⡄
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣌⣉⣉⣛⠛⠛⠓⠚⠛⠛⠛⠉⠉⣁⣀⣀⣠⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣾⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡟⢉⡟⠁⡞⠉⢩⣹⣦⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⢧⡀⢷⡀⠘⢿⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡽⢀⡿⠀⣼⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⢰⡏⠀⢸⡙⢦⣬⠇
⠀⠀⠀⠀⠀⠀⢀⣀⣼⡆⠙⢦⠙⢦⡀⠹⡟⢋⣩⣭⣭⣝⡛⠛⢛⣲⠶⠶⣦⣤⣄⣀
⠀⠀⠀⠀⣠⣾⡿⠛⣩⠴⢚⣩⡤⠾⠃⢠⡇⢈⡤⠶⠶⢤⣉⠉⣉⣠⠤⣤⡀⠙⢮⠙⣿⣶⡄
⠀⠀⠀⠀⣿⣿⣷⣴⡇⢰⠋⠀⡤⠶⢚⡉⢰⠋⢠⠤⢤⣀⡈⠉⠉⣠⠤⢤⡙⠦⣄⣡⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣭⣛⣻⠶⠶⣧⣤⣯⣤⣼⣄⣿⣠⣶⣈⣩⣽⣯⣥⣤⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢰⣭⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣵⠂
⠀⠀⠀⠀⠈⣻⢿⣿⣶⣦⣭⣉⣙⣛⡛⠛⠛⠛⠿⠿⠿⠛⠛⠛⣛⣛⣋⣩⣭⣴⣶⣿⠿⡛
⠀⠀⠀⠀⠀⠹⣷⣦⣭⣙⡛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⣛⣫⣭⣶⣾⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁

⣏⣈⣯⣏⣟⣯⣿⣹⣽⣿⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠄⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢌⡔⠊⣠⣶⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⢘⡕⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠘⠁⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠐⡄⠀⠀⠀⠰⠀⡠⠄⡠⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠃⣠⠈⢢⠀⠀⠀⢲⠀⠠⣅⠀⠀⣠⢃⠠⠄⠒⠒⠈⠁⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠐⠀⢈⢹⣧⠀⠀⠀⠂⡼⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠔⡒⢆⡉⢰⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠂⠈⡀⠀⢠⠒⠖⠠⠤⢤⠠⣄⢀⡈⣙⣋⡉⠉⠀⠀⠀⣀⠰⠇⡾⠟⠣⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠓⠶⠤⠴⠄⠤⠄⠥⠠⠃⠀⠀⣀⡤⢎⣀⣀⣀⣀⡀⣀⣀⣀⡀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠥⠠⢍⡹⠯⠸⣁⡆⢺⡟⠳⠿⣿⡉⠶⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣮⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡤⠶⠚⠛⠛⠉⠙⠚⠾⠭⠶⣶⣿⣽⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣿⣇⣃⡀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⣤⣀⣀⣀⣀⡀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢩⠈⠀⠀⠋⣨⠁⢃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡆⢰⠉⢤⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡀⠘⡁⢡⠌⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠣⢄⡉⢳⠀⠑⠊⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡠⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠐⠣⢀⡀⠀⠀⡐⠤⠀⠠⢄⡀⠔⢊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⡀⠈⢹⢂⣍⠈⠁⠀⠈⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠒⠼⠀⠛⢃⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⡀⠀⠀⠀⠀⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠠⠐⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠴⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠒⢺⠞⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠉⠿⠀⠐⠒⠒⠒⠒⠂⠀⠘⠒⠒⠾⠿⠽⠧⠤⠤⠤⠂

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

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

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⣷⣶⠶⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠟⠛⠉⠁⠀⠈⢿⣦⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⡇⠈⠙⠻⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠙⣿⣦⣀⣤⣴⡶⠟⠋⠁⢸⡿
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠷⠶⣶⣶⣶⣶⣶⣾⣿⣷⣶⠾⠿⠿⠛⠻⣿⣯⡀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠈⠻⣿⣦⡀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠈⠻⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⢀⣴⠟⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣶⠟⠁⠀⠀⠈⠻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡉⠛⠻⠿⢶⣶⣶⣦⣶⣶⣶⡶⠾⠟⠛⢉⣠⣾⠟⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡠⠋⠀⠀⡄⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡑⠀⠀⠀⠠⠀⠀⠁⠊⠉⠛⠳⠶⢶⣦⠤⢤⡀⠀⢒⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠁⠀⠀⢀⠐⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠌⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠁⠀⠀⢀⠄⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢡⠀⠀⠀⠡⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡳⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠐⠗⠂⠀⠀⠀⠠⠸⢂⠅⠀⠀⢸⣀⠖⢄⠀⠐⣬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠑⢢⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠀⠀⡠⠖⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠘⢄⠀⠀⠈⠂⠘⡀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡀⠀⠀⠀⠀⡐⠀⠀⠁⠀⢀⠅⠀⠀⣀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠌⠀⠑⢄⠀⠁⠢⡀⠀⠀⠐⠄⠀⠀⠀⠐⠤⠄⢀⢠⠔⠀⠀⠀⠀⡐⠀⠀⠀⡠⠀⠁⢀⠄⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠡⡀⠀⢈⠖⠈⠢⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠂⢤⠊⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⢁⠔⠈⠀⠈⠢⡀⠁⠀⡤⠠⠠⠄⡄⠀⠁⡠⠊⠀⠑⢄⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢁⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⢽⠁⠈⠀⠀⠀⠀⠀⠑⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠃⠐⠐⠨⠊⠀⡶⠦⢀⡀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⣦⠐⠀⠒⠀⠂⠎⠀⢦⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⢻⡄⠁⠸⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠱⣖⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣴⠀⢶⡄⠀⢸⡆⠀⠠⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠒⠈⠙⠀⠉⠙⠠⡀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠉⠉⠛⠈⠀⠈⠠⠀⠀⠀⠈⢄⠀⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠠⠀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠡⡀⠀⠀⠀⠈⠁⠐⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⢸⡗⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠺⢦⣀⠀⠀⡠⠊⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣠⡀⢀⣬⠏⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠉⠙⠓⠤⠤⠀⣠⣄⠁⠀⣄⣀⢀⣀⣠⣄⣀⡠⠤⠶⠛⠋⠉⠁⡀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠉⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣀⣤⣶⡶⣶⣶⣤⣔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⣀⣽⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠰⢰⡿⠁⠀⠀⢀⣤⠾⠁⠀⠀⠀⢹⣧⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠋⠀⢠⡿⠓⠘⠁⠑⠀⠀⠀⠀⠀⠂⠠⢀⢹⡆⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢸⡇⡰⠁⢠⣤⡄⠀⠀⠀⣤⣤⠀⠀⠘⡇⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⡁⠀⠀⠀⠁⡗⠀⠀⠘⠛⠀⠀⠀⠀⠛⠋⠀⠀⢸⡇⠁⠀⠀⠀⢻⠗⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⡀⠀⠀⠠⠴⡀⠀⠀⠀⠰⠖⠒⠢⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠂⠀⢀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⢄⠈⠐⠄⠀⠀⠐⡀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⠔⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠄⡠⠋⠀⠐⢌⠂⠄⣀⠀⠀⢀⠀⠐⠀⡠⠐⠁⠙⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠁⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢀⣀⠠⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠉⠠⡀⠀⠈⠆⠀⠄⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠐⢤⡀⠀⠁⠢⠀⠠⠀⠐⠀⢀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢬⠀⠀⠈⣷⠀⠀⠀⠀⢀⠂⠀⢀⣀⡥⠖⣀⠄⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⡐⠚⠛⠿⠿⠒⠌⠀⣤⠂⠠⣄⣹⣇⠀⠀⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠐⠀⠀⢀⠀⠀⠀⠈⠞⡁⢰⣤⣿⣿⣏⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡉⠆⠀⠀⠀⠀⠀⠈⡄⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⢑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡴⣶⡶⢆⠀⡀⠀⠀⠀⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡄⢁⠀⠐⠂⠠⠾⠚⠉⠀⠀⠞⠛⠛⠁⠀⢀⠀⠀⡠⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣣⠞⠁
⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⡄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⠏⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡴⠋
⠀⠀⠀⠀⢀⣀⡤⠴⠋⠉⠁⠈⠉⠉⠶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣾⣿⣿⣿⣶⡎
⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⣀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢹⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠑⡦⠤⠤⠤⠤⠤⠤⠤⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣖⣛⣻⣛⣛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⠘⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⢸⡄⢻⠄⠀⠠⣎⠀⠀⠀⠀⠀⢀⣼⡵⣿⡶⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠛⠙⠈⠼⠓⠇⠀⠼⠧⠴⠖⠀⠀⠀⢿⠈⠁⢀⡇⠀⠠⠰⠆⠢⡀⠀⠰⢣⣟⣿⠞⠀⠀⠀⠀⠀⢸⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠈⠁⢀
⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠠⣤⣤⣦⠄⠀⠀⡀⠒⠀⠁⠀⠀⠀⢠⣤⣤⣴⡀
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠔⢰⡮⠃⠀⠀⠀⠶⠉⢀⠜⠁⠀⠀⠀⠉⠁⢀⠀⠀⣤⠞⣀⡈⠳⠀⠀⠈⢉⡻⠏⠁
⠀⠀⠀⡀⠃⠀⠀⠀⠘⠀⠤⠤⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠈⠡⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠉⠂⢀⠀⢠⡄⠘⠓⢠⠀⠀⠀⠉⠙⠀⠀⠀⠀⣀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣙⡧
⠀⠀⠀⠀⣾⢴⡄⠀⠛⠀⢀⡀⠀⠘⠀⠈⠀⠀⠈⠀⠀⠀⢦⣤⣤⣤⡆⠀⠀⠐⠁⡠⡄⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠁
⠀⠀⣠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠀⠀⠀⢠⠐⢄⣡⠀⠀⠀⢀⠀⢀⠀⠀⢀⣤⣤⣤⣀⡀
⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⣀⠀⢀⡀⡃⠀⠤⡥⢬⠖⠋⠀⠀⠅⡠⠀⣀⠀⠀⠀⠨⢉⠉⠁⠶⠋
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡇⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡙⠁⠀⠘⢀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⢼⣵⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠁⠀⠀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢶⣴⣄⡇
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠀⠀⠀⢠⣴⢶⠶⣦⠀⠀⠀⢀⣀⠀⠀⠀⠠⠶⠀⠀⠴⠆⠀⠀⣠⠀⡛⡀⠀⠀⠀⢠⣤⣤⡄⠰
⠀⠳⢶⣶⣶⠶⠃⠀⠈⠛⠾⠿⠛⠀⠀⢄⡈⠀⣀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⢚⠟⢑⣇⣱⠀⠛⠣⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉
⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠶
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠓⠲⠂⠀⠀⠀⠙⢿⡉⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠾⠥⠀⠀⠀⠀⠰⣦⣄⣤⡾⠃
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠄
⠀⠀⢁⡐⠀⣨⠀⠀⢀⡠⠀⣤⠐⠀⠀⠀⢶⡌⠑⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⠶⠂⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠈⠐⢎⠹⠀⠀⠀⠁⠈⠀⠁⠀⢀⣹⢿⡟⣿⡄⠀⠀⠠⠸⠠⡔⠁⠀⠀⠶⠆⡀⢠⡀⠀⠀⡘⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠐⠂⠐⠁⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⠠⢀⣠⣀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢴⡄⠀⠀⣠⡀
⠀⠀⣩⣤⣦⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⡶⠟⠋⠁⠀⠀⠀⠀⠀⣦⡉⠀⠀⢀⠀⠀⡅⢠⠡⠀⠀⠀⠐⠀⠸⠃⠿
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠋⠀⠀⠠⡿⠟⠛⠛⠃⠀⠀⠀⠀⠎⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⢿⡿⠻⡿⢿⢿⠿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣾⣶⣾⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠆⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠒⠂
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠋⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠂⠈⠁⠙⠟⠿⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣤⣀⣀⡀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣻⣳⠀⠀⠀⠀⠀⠀⠀⠚⠉⡹⢻⣿⣧⣿⣿⣷⣦⠼⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢀⣨⣠⣾⣿⣿⣿⣫⠔⠛⠿⠆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣴⣶⣶⣷⣄⢾⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⠀⠀⠁⠀⠈⠛⠻⣿⡿⠋⠀⠀⠀⠀⣤⣄⣄⣀⠀⢁
⠀⠀⢸⡳⣿⣟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠙⠻⠾⣽⣛⣻⠿⣿⠷⢿⣿⣿⣿⣿⣿⣧⣶⡦⡀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣤⣴⣾⣟⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠿⠿⠥⠤⢼⣭⣯⣷⣭⣶⠤⠀⠴⠷⠾⠿⠟⠛⠛⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣻⣟⣛⣻⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠋⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⢀⣠⡤⠶⠛⠉⠑⠂⢀⣀⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣭⠽⠟⠛⠉⠁⠀⣠⣠⣤⠖⠛⠉⠁
⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⡀⡀⡀⠤⠄⠠⠀⠤⠠⠄⢄⣀⣀⡤⠶⠚⠋⠉⠀⣀⣠⣤⣖⣚⣉⣥⣬⡭⠿⠷⠶⠖⠒⠚⠓
⠀⠀⣴⠞⢉⡠⠔⠂⠉⠈⠉⠁⠀⠀⣀⣀⣀⣀⣀⣤⠴⠖⠛⠉⠁⣀⣠⡤⠶⠚⠛⠋⠉⠉⠉⠉⠅⠀⢀⠀⣀⣀⣀⣁⣀⣠⣤
⢀⣈⣿⣭⡤⠴⠶⠖⠒⠚⠛⢛⣉⣭⠽⠟⠛⠉⠁⣀⣠⣤⣶⣾⣯⣭⣤⠤⠤⠴⠶⠶⠒⠒⠒⠛⠛⠏⡉⠉⠉⠉⠅⢀⣸⡆
⠛⠓⢶⠶⣶⣖⣒⣲⡶⠶⠚⠋⢁⣀⣤⣴⠶⡟⠋⠉⣉⢭⢨⡞⠀⣰⠄⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠈⠃⠀⠀⠀⢀⡼⣿⠃
⠀⢀⣸⡧⠞⢛⣉⣡⡤⢶⣶⣛⣉⣁⠀⠀⠋⠂⠀⠠⠸⠚⠊⠀⠀⠀⠀⠀⢼⡣⠀⠀⠻⠏⠇⠀⠀⠀⣀⣠⡤⠞⠉⢠⡟
⠀⠻⠓⢺⡏⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠛⠛⠉⠁⠀⠀⢀⡾
⠀⠀⠀⠀⢷⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠈⢷⡐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⢠⠟
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠛⠶⢤⣄⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠋⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠤⣤⣤⣤⣤⣀⣀⣠⣤⣤⡤⠴⠖⠛⠉

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣆⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⢹⣿⠀⠀⠀⠀⡀⠀⠀⠀⠠⠔⠈⠀⠀⠀⠈⠐⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠈⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠉⠛⠻⠿⠿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠠⠤⠤⠤⠀⠀⠀⠂⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣤⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⡿⢛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡾⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⠟⣁⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⢟⣡⣾⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡤⠒⠒⠀⠀⠀⠠⢟⡵⠛⠓⠢⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢛⣯⣿⣿⣿⣿⣟⡵⢋⣴⣯⣟⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣷⣶⣦⣤⣤⣤⣬⣤⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣿⣿⣿⣿⣷⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣾⣿⣿⣿⣿⣶⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠀⠒⠂⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠼⠄⣀⡀⠀⠀⣤⣀⣀⣀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠄⠀⡄⠀⡠⠈⠑⢢⡘⠿⠿⡿⠟⠛⠿⠖
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠠⠀⠒⢘⠄⠀⠀⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠁⣀⡰⠉⠢⡀⠀⠀⠀⠀⠀⠀⢎⢹⠄⣀⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⡜⠁⠈⠀⠄⠀⠀⠀⠠⠤⠒⠉⠀⠀⠀⠂⠀⣎⠙⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠀⠈⠀⡔⠐⢦⢈⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠜⠀⢀⡤⠋⠁⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠉⠻⣅⠉⠂⠤⠒⠁⠀⠀⠉⣉⠥⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠒⠒⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⣫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡜⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⢎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡰⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢀⡜⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⢎⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⡠⣔⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣠⠴⣚⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡿⠃⠀⠀⠀⠀⢀⣤⠞⣋⠤⣚⡭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⢤⣀⠀⢀⣤⠴⠶⣤⡀⢀⡞⠁⣴⠟⠀⠀⠀⢀⣠⠞⡫⢔⣫⠵⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⢀⡴⠞⠛⠋⠀⠀⠀⠀⠈⠳⠋⠀⠀⠀⠀⢙⠟⢀⣼⣋⠀⢀⣠⢖⣫⣷⡽⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢎⣠⠞⢀⣩⣗⣯⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠿⠛⠁⢻⣤⣤⡀
⠀⠀⠀⠀⣠⠖⠛⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⣠⣤⣤⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡛⠛⠛⣷
⣾⠁⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠰⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⣤⠟
⠈⢻⡆⠀⠀⠉⠑⠒⠀⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⠔⠒⠉⠀⠀⠀⣼
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡆⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠄⠒⠒⠒⠚⠉⠉⠉⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠐⣒⣒⣀⣉⣉⣭⡤⠤⠤⠤⠔⠒⠒⠒⠒⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢭⠟⠙⠯⠤⠤⠤⠤⠤⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠈⠙⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠛⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣂⡀⠀⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠒⣂⣉⡉⠉⠁⠀⡌⡄⡀⠀⡅⡀⠀⣉⠉⡁⠐⠒⠢⠤⠤⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠁⠀⠀⠀⠥⢀⣁⠴⠌⣉⡳⣉⠄⢀⣒⡘⢌⡀⠀⠐⡀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠂⠀⢐⣒⠒⠢⣄⣐⣀⣵⡀⠐⢢⣂⣈⡈⣝⡢⢌⡅⠁⠰⠠⠓⡩⠢⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⢆⠉⠓⠢⠤⢄⣀⡀⡱⠊⠄⠀⠤⢍⠲⣟⠉⠐⢒⡂⠍⠄⢛⣑⣲⠠⠵⠆⠚⠉⡰
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠈⠁⠋⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠉⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠈⠁⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠄⠒⠊⠁




⣿⣟⢹⣟⠻⣿⣛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠈⠳⣄⢀⣠⣤⣴⣦⣤⣶⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢀⡼⠋⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣤⣤⣴⣾⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠻⣿⡈⠻⣿⣿⣧⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠉⠙⠃⠀⠀⢸⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⢿⣿⡇⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⢸⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢀⡞⢹⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣯⠙⡆⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⡇⠸⣇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⡇⠀⠀⣿⣿⣿⡿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⡇⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⣤⣤⣤⣠⣤⣤⡤⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣇⠀⠀⢸⣿⡇⠳⣄⠀⠀⠀⠘⢧⣀⣀⣀⡽⠃⠀⠀⢀⡴⠃⣿⡟⠀⠀⠀⠀⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣿⣿⠻⢶⣴⣿⡀⠀⠈⠳⢤⣀⠀⠀⠉⠉⠁⠀⢀⣠⠴⠋⠀⠀⣿⠇⠀⠀⠀⢰⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⣋⣉⣭⣉⣛⣶⡀⢀⣬⣽⣛⣒⣒⣚⣻⣯⣄⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢉⣉⣉⣉⣭⣽⣿⣿⣦⣄⡉⠉⠉⠉⠁⠀⣈⣳⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠤⠤⠴⣶⡿⠉⠉⠛⠿⣿⣷⣦⣠⠖⠻⢉⢁⠬⠬⠕⠠⠲⢭⡩⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⣲⠞⠋⣽⠁⠀⠀⠀⠀⠀⠉⣹⢃⢃⠖⠉⠀⠀⠀⠀⠀⠀⠀⢹⡞⢚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠉⠉⠛⠛⣷⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠹⡜⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⣹⠦⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣥⣂⣄⣀⣀⣀⣠⣤⣲⡴⡾⢋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⡧⠞⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠦⣍⣉⠉⠉⣉⣡⣴⡯⠴⢋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⠻⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⠀⠈⠛⢿⣦⡀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀⢀⣽⣿⡾⠿⠛⢛⠉⠙⠛⠻⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣽⡿⠟⠋⠁⢤⡶⠂⠘⠷⠀⠀⣿⠀⢠⣍⠛⢿⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⣿⡿⠋⠰⣦⡀⢠⡄⠀⣤⡀⠀⣼⠃⢠⡀⠀⠙⣁⡀⠈⠻⣿⣿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣿⠏⠀⢰⣆⠀⠀⠘⠁⢀⠈⠛⢀⡄⠀⠈⠛⠀⣈⠋⢁⣤⣤⠈⢿⣆⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣦⣤⣭⣀⣀⣀⣙⣋⠁⣀⠈⠛⣀⠀⣀⣛⣋⣀⣠⣤⣤⣶⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉





⣿⣿⠿⢿⡿⢻⠿⣿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿