Butterfl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠊⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⣹⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⠀⢀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⢳⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣶⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣤⡀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠙⠻⣽⣁⢈⣹⡏⡉⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣌⣻⣿⣺⣿⣤⣽⣼⣿⣿⣿⣿⡿⠃
⠀⠀⠀⢠⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⠋
⠀⠀⢠⣿⣿⣿⣿⣧⢹⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⠿⣯⡁⠀⠈⢙⣿⣿⣿⣿
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣆⠈⠻⣿⡧⢌⡙⠶⣤⣰⣿⣿⣿⣿⣧
⠀⢸⣿⠋⢏⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠡⠟⠻⡄⠀⠀⠑⢶⣙⢶⣄⣿⣿⣿⣿⣿⣿⣆
⠀⢸⡏⠀⢀⡏⠀⠀⣻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⡇⠀⠀⠀⢠⠀⠀⠀⠀⠈⠑⠹⠿⣿⣿⣿⣿⡿⠏
⠀⢸⡇⠀⠸⡇⠀⠀⣻⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣈⣷⣤⣶⣶⣾⡀
⠀⠈⢿⣷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⠉⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁

⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⠠⠤⠤⠄
⠀⠀⣞⣝⢤⡀⠀⠀⡰⠒⠂⠶⡶⠨⣄⣀⠀⠀⠀⠀⣀⣀⠀⠀⡀⠄⢀⣥⠁⢶⠶⠐⠒⢆⠀⠀⢠⡤⣿⣳
⠀⠀⠘⠚⣷⣍⠛⣆⠈⠲⠤⣶⣇⣸⣧⣏⠀⠂⣵⣤⣿⢹⣤⣮⠀⠀⣹⣼⣆⣸⣶⠤⠖⠁⣰⠛⣭⣾⠛⠃
⠀⠀⠀⠀⠀⠛⢷⣤⡻⢄⡀⠀⠀⠙⠴⠷⠀⠠⠼⢿⡿⢿⣿⠧⠄⠀⠾⠤⠛⠀⠀⢀⡠⢞⣤⡾⠛
⠀⠀⠀⠀⠀⠀⠈⠉⢿⣦⣍⡢⣄⡠⠀⠀⠀⠀⠀⡼⡧⢽⢧⠀⠀⠀⠀⠀⢄⣠⢔⣫⣴⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣟⠉⠀⠀⠀⠀⠀⢠⠃⣏⣸⠘⡄⠀⠀⠀⠀⠀⠉⣻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⣺⣆⡀⠀⠀⢀⣀⡘⠀⢻⡟⠀⢃⣀⡀⠀⠀⢀⣰⣗⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠛⢿⣺⡇⡿⠿⣃⡄⠀⠀⢠⣘⠿⢿⢸⣗⡿⠛⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣬⠠⢨⡏⠙⠶⠁⠀⠀⠀⠀⠈⠶⠋⢸⡧⠄⣥⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆

⢾⣶⣀⡀⠀⠀⢀⣔⣾⡇⠀⣿⣓⣄⠀⠀⠀⠀⣠⡲⣷⠀⢀⡄⡄⢀⠀⠀⠀⠀⢀⢀⣀⡀⠐⣿⣷⠦⡀⠀⠠⢶⣿
⢸⣫⣯⣷⣤⣴⣶⣾⣝⠇⠀⢸⠉⠉⠳⡄⣠⠞⠙⠙⡏⠀⠘⠎⣵⣿⣿⣶⣷⣾⣿⣎⠹⠁⠀⠹⢿⣤⢵⣦⣠⣼⠟
⠀⢿⣿⡿⢻⠛⣿⣿⠗⠀⠀⢀⠔⠁⠀⢸⠇⠀⠀⢤⠀⠀⠀⠀⠃⠉⠀⣿⣿⠆⠉⠚⠀⠀⠀⠀⣏⠁⠈⠁⠀⣹⠇
⠀⠀⠙⠃⠀⠀⠸⠏⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢘⠛⠃⠀⠛⢋
⣠⣄⡀⠀⠀⠀⠀⢀⣤⣄⠀⢀⣀⡈⠀⠀⠀⠈⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀
⠟⠁⣀⠤⠀⠀⢤⣀⡈⠹⠀⠈⢻⡛⣷⡀⠀⠀⣠⡞⢉⡋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⠛⠉⢀⡄⠀⢠⣀⠉⠙
⢀⣿⣿⠄⢰⡄⠰⣿⡏⡀⠀⠀⠘⣿⡞⢿⣦⣴⡟⠡⡙⠂⠀⠀⠀⣠⣿⣷⣾⣧⡄⠀⠀⠀⢰⣿⣧⠀⣆⠀⣼⣿⠂
⠘⠘⠿⡾⠛⠻⣶⠟⠁⠁⠀⠀⠀⠅⠒⣬⠉⢉⣴⠂⡘⠀⠀⠀⠀⣧⡌⠀⠈⣥⡟⠀⠀⠀⠍⠻⣷⡾⠟⢶⣾⠟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⠁⠀⠀⠉⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⣟⡽⠖⠀⠀⠀⠀⠀⠚⠾⣝⠀⠈⠰⣆⠀⠀⠀⠀⣠⠊⠀⠀⣷⣶⣄⠀⠀⠀⢀⣴⣾⠆⢸⣁⣠⡀⠀⠀⠀⢀⡀⢉
⢫⣠⣶⣶⡶⣶⢶⣾⣶⢤⡼⠀⢰⣶⠿⣷⡀⣠⣾⠿⣶⠆⠀⠸⣧⢹⣧⣤⣼⡏⣽⠏⠀⠀⢿⡙⣿⣄⠀⣴⡿⢫⡟
⠀⣦⣿⣷⣿⠿⢿⣾⣾⣸⠀⠀⠀⣩⣿⣿⣿⣿⣿⣾⡍⠀⠀⠀⢾⡄⡼⠛⢧⢈⡧⠀⠀⠀⠈⣵⡾⠿⡿⠻⢦⡉
⠀⠙⠻⠟⠁⠈⠈⠻⠟⠋⠀⠀⠀⢿⡼⠏⠘⠁⠹⢵⠟⠀⠀⠀⠜⠗⠀⠀⠀⠛⠃⠀⠀⠀⠀⠙⠟⠀⠃⠘⠟⠁
⠠⢠⢀⠀⠀⠀⠀⡀⡀⠄⠀⠀⣤⣀⠀⠀⠀⠀⣀⣤⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠉⠓⣤⣤⠊⠉⠀⠀⠀⠀⢻⡛⠓⠀⡀⠘⠉⠹⠀⠀⢸⠀⠀⠀⢀⡀⠀⠀⠀⠇⠀⠘⣿⢱⠟⠀⣠⠀⠲⣎⣿
⠀⢀⠘⠀⢻⠛⠰⢂⠀⠀⠀⠀⢉⣳⠶⢶⡿⡷⢶⣈⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⢩⣾⠖⠋⣿⠐⢶⣧⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠟⠑⢣⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠧⣀⠀⠉⢀⣠⠝

⠀⢀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄
⠀⣿⡻⢍⠣⣉⢉⡻⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠾⣋⢋⡡⢋⠜⣻⠇
⠀⠘⣟⠢⣟⠽⣛⡛⢻⢦⣭⣳⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣫⡥⢾⠛⣛⡻⢝⡧⢚⡟
⠀⠀⠹⣅⢻⡏⡴⠒⠒⠒⠩⢿⣻⣻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⣾⡿⠯⠐⠒⠒⠲⡌⣾⢃⡽
⠀⠀⠀⠹⣌⢋⢧⠙⢯⡉⠉⠑⠂⠟⡿⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡿⡟⠧⠒⠉⠉⣩⠏⣠⢏⢋⡼⠁
⠀⠀⠀⠀⢱⡌⣦⡉⠂⠬⢕⣒⠄⣀⠈⠑⢗⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡟⠗⠋⢀⡁⢔⡒⠭⠄⠊⣡⡎⣼⠁
⠀⠀⠀⠀⠈⡧⢸⣝⠮⠤⠒⣄⠌⠁⡛⠷⣤⡘⠻⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣷⠛⣀⡴⠖⡃⠉⢄⡔⠢⠬⢚⣽⠠⡇
⠀⠀⠀⠀⠀⣿⢘⣿⠗⢒⢁⠀⠉⠁⠘⢤⣂⢉⠳⢿⣿⢼⣧⡀⠀⠀⠀⠀⣠⢿⣿⣾⠶⢋⣁⣢⠜⠀⠉⠁⢀⣑⠒⢿⡗⢸⡇
⠀⠀⠀⠀⠀⢸⣒⡇⣾⢉⢠⢡⠉⢙⠐⡤⠀⡀⠢⡄⢙⢷⣽⣧⢠⣿⣧⢰⡿⣵⢟⠁⡤⠂⡀⠠⡔⢘⠉⢡⢡⠈⢹⣆⣗⡾
⠀⠀⠀⠀⠀⠀⠙⢮⣺⣍⡉⠙⠈⠉⠉⠉⠒⠓⠵⢤⣀⠀⠙⣿⣯⣿⣯⣿⡟⠁⢀⣠⠦⠔⠓⠊⠉⠉⠉⠘⠋⣉⡽⣪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣤⣄⣩⣄⡠⣐⣀⢈⣙⣶⣼⣿⡇⣿⣿⣴⣞⡉⢀⣐⠠⣀⣮⣡⣤⣤⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡫⠙⢐⡏⢹⠹⡝⠋⢛⣿⣿⣵⣿⣿⣿⣧⣽⣿⣟⠉⠛⡝⢹⠉⣗⠐⠉⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠸⡇⢸⠠⣇⠂⠀⠸⠛⣿⠇⣿⡇⢿⡟⠳⠀⠀⢂⡧⢸⠀⡿⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣸⠃⠈⣧⠀⢧⠈⣇⡒⠀⡀⡸⠀⣿⡇⠸⡁⡀⠐⣂⡏⢠⠇⢠⡏⠀⢻⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠠⠁⠀⢚⣦⠈⠳⣄⠈⢦⣵⠃⠀⣿⡇⠀⢣⣤⠎⢀⡴⠋⢠⣞⠂⠈⠡⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⢄⠸⢐⢄⠘⢳⢄⡈⢙⡲⠃⠀⠀⢿⠇⠀⠀⠳⣚⠉⣀⢴⠛⢀⢔⠸⢀⠤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⡒⡓⠄⣈⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣉⡠⠔⡓⣒⣀⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣦⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢤⡞⠁⠈⠁

⠀⠀⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⠀⢠⣿⣯⣿⣿⣿⣿⣿⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣿⣿⣿⣿⣿⣽⣿⡄
⠀⠀⠈⢿⣷⣿⣿⠛⢿⣧⣼⣿⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡾⠟⣿⣧⣼⡿⠛⣿⣿⣾⡿⠁
⠀⠀⠀⠈⠻⣿⡿⣷⡟⠛⠻⠶⣿⠛⠓⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠚⠛⣿⠶⠟⠛⢻⣾⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠖⠂⠠⠼⢄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⡠⠧⠄⠐⠲⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⣀⣀⣀⠀⠽⠦⢄⡀⠈⠻⣦⡀⢠⡄⢀⣴⠟⠁⢀⡠⠴⠯⠀⣀⣀⣀⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣌⠳⣾⣷⠞⣡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣽⣿⣿⣯⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⡶⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢉⣉⣉⣉⡝⠒⠚⠉⣉⢽⣿⣿⡯⣉⠉⠓⠒⢫⣉⣉⣉⡉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⣁⠤⡴⠋⠀⢀⡠⠊⢡⢾⣿⣿⡷⡌⠑⢄⡀⠀⠙⢦⠤⣈⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠊⢉⡠⠼⡤⠤⢲⠋⠀⡰⢃⠎⣿⣿⠱⡈⢆⠀⠙⡖⠤⢤⠧⢄⡉⠑⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣖⠉⢀⡜⠀⢠⠃⢀⠞⠀⡎⠀⣿⣿⠀⢱⡀⠳⡀⠘⡄⠀⠣⡀⠉⣲⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣎⢀⣠⠃⢀⠎⠀⣼⠀⠀⢸⡇⠀⠀⢧⠀⠱⡄⠘⣄⡀⣱⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣷⣿⣀⡼⠁⠀⠀⠈⠁⠀⠀⠈⢧⣀⣿⣾⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁

⣶⣿⣿⣿⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⣺⣿⣿⣿⠷
⢻⡼⣿⣿⣿⠳⠀⣿⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⣿⣷⠀⢸⣿⣿⣿⣼
⠀⢳⡼⣿⣿⣷⡜⢿⣿⠀⠉⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⢿⡟⣚⣿⣿⡿⣾⠃
⠀⠀⠳⣼⣿⣷⣦⣜⠛⠂⢸⣿⣿⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⢿⣿⣦⠔⠈⢉⣹⣿⡿⢶⡏
⠀⠀⠀⢻⡽⣿⣧⣈⣒⠀⠀⢻⡏⠀⣼⣿⣿⣷⣄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⡾⣿⣿⡇⠀⢘⣿⠅⠁⠶⣿⣿⣿⢗⡿
⠀⠀⠀⠀⢧⡿⣿⣿⡉⠀⠀⠨⠿⠄⣿⣿⠅⠈⢻⣷⣄⠀⡀⠙⠄⠀⠀⠀⠀⢀⠜⢀⠀⣠⣾⡋⠀⠘⢿⣷⠀⠛⠀⠀⠐⣲⣾⣿⡟⣾⠃
⠀⠀⠀⠀⠘⣇⣿⣿⣿⡎⠛⢂⢀⡀⣹⣿⢀⠀⣼⣿⡿⢷⣌⠁⡌⠒⣤⣤⠔⢁⠔⣪⣾⣿⣿⣗⠀⠀⠸⡿⠀⠄⠀⠀⢉⣿⣿⣿⢷⡇
⠀⠀⠀⠀⠀⠸⣇⢹⣿⣿⡾⠶⠒⠀⡹⠁⠀⠀⣿⣿⡃⣈⢿⣷⣜⢜⢟⣿⢿⣮⣾⡟⠁⠘⣿⣿⠀⠁⠴⠀⠀⠀⡀⢾⣿⣿⡿⣳⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣙⢿⣷⣶⣦⡤⠀⠀⢀⢀⣿⡏⠀⠐⢿⣿⣿⣾⣿⣿⣟⣿⣿⢃⢀⣀⣸⣿⣇⡀⠀⠀⠐⢶⣶⣾⣿⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠧⠶⠦⢭⠄⠛⠋⠐⣶⡀⡈⠨⣿⣿⣿⣿⣿⣿⡆⠈⢻⣿⠀⠈⠉⣿⣅⡲⠶⠾⠿⠿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⡶⢀⢠⠂⠘⣇⠀⠀⠉⡘⣿⣿⡿⡟⠆⠀⢸⡏⠀⢘⢦⣽⣟⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⣿⡟⠁⠀⠘⠀⠀⠹⡄⠈⢠⢱⢿⣿⠇⣧⠐⠀⢸⠃⠀⠀⣦⣨⣿⣿⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣾⣿⣿⡗⡐⠻⣆⠀⠀⡗⠀⠘⠸⢸⣿⡖⠟⡆⠀⡞⠀⠀⣸⠇⢼⣿⢡⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠙⣿⣿⣧⣤⠀⡠⠀⠀⣿⠀⡆⣿⠸⣿⠂⡗⡄⢠⡇⠀⠾⠉⣤⣠⣿⣾⡟⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣿⣿⣿⡏⢠⣤⠀⠀⣿⠀⠇⠀⠀⠀⢠⡗⡇⣸⠁⠀⣆⠀⠈⣿⢣⣾⣷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢹⣿⣿⣿⡟⢀⠀⣹⡀⢚⡒⠀⠀⠘⣃⠁⣿⣇⡀⠉⣿⣿⣿⡞⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⣟⢻⣿⡿⣿⠟⢿⣛⡃⠀⠀⢈⣟⣴⣿⣿⡿⣾⣯⠶⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⣻⣏⣬⣿⣤⣿⡏⠁⠀⠀⠀⢨⣋⣘⣿⣀⣸⣧⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⡟⢉⣻⣫⣼⠃⠀⠀⠀⠀⠘⣿⣝⣟⠛⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⢷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧

⢰⣶⡿⠛⠛⠙⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠒⠚⠛⠛⠻⣷⣶
⣿⡋⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠒⠂⠀⠀⠀⠀⠈⣻
⢹⡄⠠⠀⠒⠂⠀⠁⠁⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠠⠀⣸
⠀⠙⠶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⣦⡀⠠⣶⡦⠀⣠⡾⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠞⠁
⠀⠀⠀⠈⢆⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠐⢠⣤⣬⣿⣾⣿⣿⣾⣯⣤⣤⠐⠀⠀⠀⠀⠀⠂⠄⣀⡀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠿⡉⠉⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠙⢹⣿⣿⠙⠃⠉⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠉⡹⠇
⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⣀⣴⠞⠋⡀⠀⠐⠐⠀⠀⢠⡏⣿⡏⣧⠀⠀⠐⠐⠂⠀⡈⠛⢶⣄⣀⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟⣁⠄⠀⠀⠀⠀⠀⠀⢠⣾⠀⣿⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⢄⡙⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠠⠃⠀⠈⠀⠀⠀⣿⠀⢻⠃⢸⡏⠀⠀⠀⠀⠀⠣⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡠⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡼⠀⠀⠀⠀⠀⠠⠀⠑⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡴⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠐⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠆⠀⠄⠀⡀⠀⢰⠀⡴⠀⢸⡆⢠⠀⠀⡄⠀⠄⠀⠆⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢰⠀⠀⡇⠀⢸⡾⠃⠀⠀⠻⣾⠀⠀⡇⠀⠰⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣤⣧⣴⣿⠁⠀⠀⠀⠀⢹⣷⣤⣧⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢿⠀⠀⢰⣶⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⢇⡀⠀⠀⠀⠈⣷⡶⣄⠀⠀⠀⠀⠀⢠⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠘⡷⣍⠀⢀⠇⠀⢳⡀⠀⠁⠀⠸⡆⠀⢠⣄⢀⡘⠲⠒⢄⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⢰⠃⠀⡄⠁⠀⠀⠀⠉⠉⠀⠰⠞⠁⠀⣿⣹⠟⠻⣄⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⣀⠀⠖⠲⢤⠀⠀⠀⢣⡇⢀⡴⠚⢳⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⣼⠁⠀⣄⠀⠀⠙⠢⡄⠀⠓⠍⠀⠀⡸⠃⢠⠏⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⢠⡄⠀⢠⠇⠀⡎⠀⠀⠘⠂⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠃⠀⠀⡡⠘⠇⠀⠀⠀⠀⠀⠀⠀⣿⠙⣵⡄⠀⠀⠸⡏⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡴⠀⠐⠖⠃⠀⠀⡞⠠⠞⠁⠀⠀⢸⡇⡀⣹⣿⣦⡄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠀⠀⠂⠰⠀⠀⢀⠉⢀⡱⠀⣉⣘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣟⠀⠀⠀⠀⣀⠀⠀⠀⠚⢇⠈⠙⠛⠉⠉⠉⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡽⣟⣷⠀⠈⠁⠀⠀⠚⠉⠀⠀⢀⠀⠈⠣⣄⠀⠀⠀⠀⢀⡞⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⡃⠸⣷⡀⠀⠀⠀⠠⣖⡀⠀⠈⠓⠀⠀⠟⠂⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⣀⢸⣷⠀⠀⠀⠀⠀⠈⠑⢤⣀⡄⠀⠀⠀⣉⣹⡃⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣠⡤⣶⣶⠶⣶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠂⢶⣶⠖⣦⣄
⠀⠸⣿⢅⣾⢛⠂⠀⠀⢀⣰⡶⠩⠗⡢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠏⠰⣶⡀⠀⠠⠀⠈⢹⡗⣸⡿
⠀⠀⠻⣷⣴⡠⢠⡄⠀⠈⠉⠠⣀⣠⣦⢿⡟⣦⡀⠀⠀⠀⠀⣤⡾⣿⠷⣶⣄⣤⠊⢁⠀⡀⣐⡂⣽⣶⡿⠁
⠀⠀⠀⠈⠺⣿⢿⢀⡯⠄⣀⠚⣿⣄⠓⠒⠤⣌⣛⣦⡒⣢⣾⣻⡮⠒⣈⣁⣿⡟⠁⣀⠨⠅⣰⠿⠝⠋
⠀⠀⠀⠀⠀⠈⠫⡿⣆⣩⠖⢘⠻⠯⢉⣉⠘⠺⠝⠹⣷⠿⠉⠡⠒⠀⠀⠊⠹⠏⡐⢦⣠⡟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⡠⢀⡁⠄⠀⠀⠀⠊⠸⢙⠁⠈⠢⠀⠀⠈⠀⢈⠐⣹⡿⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣥⠤⢌⢀⡀⠄⠀⠀⡈⠀⠰⠀⠀⠀⠄⠱⠀⢀⢠⠆⠴⣸⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣏⠅⡴⠁⡘⠀⡄⡘⡐⠀⠀⠈⠀⠀⠀⠘⡀⠀⠈⡄⠑⢄⢌⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣯⡰⣡⢱⢠⢡⠃⠁⠀⠀⠀⠀⠀⠀⠀⢱⢰⢸⠸⣘⣬⢯⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢽⢟⡞⡾⠿⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠟⡟⣿⠻⠜⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢴⡤⠄⠀⠀⠀⠀⠤⣴⠆⠀⠀⠀⠀⣤⣆⡀
⠙⢄⡀⠘⠷⢦⣤⡤⠾⠋⠀⡠⠞⠈⠂⠀⠀⢰⡆⠀⠀⠐⠁⠀⠈⢳⡀⢳⣄⣴⠇⣰⠏⠀⠀⠀⠀⠀⣻⣿⠃
⠀⠀⠉⠒⣴⣾⣿⣾⣶⠔⠋⠀⠀⠀⠀⢆⠀⠸⠇⠀⡰⠀⠀⠀⠀⠀⣿⣄⢹⢃⣼⡇⠀⠀⠀⠀⠠⣤⡽⣸⡆
⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠉⢀⣀⠀⠀⠀⣀⠊⠁⠀⠀⠉⢂⡀⠀⠀⠀⠀⠀⠈⠉⠑
⠀⠀⢤⣄⠀⠀⢀⠀⠀⢠⣤⠀⠀⠀⢻⣿⣤⠀⢀⣴⣿⡏⠀⠀⠀⠹⣿⣷⣄⣠⣾⡿⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠉⣆⠶⠻⠶⢔⡏⠀⠀⠀⠀⠈⠛⠛⣳⣟⠛⠛⠀⠀⠀⠀⠀⢸⣿⢹⢹⣿⠁⠀⠀⠀⠀⠐⠀⠀⣥⡀
⠀⠀⠀⠀⢹⠋⠀⠉⢏⠁⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⣀⡼⠟⠋
⠀⠀⠠⣄⠀⠀⠀⠀⠀⣠⠄⠀⠀⢶⣶⣤⡀⠀⠀⢀⣤⣶⡶⢠⡤⣤⣀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠠
⠀⠀⠀⠘⣧⠀⣠⠀⢰⡏⠀⠀⠀⠀⠙⣮⠻⢶⡶⠟⣵⠋⠀⠀⠻⡊⠻⣧⢀⢠⡾⠋⣺⠋⠀⠀⠠⠀⠐
⠀⠀⠀⠀⢧⡀⠙⢁⣠⠇⠀⠀⠀⠀⠀⢻⣧⠘⠁⣼⡟⠀⠀⠀⠀⢹⣶⣜⠾⠟⡵⣶⠁⠀⠀⠀⠀⢶⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠛⠋⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠻⣿⣷⣄⠀⣠⣶⣿⡿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣠⣀⣄⣤⡀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠙⡿⣻⣷⣿⢻⠟⠀⠀⠀⠀⠠⠀⠀⠸⠇⠀⢀⠄⠀⠀⠀⠀⣉⠉⠹⠉⢉⡁⠀⠀⠀⠀⠻⢦⣠⣖⢆
⠀⠀⠀⠀⠙⠂⠀⠀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠐⠊⠀⠀⠀⠀⠀⠘⠛⠀⠈⠛⠀⠀⠀⠀⠀⠈⠛⠛⠛⠈

⠀⠀⠰⣶⠂⠀⠀⠀⠀⠀⠀⠀⢲⡶⠀⠀⢠⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⢶⢠⡦⠀⠀⠀⠀⠀⠀⢰⣄⡶⠀⢶⡖⠂⢄⠀⠀⠀⢀⠄⠒⣶⠆
⠀⠀⠀⠈⢧⡀⠀⠀⡄⠀⠀⣠⠏⠀⠀⠀⣾⢠⠞⡄⡀⣜⢢⠘⡇⠀⠀⠀⠘⡇⠀⠀⢀⡀⠀⠀⢰⡏⠀⠀⠈⡦⠀⠀⠱⣤⡄⠀⠀⢠⡏
⠀⠀⠀⠀⢠⡍⠁⠀⡇⠀⠉⣥⠀⠀⠀⠀⢛⣸⠐⣇⣿⡾⢸⣅⡃⠀⠀⠀⠀⢀⠀⠀⠸⡇⠀⠀⡀⠁⠀⠀⠀⠹⣤⢄⣠⢿⢦⡀⢤⠞⠁
⠀⠀⠀⠀⠘⣧⣄⣠⣡⣀⣤⠟⠀⠀⠀⠀⠘⣿⣆⠈⡏⠀⣼⡿⠁⠀⠀⠀⠀⠻⣧⣀⡀⢁⣀⣴⡿⠀⠀⠀⠀⠀⣇⠸⢣⠘⢘⠿⣸⠇
⠀⠀⠀⠀⢀⡼⠉⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢨⠛⠁⠈⠛⢧⠀⠀⠀⠀⠀⠀⠈⠳⠋⠀⠘⢶⠉
⠀⠀⣀⣀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠸⡇⠀⠀⠀⠀⡀⠀⠀⠀⢨⡟⠀⠘⣦⢨⣸⢦⣄⣠⡴⣇⡄⣴⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⣧⣤⠀⢀⠀⣠⣴⡏
⠀⠀⠀⠹⣄⡀⠀⠸⡇⠀⠀⣠⡾⠀⠀⠀⢸⣆⡀⢠⣸⣇⡄⢀⣰⡇⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡙⠉⠀⢹⠀⠉⠙⡀
⠀⠀⠀⠀⢻⣤⡀⠀⠃⠀⣠⣿⠀⠀⠀⠀⠀⠧⡳⢤⠈⠁⡤⢞⡼⠀⠀⠀⠀⠉⣇⠀⠀⠙⠀⠀⢰⠏⠀⠀⠀⠈⣦⠀⠀⠈⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠙⠛⠃⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠐⠚⠃⠀⠀⠀⠀⠀⠈⠛⠒⠀⠘⠻⠋
⠀⠀⠰⡆⢀⠄⡀⠀⠀⠀⡀⡄⢀⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠹⣄⠈⠁⢀⡄⠀⠉⢠⡞⠀⠀⠀⣀⠀⠀⠀⢿⣿⠀⠀⠀⢀⠀⠀⠀⠈⢰⡇⠋⢠⡄⠑⢸⡆⠁⠀⠀⠀⠀⢀⡐⣿⡇⡀
⠀⠀⠀⠀⢨⡃⠀⠸⡇⠀⠀⣋⠀⠀⠀⠈⠓⠂⠀⠀⠸⠇⠀⠀⠀⠚⠁⠀⠀⠀⢠⠁⠀⢸⡇⢀⢘⡄⠀⠀⠀⠀⢠⣌⣛⣛⣚⣫⣤
⠀⠀⠀⠀⠈⠳⢴⠄⠁⠦⠶⠃⠀⣤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⢳⡄⠀⠀⢀⡄⠀⠀⠀⠀⣼⡷⢯⣽⣿⣯⣭⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠘⠛⠛⠛⠛⠈⠋⠁
⠀⠀⣴⡶⢂⣄⠀⠀⠀⠀⣀⡀⠶⣦⠀⠀⣴⣤⣀⡀⠀⠀⠀⢀⡀⣤⣄⠀⠀⣶⣦⣄⠀⠀⠀⢀⣴⣶⡄⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⢹⠁⢸⡏⠀⢀⡀⠀⠈⣿⠀⡿⠀⠀⢹⡁⠋⡸⠷⣤⠺⡏⠛⢸⡏⠀⠀⣿⠀⠀⠠⡀⡐⠁⠀⣿⠁⠀⠀⢻⡎⠀⠀⣠⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠘⢷⡀⢸⡇⠀⣰⠇⠠⠀⠀⠀⠈⠧⠠⡿⠁⠗⠘⣿⠠⠞⠀⠀⠀⠹⣄⡀⠀⣿⠀⢀⣀⡝⠀⠀⠀⠈⢳⡄⠀⢻⠀⢠⡼⠃
⠀⠀⠀⠀⢰⣌⠛⠋⠙⠛⣁⣴⠀⠀⠀⠀⠀⠸⣆⣀⠀⠀⠀⣀⣴⠃⠀⠀⠀⠰⡇⢀⡄⠙⠠⡀⢀⡇⠀⠀⠀⠀⠸⣇⢠⡞⣄⢀⡿
⠀⠀⠀⠀⠈⠙⠻⠁⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠉⠛⠀⠙⠋

⠀⠀⠀⠀⣴⣄⡀⠀⠀⢀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢹⡟⢷⣄⣠⡾⣿⡇⠀⠀⠀⢻⡟⠒⢄⢀⣠⠖⠚⣿⠀⠀⠈⣷⡞⣤⡀⠀⢀⡔⣳⣹⠀⠀⠸⣿⣷⣦⠀⠀⣠⣶⣿⡟
⠀⠀⠀⠀⢠⡟⢈⢿⣟⡁⢯⡀⠀⠀⠀⠈⣡⣖⣾⣿⣷⣖⣮⡉⠀⠀⠀⠙⣻⣟⡾⣿⢷⣿⣛⠉⠀⠀⠀⢛⣿⡻⣷⣾⡟⣿⣟⠁
⠀⠀⠀⠀⢸⣧⡏⠈⠀⢩⣼⡇⠀⠀⠀⠀⢿⣭⠞⠁⠹⢯⣽⠇⠀⠀⠀⠘⣿⣿⠇⠋⠺⣿⣿⠁⠀⠀⠀⠸⣿⣷⠎⠈⢶⣿⡟
⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⢰⣦⣤⡀⠀⠀⢀⡤⣴⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⣄⠀⠀⠀⣤⠲⣶
⠀⠀⠀⠀⢿⣿⣾⣶⣴⣷⣿⠿⠀⠀⠀⠈⠀⠀⠀⣴⠄⠠⠀⠀⠀⠀⠀⠿⢀⡀⣱⣶⣆⢀⠠⠟⠀⠀⢠⠂⠉⠛⢲⣶⠾⠛⠀⢄
⠀⠀⠀⠀⢼⣿⣷⠻⠟⣾⣿⡇⠀⠀⠀⠀⢰⠂⠀⢿⠁⠀⢢⠀⠀⠀⠀⢰⣏⢡⣿⢿⣿⡌⣻⠆⠀⠀⠈⠙⣶⠿⢿⣿⠷⢶⠞⠃
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠘⠻⠟⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉


⠀⠀⠀⢰⡶⠲⣤⣀⣀⣤⠲⢶⠀⠀⠠⣖⠖⠒⢦⣤⣤⠖⠲⢲⡤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⣴⣦⣀⣀⣠⣶⡄⠆
⠀⠀⠀⠀⢻⣄⡈⣿⣿⣁⣠⠏⠀⠀⠀⠈⠑⣦⣀⡿⣄⣠⠖⠉⠀⠀⠀⠀⠀⠀⡈⠛⢁⠀⠀⠀⠀⠀⠀⠘⣿⡻⣿⣿⡽⣿⡇
⠀⠀⠀⠀⠈⠓⠏⠈⠀⠫⠚⠀⠀⠀⠀⠀⠀⠸⠋⠀⠙⠫⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠻⠇⠀⠀⠀⠀⠀⠀⠹⠿⠾⠻⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠾⢑⠌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣛⠛⠢⣁⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢘⠂⡱⠠⠈⠇⠀⢄⢧⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠻⢄⡉⠐⠁⠀⠀⠐⡋⢸⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢯⣯⠳⡔⡀⠀⠀⠀⠀⠂⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢾⠀⠒⠚⠁⠀⠀⠀⠀⢀⠀⠀⠙⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠙⣦⡀⠀⣯⣷⠰⠍⡆⠀⠀⠀⢀⣠⣴⣿⡿⠟⠛⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⣶⢿⢿⢳⡄⠹⣼⣄⠉⣀⡠⠔⠊⣽⠟⠉⠀⠀⠀⠀⣠⣾⠇⡉⠿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⠟⣁⣺⣦⣧⢻⣷⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡽⢻⡤⠔⣻⣆
⠀⠀⠀⠀⠀⢠⣿⣳⠸⣿⠻⢧⠸⣄⣧⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢶⣷⣋⢷⡂⡹⢟⣆
⠀⠀⠀⠀⠀⠸⣷⡏⢐⣾⣯⡘⠣⣿⣿⡾⡄⠹⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣠⡭⢝⢿⡥⠚⣧⠐⢩⢻⡆
⠀⠀⠀⠀⠀⠀⠙⠧⣿⣿⠛⠀⠈⢹⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠘⣉⣽⣺⣼⢞⣁⠼⢟⡁⠈⣇⡀
⠀⠀⣴⣾⢿⣟⠻⣿⠺⣿⣦⣠⢄⡀⠨⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢱⣿⣯⡤⠴⠞⣠⠈⠀⠙⢦⡀
⠀⣸⣲⠋⣬⣍⣠⡛⠋⢙⡻⢽⣿⣽⣮⣻⣧⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠁⠋⣻⣤⠖⠉⠚⣫⣤⠤⠾⢧⡀
⠀⠸⣞⣧⡰⢃⣬⣉⢓⣶⣾⡿⠿⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣀⡀⠀⠹⣾⡻⣍⠀⠀⣷⡂⠀⠚⠃⣤⣀⣀
⠀⠀⠉⠒⠷⠾⠗⠛⠉⠁⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡖⠶⠮⢷⣞⣤⠤⢼⣧⣀⢏⣻⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠉⠛⠺⠤⠻⠬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢿⣿⣿⣿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠈⠙⢆
⠀⠀⠀⠀⠐⣯⣿⡇⡄⣤⡾⢿⣿⣿⣷⣄⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⢻⣻⣿⣫⣿⣧⣿⡟⣹⣿⣿⣧⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣄
⠀⠀⠀⠀⠀⠸⣯⣿⣧⠦⢾⣿⣶⡿⣿⣟⠻⣿⣄⠀⠀⠀⠀⠀⠠⠐⠂⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣠⣽⠿⢷⣾⡿⠿⢤⣤⣉⣓⢾⣿⣆⣴⣶⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⣾⣽⣷⢾⡟⠁⠀⠀⣈⣭⣽⣿⣿⣿⣿⣿⣿⣶⣾⣿⡛⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢻⡗⣻⣿⣿⣷⣀⠀⠀⣀⣤⣶⣿⡟⣿⣟⣿⢿⣿⣿⣶⣍⡙⠛⣿⣿⣸⣿⣋⣿⠇⡀⢹⣿⣿⢿⣿
⠀⠀⠀⢴⣾⡃⠘⣿⣯⣼⠟⣻⣿⣿⡟⣿⠋⣸⡟⣾⡟⢸⣿⡝⢪⡙⠟⠳⣿⣿⡿⡏⡛⢉⣷⣵⣿⢿⡿⠟⠋
⠀⠀⠀⣴⣿⣇⠀⢹⣿⣇⣼⡿⠟⠈⣸⠇⢀⣿⢽⠏⠀⡿⣿⣷⠀⠀⠀⠀⠸⡿⣦⣼⣾⡿⣿⡽⠞⠉
⠀⠀⠀⠻⣾⣥⡔⣡⣿⣿⣿⠟⠓⣴⡟⠀⢸⣿⠋⠀⣼⠇⢹⣿⣷⣀⠀⢀⣰⣿⣈⣿⡉⠙⠉
⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⢿⠀⠀⢺⠁⠀⠘⠁⠀⣴⣏⡀⢸⣿⡇⣿⡛⣿⣻⣾⣿⣽⠇
⠀⠀⠀⢰⡿⠟⠛⠿⠛⢿⠿⢦⣠⡟⠀⠀⠀⢀⡼⠋⠀⢹⣧⣿⣤⣿⣷⡿⠟⢋⣷⠏
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⡴⣿⣿⣿⡟⡏⠉⢀⣤⣿⡅
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣯⣿⣿⣧⣧⣼⣿⣿⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⡿⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢻⡛⠦⣀⣀⡴⠛⡿⠀⠀⡤⢀⠄⠀⠀⠀⠠⣄⢠⡄⠀⢸⣷⣄⠀⠀⢀⣴⣿⠀⠀⠀⣶⣶⣦⡀⠀⢀⣴⣶⣶⠀⠀⢻⣶⣄⠀⠀⠀⠀⡠⣶⡟
⠀⠀⠀⠈⠃⠀⠸⢇⠀⢐⠃⠀⠀⠱⠁⠀⠀⣴⡀⠀⠀⠛⠁⠀⠀⣿⢻⣧⣠⣿⣳⡇⠀⠀⠀⢾⣟⣹⣿⣴⣿⣏⣻⡗⠀⠀⠈⣷⣿⣷⣄⣠⣾⣿⣾⠁
⠀⠀⠀⠀⢹⣤⠂⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⢿⣯⣏⠀⠀⠀⠀⠠⣿⣬⡿⠿⣿⣭⣿⠀⠀⠀⠀⠈⣽⣿⠟⠻⣿⣯⠁
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠹⡟⠀⠀⠀⠀⠀⠙⠛⠇⠀⠸⠛⠋⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⢠⣴⡆⠀⣤⠤⢄⠀⠀⠀⠀⢀⠤⢤⡄⠀⣶⣤⡀⠀⠀⠀⢀⣴⣶⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⣿⣿⢗⣤⣴⣦⣤⡲⢿⣿⠀⠀⢫⣴⣾⣤⣾⣶⣌⠇⠀⠀⣀⠀⠹⣄⣀⡶⠁⠀⡀⠀⠀⠘⣿⢿⣆⣀⣰⡿⣿⠇⠀⠀⢸⡿⢷⢀⠀⠀⣀⡾⢿⡇
⠀⠀⠈⢷⣸⣿⣿⣿⣿⣟⡼⠃⠀⠀⠈⢉⣿⢿⢿⡏⠉⠀⠀⠀⢀⠐⠀⢈⣏⠀⠐⢀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⢉⢊⣉⣿⣿⣃⡙⠈
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠃⠀⠈⠃⠀⠀⠀⠀⠀⢦⠀⡞⠹⡄⢠⠆⠀⠀⠀⠀⣿⣿⠉⠀⠉⣿⣿⠀⠀⠀⠀⢸⡸⠿⠁⠀⠿⠇⡆
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠉⠉⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉
⠀⠘⣇⠉⠀⠄⠀⠀⢀⠔⠉⢠⠇⣶⣦⣄⠀⠀⠀⢠⣴⣶⠄⠸⡟⡷⢀⠀⠀⢀⢸⡟⡿⠀⠰⡾⠂⠀⠀⠀⢀⠠⠐⣿⠄⠀⣤⠄⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠈⢦⣴⣾⣦⣰⣿⣶⡴⠋⠀⢸⡟⢹⣷⡤⣼⣿⠙⣿⠀⠀⠃⠀⡜⢱⣶⠙⡄⠀⠁⠀⠀⠅⠀⠒⠃⣴⠘⠓⠀⠨⠀⠀⠁⢠⠀⠀⢰⡆⠀⠀⡄⠘
⠀⠀⠀⢀⣼⣿⡿⢿⣿⣧⡄⠀⠀⠀⢴⠈⠿⠻⠻⠇⢰⠀⠀⠀⠠⡀⠀⠈⠏⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠈⡿⠞⠁⠀⠁⢺⠅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⢰⣤⡀⠀⠀⠀⠀⣠⣶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⢤⢤⣄⠀⠀⠀⠀⣠⡤⣤
⠀⠀⠘⣿⣋⣴⣄⢠⣴⣝⣿⡇⠀⠘⣿⢚⣦⣀⣠⡟⣽⡇⠀⠀⡇⣧⠀⠀⠀⠀⢠⡇⡇⠈⢻⡿⣷⣄⠀⠀⠀⣠⣾⢿⡟⠀⠘⡍⠈⢳⡄⢠⣾⠁⢉⠇
⠀⠀⠀⢻⡟⠛⠻⡿⠛⠻⣿⠀⠀⠀⣡⣾⣿⢿⣿⣿⣬⠀⠀⠀⠁⠸⡿⢷⣷⡿⡿⠀⠁⠀⠀⠻⠌⣻⣷⢶⣾⣟⠡⠟⠀⠀⠀⠘⣡⣿⣿⣿⣷⣌⠃
⠀⠀⠀⠘⠷⣤⠂⠐⣤⡾⠃⠀⠀⠀⢹⢉⡛⠀⠘⣃⣻⠀⠀⠀⠐⣄⠃⠁⠂⠀⢃⡔⠀⠀⠀⠀⢾⣅⡉⠚⢉⣩⡷⠀⠀⠀⠀⠈⠢⠝⠀⠀⠫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⡔⣻⣍⠻⢒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡒⠟⣩⣟⢢
⠀⠀⠀⡇⠈⠁⢰⡦⠑⢄⠉⢒⢄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⡠⡲⠉⡠⠊⢴⡆⠈⠁⢸
⠀⠀⠀⠘⡄⢠⣤⠀⡠⠂⠑⢄⠀⣑⢄⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⣊⠀⡠⠊⠐⢄⠀⣤⡄⢠⠃
⠀⠀⠀⠀⠀⠈⢉⡀⠀⣤⡆⠤⠑⢍⠊⠢⡀⠈⠂⠀⠀⠀⠀⠰⠁⠀⠔⠁⡩⠊⠤⢠⣦⠀⠀⡉⠁⠈
⠀⠀⠀⠀⠘⢄⠛⠛⠀⣨⡀⠀⠀⢌⡑⢔⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⡣⢊⡡⠀⠀⢀⣅⠀⠛⠟⡠⠃
⠀⠀⠀⠀⠀⠀⢡⣤⠈⠛⠡⢀⣠⠀⠉⠐⠑⡪⣣⣠⣿⣿⣄⣜⠕⠪⠂⠉⠀⣀⡀⠈⠛⠁⣤⡌
⠀⠀⠀⠀⠀⠀⠈⢯⣀⠀⠀⢛⣋⡰⠢⠐⢺⣿⣺⢿⣿⣿⡿⣗⣿⡗⠒⠄⢆⣙⡛⠀⠀⣀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠛⢉⣠⣤⡌⠰⠶⢾⣿⣿⣿⣿⣿⣿⡷⠶⠗⢡⣤⣄⡉⠛⠯⡁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⡞⣁⡴⠎⢀⣠⣿⣿⣿⠋⣿⣿⠙⣿⣿⣿⣄⡀⠱⢤⣈⢳⣄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⠋⠁⢀⠘⠛⠉⠉⠾⠃⡼⣿⣿⢧⠘⠳⠉⠉⠛⠃⡀⠀⠙⠋⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣿⢀⡆⢠⣉⠀⠰⠁⣿⣿⠈⠆⠀⢍⡄⢰⡀⣿⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⣾⠃⠸⠡⢀⠃⠀⢿⣿⠀⠘⡀⠌⠇⠘⢷⠉⠀⢀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣕⠄⠀⠀⠀⢀⡡⡏⠀⠀⠘⠃⠀⠀⢹⢄⡀⠀⠀⠀⠠⢪⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠑⠤⠒⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠒⠤⠊⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣽⣛⣿⣿⢿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⡿⣿⣻⡯⢹⠀⢸⢸⣟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣦⣄⠀⠀⠀⣾⡟⠛⢻⡟⠉⠙⣿⠟⢿⡀⣸⣀⡇⡸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡹⢿⡛⠛⢿⠿⢿⣷⣦⡀⣿⡇⠀⠀⡇⠀⠀⡟⠀⢸⣿⡏⣙⣻⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠹⡄⠈⡇⠀⣏⠻⣿⣿⡇⠀⠀⡇⠀⠀⠃⢀⣏⣼⢻⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⡇⠀⠉⠢⣄⢠⣄⣙⡀⢰⠀⣿⣿⠀⠀⠀⠇⢀⣴⠟⠛⠉⣽⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠓⢶⣤⣈⠻⡇⠉⠳⣼⣰⣿⡿⠀⠀⠀⣠⠞⠁⠀⢀⣼⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠲⢤⣀⠉⠛⠷⣧⠀⠀⠈⣿⣿⡇⠀⠀⣠⠋⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣀⡈⠙⠷⣄⠈⠳⣄⠀⢸⣿⡇⠀⠀⠁⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠌⠙⠢⣈⠳⣸⣿⡇⠀⢀⣤⠶⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⣤⣤⡾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⣿⠿⣿⣿⡿⠿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⢀⣠⠖⠉⣠⠎⢸⣿⡇⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⣀⡴⠞⠋⢁⣠⠞⠁⠀⡼⣿⡇⠀⠠⡀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠉⠁⣠⣴⡾⢋⠇⠀⢀⣰⣇⣿⡇⠀⠀⠙⣄⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢿⠖⠛⠉⢁⡤⢾⣀⢴⠋⡇⢸⣿⡇⠀⠀⢀⠙⣦⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣄⣤⠖⠁⢀⠎⢀⡆⠀⡇⢀⣿⣷⠀⠀⢨⠀⠈⠳⢦⣤⣈⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣇⡀⣠⠋⠀⡼⠀⣸⣧⣿⢿⣿⠀⠀⢸⠀⠀⢰⠀⠹⣉⣧⣾⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣶⣾⣿⣿⡿⠋⠁⢸⣿⠀⠀⣸⠀⠀⢸⡆⠀⣿⣿⣌⣯⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠘⣿⣶⣴⣿⣤⣤⣼⢷⣼⣏⢈⡏⢹⠈⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣿⣿⣯⣿⣨⡇⢀⡄⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣯⣿⣿⣷⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣏⣏⠉⢉⣷⢶⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣉⡁⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⣠⣼⠇⡌⠉⠉⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢊⣿⣍⣥⣄⣒⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣏⠉⠉⠉⠉⠻⡍⠛⠻⣶⣔⠂⠀⠀⠀⠀⠀⠀⠀⢀⡵⠛⠋⣻⠟⠋⠙⠒⢿⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣓⣗⠀⠀⠀⠀⠻⢦⠀⠈⠙⣷⡄⠀⠀⠀⢀⠀⡴⠋⠀⢀⡴⠓⠂⠀⠉⠁⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠆⠒⠂⠀⠉⠙⠓⢠⣀⠀⠛⣦⣵⣶⣥⠎⠀⢀⠔⠋⠈⠁⠀⠀⠀⢸⣷⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⣶⣶⡶⢾⡿⣿⠿⠿⢿⡟⠶⣾⣿⣿⣇⡴⣾⠶⠒⠲⣾⣶⣾⣶⣶⣯⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⠄⠛⠉⠉⠀⡦⠀⠈⠟⡝⣿⣿⢹⡓⡇⠶⣆⠁⠀⠉⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⠠⠀⢀⡘⠉⢠⠊⠀⠌⠀⢻⡇⠘⡕⡌⢆⠀⠹⢌⡀⠀⠈⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⠀⠈⠴⠁⢲⠁⠀⡘⠀⠂⣸⣧⠀⠱⠈⡄⠑⠖⢤⠀⡀⠀⠀⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⡄⠀⠀⠀⠄⠀⡘⠀⡀⠔⢻⡇⠀⠀⢣⠈⣄⠈⢆⠱⡌⢐⣾⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢫⣶⡆⣠⡄⣠⣄⣰⠀⠀⠸⠃⠀⠘⢄⣆⠈⣄⣈⣦⡼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠼⠷⠿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠿⠖⠷⠽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢋⡿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⢻⡷⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣧⣾⠷⣿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⢡⠋⢀⡠⠛⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⠶⣇⠔⠋⢀⡴⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⡟⠀⢸⢃⡠⠖⠁⢀⣠⣾⠟⠁
⠀⠀⠀⣴⣶⣶⡦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⡞⠉⠀⢀⣴⣿⠟⣁⣀⣤⣀⡀
⠀⠀⠀⠘⢿⣿⡙⣾⡛⠫⣿⣿⣷⣦⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡰⠁⢀⣴⣿⣿⠿⠋⢉⡹⠿⢿⣿⣧
⠀⠀⠀⠀⠀⠙⢾⣿⣭⣽⠯⢅⣊⡽⠻⢿⣷⣮⣄⡀⠀⠀⠀⠀⠀⢸⡇⢠⣃⣴⡿⢿⣟⡡⠔⢊⣁⠤⠐⠚⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡤⠵⠦⢄⣀⠉⠛⠻⢷⣤⣀⢠⣶⣼⣥⡾⠟⣫⠞⠉⠙⠒⠚⢓⣤⡔⠒⠂⢉⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡤⠄⠒⠋⠉⠁⠒⠒⢒⣻⣿⣿⣿⣷⣴⠯⠤⠤⠴⠶⠶⢏⣁⠀⠉⠙⠒⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣤⣤⣤⣶⣶⣿⡿⠟⣫⠜⣿⣿⣿⡯⣓⠦⠤⣀⡀⠀⠀⠉⠓⢦⣼⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠛⠛⣳⡖⠉⠀⡸⠀⡝⡟⢿⡎⠕⣦⣀⠉⠙⠒⠦⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡎⢀⡾⠀⢰⠃⠀⢧⠘⡜⣿⣄⠀⠈⠑⠲⠴⠾⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡀⡟⢏⠣⡀⠘⡀⠱⣏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣦⣑⣄⢁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠋

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

⠀⣠⡤⣤⣄⣀⡀
⠀⣧⣿⡿⣷⣶⣤⡉⠳⠶⣠
⠀⠻⣷⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⣦⣀⡀
⠀⠀⠸⣿⣤⣿⣿⣏⣉⣻⣾⠿⠿⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⢽⣿⣽⣙⣷⠤⠼⣿⠀⠀⣠⣾⣿⢯⣷⣄⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⣏⣉⣿⣗⠒⠛⣣⣀⠿⡿⠉⠀⣩⣮⣳⣄⡀
⠀⠀⠀⠀⠈⣻⣏⣛⣿⣏⠁⢈⣉⣓⣦⣀⠺⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤
⠀⠀⠀⠀⠀⢈⢫⣩⣽⣿⣁⠀⠀⠉⣁⣿⣿⣶⣭⡃⠈⢿⣿⡄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠫⣿⣭⣼⣏⣀⠀⢀⣉⣹⣿⣿⣇⠈⠱⢦⣻⣿⡀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⢀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⣾⡧⠥⠿⣤⣤⡤⠤⠤⠤⠬⠍⢙⣓⡻⢿⣿⣿⣿⣶⣿⣿⣠⣤⣤⢴⠶⠾⠿⠿⣿⣿⣿⣟⣛⣓⠲⠾⢭⣽⣛⠲⢦⣄
⠀⠀⠀⠀⠀⡿⣧⣬⡷⠒⢻⠋⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⢿⣾⡿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⡀⢰⣿⣿⠀⠸⣿⣽⠉⠙⢶⣮⣭⣟⣾⣟⡿⢷⣄⡀
⠀⠀⠀⠀⠀⣿⣏⣱⣿⠆⢙⣦⣀⡀⠀⣀⣤⠞⠋⠁⢀⡠⣺⣿⣛⣿⣿⡷⠪⠙⠳⢄⡀⠀⣠⣿⣿⣿⡦⣄⣻⡟⠁⠀⣀⡼⠣⣄⣹⣿⣻⣿⣿⣟⠹
⠀⠀⠀⠀⠘⣿⡟⣍⣿⣶⠁⢠⠏⠙⢋⡻⠋⠀⠀⣰⠟⣰⣿⣳⣾⠏⠈⢰⡄⠀⠑⠦⡉⠻⣿⣿⡿⠋⠙⠁⠉⠋⠉⠛⣭⣑⣦⣾⠿⣍⣙⢿⣆⡿⠟
⠀⠀⠀⠀⢶⣟⢛⣋⣿⣿⣾⣿⣀⣄⣭⡀⠀⣠⣾⠋⣰⣿⣿⡿⢃⡼⠀⠀⣧⠀⠀⠀⠹⣷⢄⣹⣷⣬⣦⡀⢰⣤⣤⣶⡿⢯⡝⣹⣧⣼⠟⠛⠚
⠀⠀⠀⠀⢀⣿⣿⠻⡉⣫⣿⠿⣿⣿⣛⣿⡶⣥⠃⢰⣿⡿⠟⢠⠞⠁⠀⢈⡟⢧⡀⠀⢀⠿⣆⣹⣾⣿⢿⣿⣿⣭⣿⣼⣿⡟⠛⠏
⠀⠀⠀⠀⣼⢃⠐⠀⢼⡻⠛⢺⣿⠙⠛⡟⣭⠋⠀⠛⠋⢀⢐⡿⢶⣤⠀⢸⠃⢸⠋⠒⠘⣆⣹⣽⣼⣿⠀⠈⠉⠈⠁⠀⠈
⠀⠀⢀⣼⡖⠁⠀⠀⠀⠀⠀⠘⠛⠀⠀⠉⠁⠀⠀⠀⠀⣴⠹⣿⢇⣿⣇⣜⠀⣸⣄⣸⣶⡟⠿⣤⣿⡇
⠀⠀⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣤⣾⣿⣿⣿⣶⣿⡿⣿⡍⢻⣶⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣃⣿⠿⣿⣯⣿⣥⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⡛⣶⣿⣿⣿⠿⣿⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⣴⠉⡟⢓⣶⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣖⠛⡏⢱
⣿⣿⡻⣿⣿⢿⣍⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣋⣽⢿⣿⡿⣻⣿
⠹⣿⣬⣿⣿⡿⣏⠉⠉⠁⣈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⡀⠉⠉⣉⣿⣿⣿⣯⣼⡿
⠀⠸⣿⣿⠿⣃⠐⢫⣿⣿⠛⣿⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣿⡟⢻⣿⣯⠓⢀⣻⢿⣿⡿
⠀⠀⠹⣿⡤⠾⣿⣿⣿⠟⠛⢿⠋⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢻⠟⠛⢿⣿⣿⡿⠦⣼⡿⠁
⠀⠀⠀⢻⣿⣼⡟⠉⠀⠀⠀⠀⠑⢄⠀⠙⢿⣷⣄⠀⠀⠀⢀⣴⣿⠟⠁⢀⠐⠁⠀⠀⠀⠈⠙⣿⣼⣿⠃
⠀⠀⠀⠘⣟⢻⡽⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣿⣦⣶⣦⣾⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠺⣽⢛⡟
⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣈⣿⣿⣿⣏⣀⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠈⠛⠿⢿⣿⢿⡿⠿⠿⠿⢿⠿⠛⠉⠁⠀⣿⡇⠀⠉⠙⠻⢿⠿⠿⠿⠿⣿⢿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠠⢿⠇⠊⠈⠀⠀⠶⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠱⠆⠀⠈⠈⠒⢿⠧
⠀⠀⠀⠀⠀⠀⣾⠙⡧⠀⠀⠀⠠⠟⠒⠂⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠒⠚⠧⠀⠀⠀⠠⡝⢹⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣙⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠉⠁⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣹⣇⣀⡀⣂⣀⡤⠂⠀⠀⠀⠀⠀⠀⠢⣄⣀⡂⣀⣀⣿⡩⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢱⣇⣀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣥⡀⠀⠐⠟⢛⣿⢾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠙⠳⢤⣤⣽⣿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⠄⠀⠀⠀⠈⣙⣛⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠷⢣⠀⠀⢠⠞⠋⠀⠙⢛⠟⠃⠲⣷⠀⠀⠿⠇⢹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⢁⡴⠋⠀⠀⢦⣴⣻⡄⠀⠀⠀⠀⠨⣦⠉⣟⡉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⠾⠀⠀⠀⣀⡿⢟⣏⠁⠀⢰⣄⣰⣦⣍⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢠⣿⡀⠀⠀⣶⠈⠀⠀⠉⠒⠚⠻⣿⣿⣭⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⣿⡿⢃⠞⠃⠰⢦⣤⠄⣀⣀⠀⠀⠈⢛⣻⣃⣙⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣈⢁⣿⣧⠞⠁⠀⠀⠤⠶⠾⡶⠄⠀⠀⢠⣬⣭⣋⡀⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡆⠒⠒⠀⠀⠀⠒⠒⠀⠀⠐⢸⣯⣟⣡⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠻⣦⠀⠂⢄⡀⠀⠀⠀⠀⣷⣾⣝⠋⣹⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠒⢤⣀⣴⣿⣟⣻⣷⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠻⠟⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠖⠀⠀⠄⠴⠶⣾⣿⣿⣿⣷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡤⣤⡀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⣤⡄
⠺⡄⠀⠀⢰⣦⣄⠀⠀⣠⣴⡶⠀⠀⢀⡗⠘⠇⠀⠀⠀⢠⡄⠀⠀⠀⠸⠃⠀⠀⠹⣦⠀⢳⣄⠀⣴⠇⢀⣼⠃⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠈⠓⢤⡀⢈⣩⣽⣟⣍⡁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⠻⣿⠋⢠⣾⠁⠀⠀⠀⠀⠀⠀⠰⣟⢹⣄
⠀⠀⠀⠀⠈⠿⣿⡿⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠘⢦⣀⠈⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⢿⡷⠆⠇⠰⣿⠟⠀⠀⠀⠀⠀⠈⠳⠞⣣⣮⡿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⢠⣤⡄⠀⠀⢀⡀⠀⠀⢀⣤⡄⠀⠀⠀⠹⣟⣷⣄⠀⠀⣠⣾⣻⠏⠀⠀⠀⠀⢻⣯⣷⣄⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠳⡤⣠⡼⡧⣤⡠⡞⠉⠀⠀⠀⠀⠀⠻⠿⠿⢷⡾⠿⠿⠟⠀⠀⠀⠀⠀⠀⢹⣾⡏⡟⢽⣿⠃⠀⠀⠀⠀⠀⠠⠀⡀⠈⡃
⠀⠀⠀⠀⠀⠷⡶⠂⠑⢶⡾⠃⠀⠀⠀⠀⠀⠀⠰⠀⠠⢚⡗⠄⠀⠆⠀⠀⠀⠀⠀⢀⣨⠟⠃⠃⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡷
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⠛⠉
⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⣰⠖⠀⠀⠀⠻⣟⢷⣦⣀⠀⠀⣀⣴⡾⣿⠟⠀⣶⡲⣦⣄⡀⠀⠀⠀⢀⣤⡶⣲⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⣧⠀⢀⡄⠀⣴⠏⠀⠀⠀⠀⠀⠘⢷⡝⠻⢷⡶⠟⢫⡾⠃⠀⠀⠈⢿⠊⠻⣷⠄⡀⢴⡿⠋⢚⡟⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠸⣇⠀⠹⠏⠀⣠⡇⠀⠀⠀⠀⠀⠀⠸⣿⣄⠸⠇⣠⣿⠇⠀⠀⠀⠀⠈⢳⣤⣘⢶⣷⢞⣡⣴⡏⠀⠀⠀⠀⠀⢰⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠘⣟⡾⠀⠀⠸⢗⡿⠁⠀⠀⠀⠀⠀⠀⠳⠞⠁⠐
⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠈⠹⣿⣿⣷⡄⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣶⣴⣶⣶⠂⠀⠀⠀⠀⣀⠂⡀
⠀⠀⠀⠀⠙⡟⢻⣿⡿⣟⢻⠛⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⣤⠈⠀⠇⠈⢠⡄⠀⠀⠀⠀⠀⠙⠳⣦⣶⣟⢇
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠘

⠀⣿⣿⠛⣧⠼⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠧⣼⠛⣿⣿
⠀⢿⣿⣛⡷⠤⠴⠾⣾⡉⢻⣗⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣺⡟⢉⣷⠷⠆⠤⢾⣛⣿⡿
⠀⠘⣷⡟⢻⡶⠚⠛⣷⣤⠛⠻⣿⣭⡓⢦⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⢚⣭⣿⠟⠛⣤⡾⠛⠓⢶⡟⢻⣾⠃
⠀⠀⠘⢿⣻⣽⡶⢶⣿⠟⠛⠛⠫⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠝⠛⠛⠻⣿⡶⢶⣯⣟⡿⠃
⠀⠀⠀⠈⢻⣾⣧⣴⣿⡀⠀⠀⢀⣠⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⡀⠀⠀⢀⣿⣦⣼⣷⡟⠁
⠀⠀⠀⠀⠘⣿⣿⣾⣿⡟⠉⠀⠈⠁⠉⠂⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠐⠉⠈⠁⠀⠉⢻⣿⣧⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣷⡾⣇⣀⢀⣀⣀⠤⠤⠾⠦⢄⡀⠀⠀⠙⢦⠀⣀⣀⠀⡴⠋⠀⠀⠀⡠⠴⠷⠤⠄⣀⣀⡀⣀⣸⢷⣾⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠻⣿⣿⠟⠀⣀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣷⣼⣿⣆⣀⣀⣠⣤⣴⣶⣤⣤⣄⣀⣀⣀⣉⣴⣿⣿⣦⣉⣀⣀⣀⣠⣤⣤⣶⣤⣤⣄⣀⣀⣰⣿⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠛⠛⠉⠉⠛⠿⠋⠉⠭⠉⠉⢉⢿⣿⣿⡿⡉⠉⠉⠭⠉⠙⠿⡛⠉⠉⠛⠛⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣯⣤⡄⠤⠤⠤⠆⠀⠀⠀⠀⣀⠔⠁⡜⣹⣏⢣⠘⠢⣀⠀⠀⠀⠀⠱⠤⠤⠤⢤⣤⣽⣧⣹⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⠋⠀⠀⠀⢀⠎⠀⣀⣠⡴⠊⠀⠀⡀⠀⣿⣿⠀⢀⠀⠈⠑⢦⣄⣀⠀⠱⡀⠀⠀⠀⠙⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢻⣻⣿⣦⡤⠀⠈⢉⠄⠉⠁⠀⠀⠀⠀⠈⢀⠆⢻⡟⠰⡀⠁⠀⠀⠀⠀⠈⠉⠠⡉⠁⠀⢤⣴⣿⣟⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠸⠇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠿⣿⣿⣦⣀⣀⣴⠀⠀⡴⠀⢠⠟⠀⠀⠀⠀⠀⠀⠻⡄⠀⢦⠀⠈⣦⣀⣀⣴⣿⣿⠿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⡿⣭⣿⣻⡶⣾⣅⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣨⣷⢶⣟⣿⣭⢿⣯⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣯⣾⣿⣼⣷⣦⡀⠐⢄⠀⠀⡠⠂⢀⣤⣾⣷⠿⣯⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣯⡉⢙⣏⠉⠻⣆⠀⠂⠘⠀⣴⠟⠉⡴⠀⠒⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠤⠤⠔⠛⠢⢌⢳⣰⣦⠞⢀⠤⠚⠒⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣶⣶⣶⡶⣿⣿⣿⡿⠷⢶⡿⠿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⡀⠋⢁⠰⢡⣿⣿⠁⢄⠀⠲⡀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠁⠐⠒⠁⠀⣸⢻⡿⡀⠀⠡⠐⡁⢈⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣴⣀⣀⡀⣠⠃⠺⠇⠰⡌⢄⣡⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠋⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢿⡟⠈⠳⣄⠀⠀⠀⠀⡤⠊⠁⣻⠗⠀⠀⠀⣿⡇⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⡆⣿⡇⠀⠀⠘⢻⡷⡦⣄⠀⠀⠀⠀⠀⣠⣴⡾⣿⠓
⠀⠀⠀⡉⠁⠀⠈⠁⣴⡄⠊⠀⠀⠈⣩⠀⠀⠀⠀⠸⣷⡙⠻⣤⣇⢀⣄⢀⣧⡼⠛⣱⡿⠀⠀⠀⠀⠫⢿⡹⡟⠀⣀⣸⣀⡠⠘⡟⣽⠯⠃
⠀⠀⠀⠛⣳⠖⠶⠖⣿⡗⠲⠖⠲⡛⠋⠀⠀⠀⠀⠀⠙⣷⡾⠉⠉⣹⣿⡉⠉⢹⣾⡟⠁⠀⠀⠀⠀⠀⠻⣿⣛⡈⣹⣿⣏⠁⣘⣿⡟⠁
⠀⠀⠀⠘⡀⢠⠔⠀⣿⡇⠑⢤⠀⣈⠀⠀⠀⠀⠀⠀⠸⣿⣷⠘⠻⠏⠏⠿⠛⢸⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⠁⢸⠈⢠⣟⣿⣿⣆
⠀⠀⠀⠀⢳⣀⣀⠂⠀⠀⠂⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡞⠂⠀⠛⣾⣿⡟⠃⠀⠀⠀⠀⠀⠸⣨⣻⣴⠇⠀⠀⠀⠘⣧⣝⣉⡇
⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱
⠀⢿⣿⣶⣦⢀⠀⠀⠀⠀⢀⠀⡠⣴⣾⣿⡇⠀⠰⣄⣀⣶⣶⢤⡀⠀⠀⠀⣠⢴⣶⣆⣀⡶
⠀⠈⣿⡯⠨⠈⠳⣄⠀⠀⡠⠋⠩⠁⣿⡏⠀⠀⠀⠘⢷⣮⡁⠀⠈⣶⣷⡎⠀⠀⣩⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢸⣿⣀⣈⣀⣈⣶⣞⣁⣊⣀⣰⣿⠃⠀⠀⠀⠀⠈⢿⡿⠛⣋⣹⣿⣉⡛⠻⣿⠏⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⢺⣿⡗⠂⠀⠀⠀⡰⡾
⠀⠀⠀⣿⠁⠈⣉⠉⣿⣏⢉⡉⠀⠹⣯⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⡉⠃⣉⠁⢠⡿⠀⠀⠀⠀⠀⠀⠈⠀⡤⡖⠉⠘⣿⡇⠈⢐⣤⡄⠋
⠀⠀⠀⢿⣥⣀⡀⠘⠙⠙⡀⣁⣡⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠲⠚⠁⠀⠙⠲⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠿⠄⠀⠀⠄
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣾⣷⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿
⠀⠴⠀⠶⣤⢀⠀⠠⢴⡤⠀⢀⡀⡴⠖⠰⣄⠀⠀⡏⠁⠂⠀⠉⠢⣠⣦⡠⠚⠁⠀⠂⠉⡇⠀⠀⠹⡶⠻⠹⠊⠶⡄⠀⢀⡶⠂⠏⠝⠳⡏
⠀⠻⣷⡀⠀⢀⣠⠔⢻⡃⢤⣄⡀⠀⡐⡾⠋⠀⠀⠑⠒⣶⠶⠦⠤⣾⣿⡦⠤⠴⢶⠒⠒⠁⠀⠀⠀⠷⣀⣀⣀⣀⣸⣶⣏⣀⣀⣀⣀⠸⠃
⠀⠀⠈⢃⠈⠉⠀⠀⣼⡄⠀⠈⠉⠀⠛⠁⠀⠀⠀⠀⠘⠁⢀⠄⢀⡿⡿⣇⠀⢤⠀⠙⠀⠀⠀⠀⠀⢰⡏⠀⠈⡀⠘⣿⡧⠀⡉⠀⢘⣦
⠀⠀⠀⠈⠢⢀⠠⠜⠁⠈⠢⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡦⠀⠠⠃⠀⠀⠈⠣⠀⠠⣆⡀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠋⠹⠙⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠛⠁
⢀⣤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣄⠀⠀⢰⣿⣿⠳⢄⠀⠀⠀⠀⢀⠴⢻⣿⣷⠀⠀⠀⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷
⠀⢿⠂⠀⠙⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⢘⠟⠀⠀⠘⣿⡏⠂⠀⠐⠀⠀⠀⠀⠀⠊⣿⡟⠀⠀⠀⠘⣿⣿⠷⣟⣳⣄⠀⢠⣖⣻⡾⣻⣿⡏
⠀⠀⡛⢐⠢⠀⠈⠀⢰⡄⠔⠁⠠⠐⠘⠋⠀⠀⠀⠀⠹⢿⡥⠄⠐⢶⣷⠖⠀⠤⣽⠟⠁⠀⠀⠀⠀⠘⣿⣷⡉⣿⣿⣿⣿⣿⣉⣴⣿⠏
⠀⠀⠈⠂⢠⡤⠀⢠⣾⣧⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠾⡟⠆⠀⠂⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣧⡀⢸⣿⡅
⠀⠀⠀⢰⠏⠀⠀⠀⢿⡇⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠀⠁⠸⣦⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠉⢹⣿⣿⡿⠃
⠀⠀⠀⠈⠃⠼⠄⠀⠀⠀⠀⠤⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⣶⣄⠀⢀⣴⡶⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢠⢤⡀⠀⠀⠀⢀⡠⡄⠀⢠⣤⡀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⢿⠹⣶⡾⢹⠃⠀⠀⠀⠿⣈⣱⣴⣞⣁⠽⠃⠀⠈⠿⣼⣦⣤⣴⣧⡿⠃⠀⠘⣿⣿⣦⣀⣴⣿⡿⠁
⠀⠀⠀⠰⣏⡖⠙⠑⣚⡇⠀⠀⠀⢸⣟⣿⠛⢿⣛⡧⠀⠀⠀⢰⣿⡮⠿⢵⣿⡆⠀⠀⠀⢾⣿⣜⠛⣣⣿⡇
⠀⠀⠀⠘⠙⠁⠀⠀⠙⠑⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⣶⣶⢄⠀⢀⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠠⠀⠀⠀⠆⢻⡇⠀⠀⠀⣀⡀⠀⢀⣀
⠀⠀⠀⢈⣿⣿⣿⣟⣿⡏⠀⠀⠀⠀⣈⠀⣿⠀⢀⠁⠀⠀⠀⣉⠤⢸⣿⡧⠠⣌⠀⠀⠰⣤⣀⣭⣿⣍⣁⣠⠆
⠀⠀⠀⠘⢿⠗⠈⠸⢿⠏⠀⠀⠀⠀⠁⠀⠙⠀⠀⠁⠀⠀⠀⠹⣦⠟⠙⠻⣴⠏⠀⠀⠀⠀⠋⠝⠙⠭⠙


⠀⠀⠀⢾⠒⢦⣤⣤⠖⢺⠆⠀⠰⣖⠋⠲⣴⠶⠊⢒⠖⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⢡⣶⣦⣤⣴⣶⡌
⠀⠀⠀⠈⣷⡦⠿⢧⢴⠏⠀⠀⠀⠀⠹⣶⠟⣦⡞⠀⠀⠀⠀⠀⠀⣤⠈⣠⡄⠀⠀⠀⠀⠘⣿⣛⣿⣛⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⢀⣤⡤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⡤⣤⡀
⠀⠀⠘⣿⡇⣿⣿⢸⣏⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠰⡍⡇⢹⣿⡧⣿⠇
⠀⠀⠀⠹⣯⣾⣷⣀⣹⠤⣃⣀⡾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠑⢷⣄⣈⢤⣇⣁⣾⣿⣼⡟
⠀⠀⠀⠀⠹⣧⣾⣿⡤⠔⠚⢻⣤⣤⣾⣿⡟⢦⡀⠀⠀⠀⠀⢀⣴⢟⣿⣷⣤⣠⡟⠛⠒⢤⣽⣟⣾⠏
⠀⠀⠀⠀⠀⠙⣿⢻⣷⠖⠉⢁⣀⠹⠿⣿⣿⣿⣿⣦⣴⣶⣠⣿⣷⣿⣿⠿⠯⣀⡈⠉⠓⢶⡿⣾⠟
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠞⠉⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠓⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⣠⣤⡤⠶⠒⡛⠛⠻⣿⣿⡿⢿⣿⣿⡟⠛⢛⠒⠶⢦⣤⣄⡐⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢻⣯⠀⡀⠴⠁⢀⣴⡟⠙⡿⢺⠏⢹⣦⡀⠀⠦⢀⠀⣿⡟⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⡟⣷⠚⣿⡁⠐⠣⠔⡋⢸⠀⠀⡇⢸⠀⢀⡇⠉⠲⠔⠂⣌⣿⠓⣾⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⡶⢿⣅⡀⡆⠀⡇⡞⢀⠀⢧⢸⠀⠠⢧⢘⠀⠐⣀⣸⡿⢷⠏⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣼⠛⢿⣷⣸⣄⣧⡈⠀⠈⠀⠀⢀⣼⣨⣆⣶⣿⠛⣧⣼⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣛⣿⣦⣄⣋⣻⣩⣧⠀⠀⠀⠀⣼⣏⣛⣉⣠⣼⢿⣻⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣝⣻⣝⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢐⣾⣻⣻⣿⠖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⣿⣟⣟⣶⡂
⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⢰⣟⣿⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⣻⡆⠀⠙⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣶⣛⣻⣍⠙⠛⢷⡄⠀⠀⠀⠀⢠⡾⠛⠋⣩⣟⣛⣶⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣉⣠⡤⠬⠷⠦⣄⡹⣆⢀⡀⣰⢏⣠⠴⠾⠥⢤⣄⣉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⣁⣀⣠⣤⣤⣤⣤⡭⢻⣿⣿⡟⢭⣤⣤⣤⣤⣤⣀⣈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣍⠻⡿⠛⢋⡝⢿⡿⢫⡙⠛⢿⠟⣩⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣏⠽⢗⡚⢀⣴⠋⠀⢨⡅⠀⠙⣦⡀⢓⡚⠯⣹⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣡⠴⢫⠏⡽⠁⠈⠀⢨⠅⠀⠠⠈⢯⠹⡝⠦⣌⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⠋⣼⠁⢌⠄⠀⠈⠁⠀⢠⡡⠈⣧⠙⣦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣷⣾⡞⠀⠀⠀⠀⠀⠀⢳⣷⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣆⠶⣿⡿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣦⣹⠆⢋⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠲⣦⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣿⡏⠀⣰⣿⣯⠋
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡦⣄⡀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⢿⣮⡂⠀⡀⣿⣏⡇
⠀⠀⠀⢠⣤⣻⣿⡿⢆⣷⣿⣿⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣦⠝⠉⠛⠈⠘⢿⣷⢀⣴⣿⡗⡁
⠀⠀⢀⡦⣿⣿⣿⣀⠀⠀⠙⢿⣳⣼⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣉⣣⣤⣴⣶⣦⣔⣠⣤⡞⠉⢹⡿⠝⢄
⠀⠀⠀⠲⠙⡿⢻⡏⢴⣿⣿⠿⡻⠛⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠿⠿⠛⠛⠼⡻⠟⡿⡻⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠢⣄⢠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡈⢑⠀⠈⠀⠀⠀⣀⠀⢆⡀⠙⡿⠛⠁
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠨⠄⣶⣿⠁⠀⠰⣤⠺⠝⠋⠀⠀⠀⠀⢀⣤⣾⣯⢹
⠀⠸⣿⣏⢛⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⣴⣛⡯⢰⡯⣽
⠀⠀⠘⣿⣿⠩⠭⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣅⣿⣗⡏
⠀⠀⠀⠘⣷⠖⠂⣀⣀⣀⣀⣱⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣯⣷⣈⣷⠙⣧⣀
⠀⠀⠀⠀⣿⡛⠻⠋⠉⢉⣩⣿⢿⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡹⠿⠿⣿⣿⣧⡽⣳⠖⠛⠃
⠀⠀⠀⠀⠹⣧⣀⠘⢀⣾⡿⠃⢸⡇⠀⡈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣄⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠛⢻⡏⠠⠊⣸⡇⢀⢀⡤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡛⠂⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣘⣧⣼⣠⣧⣟⡻⣧⠀⠀⠀⠀⠀⠀⠀⠉⠩⠛⠛⢉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠛⠻⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣾⣟⡻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡉⢩⣿⣸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⣏⡯⠭⢭⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢦⣤⡾⠿⢿⣑⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣩⠿⠿⢷⣤⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣤⣀⣀⣈⣣⡀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⢠⣊⣀⣀⣤⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡁⠀⠀⠀⠀⠙⢢⡀⠀⠈⠳⣄⠀⠁⠀⢀⠁⢀⣴⠟⠁⠀⣠⠞⠁⠀⠀⠀⠀⣸⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠛⠋⠉⠉⠉⠉⠉⠓⠤⣀⠈⢷⣄⣷⡆⣰⠟⠁⣠⠴⠋⠉⠉⠉⠉⠉⠉⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠑⠂⣽⡟⣿⡧⠒⠉⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣩⣹⠿⠿⠿⠟⡛⠛⠛⠛⠻⣿⡇⣿⣿⠙⠛⠛⡛⣛⠻⠿⠿⠿⣏⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⠀⠀⠀⢐⠞⠁⠀⢀⠔⠉⠿⣿⣿⠧⠑⠄⡀⠀⠈⠳⠀⠀⠀⠠⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⡀⠀⠀⠘⠁⢀⣠⠞⠁⠠⠀⠀⣿⣿⠀⠐⡀⠈⠢⣄⡀⠘⠂⠀⠀⢀⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢀⠄⠊⡗⠋⣡⠃⠀⡐⠁⠌⡜⣿⡟⢆⠀⠈⢄⠀⠰⡈⠑⢎⠀⠠⡀⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⡜⠀⠰⠋⠀⡜⠀⢀⠜⠀⢿⡇⠀⢂⡂⠈⢆⠀⠙⡄⠈⢂⠀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣦⣤⣇⢀⡜⠀⣠⠊⠀⠀⠈⠁⠀⠀⠹⣄⠀⢢⣀⣴⣤⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣵⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁