Polynesian Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢰⣦⡀⢀⣾⣆⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⢠⣿⠿⠆⠛⢛⣛⣛⣋⣙⣛⣛⠛⠣⠾⢿⣧⢀⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡸⠟⣋⣥⡴⠖⡛⠉⡉⠉⠁⢸⢀⠉⠉⡉⠙⡓⠲⣤⣍⡛⠿⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣬⠟⣩⠴⡚⡙⡀⠐⣐⣠⠤⠶⠔⠓⠚⠒⠓⠴⠧⢤⣐⡐⠠⡘⠙⡲⢬⡙⢯⣤⣤⡆
⠀⠀⠀⠀⠀⢀⣀⣀⡻⢋⣤⠊⠱⡐⢐⡤⠞⣋⣥⣴⡶⠋⠉⠙⢯⠟⠉⢉⠳⣶⣤⣍⡛⠦⣔⠐⡰⡙⢢⣌⠻⣇⣀⣀
⠀⠀⠀⠀⠀⠘⣿⠟⣠⠫⡀⠕⣬⠞⣩⢴⠏⢄⣀⠈⠧⠂⠛⣈⣈⣈⡘⠓⠃⠏⠁⣀⠌⢷⢤⡙⢦⡔⠅⡨⢣⡘⢿⡟
⠀⠀⠀⢰⣶⡶⢃⡞⠑⢄⣈⠟⣡⢚⠉⡛⠆⢈⣡⣴⣦⣤⡾⠛⣿⡟⠻⣦⣤⣶⣤⣉⠂⢞⠋⢙⠢⡙⢯⣀⠔⠙⣆⠳⣶⣶
⠀⠀⣀⣀⡹⢡⡟⠉⠢⡴⢁⣾⣇⢀⠛⣠⣤⣬⣙⠻⢿⣦⡀⠺⣿⡿⠂⣠⣾⠿⢛⣩⣤⣤⡘⢇⢀⣿⣆⠱⡤⠊⠙⣧⠹⣁⣀⡀
⠀⠀⠻⣿⢃⡟⡀⠅⡾⢡⠋⠍⡉⢁⠜⠙⠛⠻⠿⣿⣦⡉⢿⣦⠙⢡⣾⠋⣡⣾⡿⠿⠛⠛⠙⢀⠙⠉⠍⢣⠹⡆⠅⡘⣇⢹⡿⠃
⢀⣤⣶⡇⣼⠀⢂⣹⢁⢿⡀⡘⠁⠄⣴⣿⠿⠗⢀⣤⡙⢿⣦⠹⡇⡿⢡⣾⠟⣡⣄⡐⠿⢿⣷⡄⠂⠙⠄⣸⢇⢹⣁⠂⢹⡄⣷⣦⣄
⠀⠙⢻⢀⡧⠄⢠⡇⡼⢛⢉⠁⣴⣶⣶⣶⠶⠚⠛⠻⢿⣆⠙⣧⠀⢠⠟⢁⣾⠿⠛⠛⠲⢶⣶⣶⣶⡄⠸⢙⠻⡄⣧⠀⠤⣧⢸⡟⠁
⢴⣾⡏⢸⠇⠈⢼⠀⡇⢀⠛⢰⡟⣉⢻⡓⠶⣤⣀⠀⠀⠙⣆⠈⣇⡟⢀⡞⠁⠀⢀⣠⡤⠖⣻⢋⡙⣷⠐⠇⠀⡇⢸⠌⠀⢾⠈⣿⣶
⠀⣈⡇⢸⠀⢀⢾⠀⣿⠶⠆⢸⣧⡉⠀⢷⣄⠀⠈⠉⠒⠀⢸⣦⣈⣠⣾⡀⠐⠚⠉⠀⢀⣴⠇⠈⣡⣿⠀⡶⢾⡷⢸⠆⠀⢸⠀⣏⡀
⠺⢿⣧⢸⡆⢀⢺⠀⡇⠀⡧⢸⣿⣷⠀⠈⠻⣷⣶⡶⠖⠋⠉⠈⢿⠋⠈⠉⠓⠶⣶⣶⡿⠋⠀⢰⣿⣿⢠⡎⠀⡇⢸⢂⠀⣾⢠⣿⠿
⠀⣠⣾⠘⡗⠂⠙⡇⢳⣬⣰⠀⢿⠃⣴⠛⠳⡄⠀⠀⢀⣀⠀⠀⣼⡀⠀⠀⣀⠀⠀⠀⡴⠛⢳⡄⢻⠇⣨⣨⣴⠃⡟⠁⠒⡏⢸⣦⡀
⠈⠛⠿⡇⢻⠀⠍⣹⡈⣾⠁⢢⡘⣧⣙⠒⣀⠏⠀⠀⠚⠛⠷⠾⢿⠿⠶⠿⠛⠃⠀⠀⢧⡐⢚⣡⡟⣠⠁⢹⡎⣸⡉⠅⢸⠃⡿⠟⠋
⠀⠀⣴⣿⡈⣯⠁⡂⢷⡘⣌⣂⣰⠌⢻⣭⣥⡤⠀⣀⣤⣴⣶⠶⠿⠷⢶⣶⣤⣄⡀⠠⣤⣭⣽⠋⣀⣁⣊⡜⣰⠇⡂⢩⡏⣸⣷⡄
⠀⠀⠉⠉⣱⡘⢧⣀⠔⠳⡈⢿⡏⠈⣦⠙⠋⢠⣾⣿⠫⠥⠒⠒⠒⠒⠒⠢⠭⢿⣿⣆⠈⠛⣡⡄⠈⣿⠏⡰⠓⢄⣀⠟⣰⡉⠉⠁
⠀⠀⠀⠸⠿⠷⡌⢧⡠⠪⢉⢦⡙⢬⣀⣬⠆⢌⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣉⠀⢦⣅⣨⠜⣡⢎⠉⠢⣤⠏⡴⠿⠿
⠀⠀⠀⠀⠀⢠⣿⣦⡙⣔⠁⡢⠛⢦⣙⠺⣆⡊⠁⣠⡆⠤⣬⢉⢩⢉⢡⡄⠐⣦⠊⠁⣂⡾⢚⣡⢞⠣⡂⢑⡜⣡⣾⣧
⠀⠀⠀⠀⠀⠈⠉⠉⣵⣌⡙⢤⡰⠡⠨⡓⢦⢍⣛⠻⠷⣬⣀⣥⣞⣦⣁⣠⡴⠯⢛⣋⢥⠖⠫⡠⠑⣠⠜⣉⣴⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢛⣦⣙⠲⢥⣠⠑⠠⠩⡙⡓⡶⠲⠤⢤⠤⠴⠲⡖⠛⡩⠡⠀⢱⣡⠵⢚⣡⣾⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢱⣦⣌⡙⠳⠦⢥⣀⣁⣀⡈⢸⢀⣀⣀⣁⣠⡥⠶⠛⣉⣤⣶⠙⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠘⣿⣷⠖⣦⣬⣭⢭⣭⣭⢭⣥⣤⡔⢶⣾⡟⠈⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⠟⠁⠈⢿⠏⠀⠙⠿⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣴⣾⠟⠛⠻⣦⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⡏⢰⣿⣿⠁⣴⡖⠀⢸⣿⡇⢹⣿⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⣿⣿⡇⠸⣿⣿⠀⢿⣿⣿⣿⣿⠇⢸⣿⣿⡀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⣿⣿⣧⠀⡌⠛⢓⠀⠉⡛⠛⢡⠀⣼⣿⣿⠁⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠀⣀⠈⠻⣿⣦⠁⣼⣿⡇⢸⣿⣷⠈⣰⣿⠿⠃⣀⡀⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⣈⣉⣁⣀⡈⠙⢇⢸⣿⠇⢸⣿⡇⣸⠛⠁⣀⣈⣉⣁⠈⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣡⣶⠟⠛⠻⣿⣿⣿⣦⠈⢨⣿⠀⠀⣿⡇⠁⣴⣿⣿⣿⠟⠛⠻⣶⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠇⢶⠀⣠⠄⠙⣿⣿⠆⣸⡟⢀⣀⢻⣇⠀⣿⣿⠋⠀⣄⠀⡶⠸⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡶⠶⢦⡀⠻⢶⡾⠿⢋⣤⣍⠱⣿⣿⠎⣉⣤⡙⠿⢷⡶⠟⢀⡴⠶⠶⣌⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡇⠾⠏⠓⣈⣠⣤⣤⣬⣉⡛⠿⣿⣌⣡⣾⠿⢛⣋⣥⣤⣤⣀⡉⠚⠹⠷⠸⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠰⢂⡴⢚⣩⠥⠴⠤⣬⡉⠻⢷⡈⢿⡿⢁⣶⠟⢉⣡⠤⠴⠬⣍⡛⢦⡀⠆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣰⢋⣴⠋⢀⣠⠴⢤⣄⠙⣦⡈⢻⡌⢁⡟⢁⣴⠋⣠⡤⠤⣤⡀⠙⣦⡙⣦⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⠇⣼⡇⢠⣿⠁⢰⣦⠸⡇⢸⣿⡌⡇⢸⢁⣿⡇⢸⡏⣴⡦⠈⢿⡄⢸⣧⠸⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⠀⣿⣇⠘⢿⣄⣀⣁⡼⠃⠘⣿⡇⠇⠸⢸⣿⠇⠘⢧⣈⣀⣠⣿⠃⣸⣿⠀⣿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣇⢹⡙⢦⣄⣉⣉⣭⣾⡇⢸⣿⡇⠀⠀⢸⣿⡇⢸⣷⣭⣉⣉⣠⣴⢋⡏⢰⡿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⣿⣦⡙⢾⣿⣿⡿⠟⠩⢀⣾⣟⣤⣶⣶⣤⣻⣷⡀⠍⠻⢿⣿⣿⡷⠎⣴⣿⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡘⢷⣄⡀⠒⠒⠒⣁⣤⠾⠋⢨⡖⢈⡁⢲⡅⠙⠷⣤⣈⠒⠒⠒⢀⣠⡾⢃⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠂⢉⡛⠻⠟⠛⠋⢁⡴⣀⠰⠴⠾⠷⠦⢂⡄⢄⠈⢙⠛⠿⠿⠛⡋⠰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⣙⠛⣋⣩⡴⢋⡀⣨⠵⢒⡛⠲⣌⢉⠑⢎⠳⣄⡉⠛⠛⢋⣡⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⣅⢸⡏⢰⡏⠠⣈⣹⠆⢸⡆⢹⡆⠀⣦⢙⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠳⠜⢿⠆⠈⠁⠴⠛⣠⡾⣣⠂⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣄⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠙⢷⣾⣦⣀⣁⣀⡱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣾⡿⠂⡸⠟⠛⠉⠉⠉⠓⠲⢽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣍⡂⠛⠂⢠⠀⠀⠀⣟⣀⣉⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠻⣿⠷⢶⡶⢃⣤⢾⡻⡿⠯⠯⢟⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⢸⣷⣾⣏⠹⢿⡉⠀⠀⠀⠀⠀⠀⠑⢾⡽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⣿⣯⣶⣤⡉⠿⣍⣉⣉⣉⣉⣉⣉⣙⣽⣧⠀⡴⢊⡉⢻⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣀⣠⣼⣗⡆⠈⢻⣿⣣⣌⠛⢦⣤⠤⠥⠤⠤⢭⡽⣾⢣⣈⡛⣋⣴⡿⠆
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠁⠀⠈⠙⢷⡀⢻⡿⡇⠀⠀⢣⢹⡿⣿⣦⣉⠻⣿⡋⠉⢹⣯⡿⠛⠉⠛⠷⣼⠀⣾
⠀⠀⠀⠀⠀⠀⢸⣿⡃⢠⣶⣶⣦⠀⠀⠛⠚⢿⡽⣄⠀⠘⡄⢿⡘⡟⣿⣷⣬⠙⢦⣼⣗⡇⠀⠀⠀⠀⠘⡷⡌
⠀⠀⠀⠀⠀⠀⠀⢯⣷⣄⣙⣡⠋⠀⠀⠀⠀⠀⠹⣯⣖⣄⣳⠨⣧⢹⣹⡈⢻⣿⣶⣌⢻⣇⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣆⠉⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⣷⣟⣖⣟⣟⣻⠽⠿⠛⠛⠻⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⣶⠀⢹⣳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢩⣤⡟⢉⣉⠙⠯⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠤⠤⠤⠄⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⣡⠶⠶⣫⣴⣿⣶⣬⡳⠶⢦⡉⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⡄⠀⠖⠁⣀⣈⠙⠛⠿⠿⠛⢉⣀⡀⠑⠆⠀⣦⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠃⠀⢀⠺⠉⣽⣿⢷⣤⣴⢿⣿⡏⠹⢂⠀⠀⠣⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢀⠆⢆⠀⣼⣃⣤⠖⣋⡓⢦⣄⣻⣄⢁⠆⣆⠘⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠁⠀⠨⠀⠐⢩⠋⠁⣺⠟⢿⡂⠉⢣⠁⡀⠠⠀⠀⠡⠀⢡
⠀⠀⠀⠀⠀⡠⢒⣥⡀⠂⣀⠀⠈⠀⣀⠀⠀⢾⣮⡎⣾⣾⠆⠀⢀⡀⠈⠀⢀⠀⠂⣠⣅⠢⡀
⠀⠀⠀⢠⠊⠀⠲⡽⣿⣰⡇⠀⠂⠀⠿⣶⠀⣷⣝⣥⣝⣵⡇⢰⡾⠇⠀⠂⠀⣷⣸⡿⡵⠂⠈⢢
⠀⠀⢠⢡⣦⠀⠀⠹⣮⡭⢊⡀⠀⠀⢰⠃⠌⠐⢿⣇⣿⠗⠈⠀⢳⠀⠀⠀⣘⠾⣭⡾⠁⠀⢠⣦⢡
⠀⠀⠀⢂⠱⠀⠀⠀⠈⢿⣯⠄⠉⠓⢺⠄⠀⢀⠳⣿⡷⢃⠀⠀⢾⠒⠋⠑⢬⣿⢏⠀⠀⠀⠰⢁⠂
⠀⠀⠀⠈⠰⣄⠀⠠⡄⠈⠁⡆⡠⠀⠀⢀⡀⣀⢙⢒⢚⣁⡄⣀⠀⠀⠠⣀⡆⠋⠀⠤⠀⢀⡴⠈
⠀⠀⠀⠀⢃⢿⣶⣄⠀⠀⠀⢀⣀⣤⠀⠀⠠⣈⡙⢛⠛⣋⡠⠂⠀⢀⣄⣀⠀⠔⠀⢀⣴⣾⢇⠃
⠀⠀⠀⠀⠈⠌⠻⣿⣿⣦⡀⠀⢉⡉⠃⠀⠀⠹⡇⠈⠀⡟⠀⠀⠀⠋⣉⠁⠀⣠⣾⣿⠿⠋⠌
⠀⠀⠀⠀⠀⠈⢆⢢⣍⡛⠓⠄⠈⠛⢶⣤⣤⡀⠀⣀⣀⠀⢠⣤⣴⠞⠋⠀⠔⠛⣉⣥⢂⠎
⠀⠀⠀⠀⠀⠀⠀⠣⡀⢉⣙⠓⠓⠂⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠒⠓⢛⣉⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢝⠾⣶⣷⡍⠒⠢⡠⠄⡀⠀⢤⡠⠐⠂⣵⣷⡾⢞⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⢛⡲⠿⢿⣦⣤⣴⣾⠿⠷⣚⠫⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠋⠀⠈⠁⠀⠛⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠓⠠⠨⠠⠀⠃⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠠⡤⠔⠐⡀⣐⠀⠠⡤⠀⠄⠶
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⣈⠍⢴⡆⢲⡮⠹⣁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠶⠀⢁⣤⣶⣘⡼⠿⢠⠼⠿⣴⣠⣦⣄⠀⠰⠆
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢔⣫⡝⣉⠈⣭⣭⠉⣙⢯⣟⢤⠀⠀⠀⡤⠀⠀⠀⠤⠀⠰⠪⠵⣟⢰⠖⢸⣦⣾⠐⢦⢙⡷⠭⠲⠀⢠⠄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠴⣤⡽⡯⠈⢍⡩⠉⡽⢫⣤⠦⠀⠀⠀⢀⠀⠀⢀⡀⠃⠠⠶⣦⡜⢿⡤⠤⢢⠠⠤⢤⠟⣦⡶⠦⠀⠃⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⣴⠖⣹⠔⠟⢆⠲⠟⢪⣏⢶⡦⠂⠀⠀⠈⠀⠀⠀⢀⠆⢢⣴⡶⣹⡅⠾⠶⡞⡶⠾⠆⣽⡰⣶⣤⠂⢂
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣢⡅⠀⢒⡀⣀⡂⠑⢩⡔⠀⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠄⢆⡛⢔⠠⠐⠄⠰⠠⢐⠜⣃⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠡⢄⠙⢣⡙⠋⡠⠋⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠛⠀⠄⠛⢷⠀⠲⣾⢧⢿⡶⠂⣰⠟⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠃⢐⡀⠙⠂⠩⠼⠬⠁⠚⠁⣀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡤⠀⢠⡄⠀⣤⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠆⠀⢰⠄⠀⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠰⠆⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⠥⠲⠀⡰⠠⠥⣤⠖
⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠰⠆⣀⡂⣀⡀⠰⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠈⠃⣠⡌⢆⡺⣿⢁⢹⣿⣂⠎⣤⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡴⣦⠵⠹⠣⠾⠹⢤⡶⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⢉⡄⡟⣭⢞⢩⡭⠡⡜⡴⢡⣭⢙⢯⡙⡧⡌
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣑⡘⢧⡟⠡⡗⠷⠈⢷⡟⢐⡉⠀⠀⠈⠁⠀⠀⠀⠘⠀⢂⡁⠹⣧⡋⠤⢚⠋⢛⠤⠌⣧⡿⠁⣁⠂⠘
⠀⠀⠀⠀⠀⠐⠇⠀⠀⢆⣉⡛⢽⢻⣍⡀⣈⣵⡻⡜⣋⡉⡆⠀⠀⠒⠀⠀⠀⠶⡄⠉⠿⢟⣬⢟⣉⣉⢰⢈⣉⣛⢯⣜⠿⠉⠁⠴⠂
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡙⠑⠏⠁⠠⢑⠠⡀⢈⠷⠙⠋⠀⠀⠠⠆⠀⠀⠀⠰⠘⡿⠿⢥⡶⢌⠉⡙⠥⠟⠉⠉⠼⣦⠹⠿⡎⠤
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠻⢇⠐⢶⠆⢶⠶⠁⠾⠃⠀⠀⢀⣄⠀⠀⠀⠀⠀⣠⠁⢫⣼⠑⠁⠒⢙⡉⣉⠑⠢⠑⢹⣌⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠃⠠⠼⠦⠀⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠛⣄⠈⠛⡿⢣⢻⡟⠋⣀⡟⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⣀⠀⠀⠀⠀⡀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠙⣒⠠⢾⠤⢐⡚⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁

⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣄⢠⠄
⠀⠀⠀⠐⢱⠲⠦⠄⠥⢆⢢⢡⠀⠀⠀⠀⠀⢀⣀⣀⢈⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣯⠁
⠀⠀⠀⠰⣜⠈⣋⠅⢍⠃⣊⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠁

⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢄⣠⠤⠀⠀⠒⠶⢒⠀⠤⣤⡄
⠀⠀⠀⠀⠀⠀⢘⠀⠁⠀⠀⠀⠀⠀⠈⠀⠁⠐⡠⢾⠀⠃⢛⠦⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⢀⢐⡴⠾⠒⠁⠸⠸⠀⠓⠚⡷⣙⡀⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⠀⠠⠂⠀⣀⣠⠶⠐⠐⠰⢧⣀⡠⠘⠀⠀⠀⠀⠀⠀⠀⣟⢉⡧
⠀⠀⠀⠀⠀⠀⠸⠀⠃⠀⠀⠀⠀⠀⠀⠒⡀⢅⠀⠀⠨⠬⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠂⠆⠀⠀⠀⠀⠀⠀⠀⣥⣄⠀⣤⢰⢰⢠⠄⢠⣬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⠰⠜⠘⠠⠤⠍⠃⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⡰⢺⣟⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣯⣗⢆
⠀⠀⠀⠀⠀⢱⣷⣏⣼⠃⡀⠀⠀⠀⠀⠀⠀⠖⠒⠯⣀⣀⡽⠒⠲⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠾⢿⣸⡅
⠀⠀⠀⠀⠀⠈⠛⠽⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣽⢿⡟⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢦⡴⢢⡄⢠⡤⢤⡄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⣎⣁⣠⠤⠤⠤⠤⣤⢄⣀⡈⠉⠿⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠷⠖⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠄⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠘⠁⠀⠀⢠⠀⠀⠀⠀⠀⠶⠤⢤⣄⡀⠀⠀⠀⠈⠒⢆⡉⢄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢀⠄⠊⠀⠀⠀⠀⢀⡀⢀⡀⣀⣀⡈⠑⠲⢄⠀⠀⠀⠙⢦⡤⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠐⠂⠀⡤⢈⡁⠀⠀⠁⠠⢂⠀⠩⠘⠉⠟⢳⡦⣌⣢⠀⠀⠀⠻⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡐⠀⠀⢈⡠⢈⡀⠠⠀⠈⠁⠀⠄⠀⠀⠀⠢⠈⠰⢊⠩⠷⡀⠀⠁⢻⡆⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠁⠀⠈⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠤⠉⠤⠐⠳⡐⠓⣾⢠⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠀⠀⠂⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠔⠐⠂⠀⠂⠀⠿⣦⡀⣸⠀⢨⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢣⠀⠈⡐⣀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠄⢸⡆⠁⠀⡄⠀⠈⠋⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡐⠄⠈⠃⠱⠦⠶⠴⠋⠀⠀⠀⠀⠀⠀⠀⠠⢀⠉⢔⠡⠘⠁⠀⣀⠀⠀⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠲⠢⠤⠤⠶⠆⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠄⠂⠁⣠⠃⢀⠟⠀⢀⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣠⠾⠁⢠⡌⠀⠀⠌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠂⠤⠀⣀⣀⣶⠦⠟⠋⠁⢀⠀⠈⠁⠀⠐⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠉⠛⠙⠉⠉⠀⠀⠀⠀⠀⡤⠀⠙⠃⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⠄⢤⣤⠄⠠⣤⠖⢀⠞⠁⠐⠣⠂⠀⠀⣸⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⠀⠀⣆⡉⠀⠴⢌⠁⠐⠮⣀⡀⠉⢱⠶⠀⠀⢀⡀⠁⡙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠁⠀⠀⠈⠙⠂⠀⠺⠿⠶⠶⠿⠛⠃⠀⠀⠔⠈⠟⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⣠⣶⠟⠛⠛⠁⠁⠲⢂⣤⣀⡀⠀⠀⠀⢀⠀⠀⠀⢲⠞⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠋⣉⡁⠀⣦⣤⣴⡿⠟⠛⠉⠁⠀⠀⠀⠐⠋⠀⠈⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠉⠡⣀⠈⢉⣡⠾⠛⠉⠀⠀⠀⠠⡐⠀⠀⠠⠊⠄⠀⡠⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢠⢇⣀⣶⠿⠛⠁⠀⢀⠠⣀⡄⠉⠐⠦⠀⢀⣠⠴⠗⠈
⠀⠀⠀⠀⠀⢀⠂⢸⠃⣼⡿⠋⠁⠀⠀⣠⡖⠀⠀⠋⣀⠀⠐⠒⠊
⠀⠀⠀⠀⢠⠁⡴⢂⡼⠋⠀⡠⠀⡠⠘⠉⢀⠀⠀⠀⠁
⠀⠀⠀⣀⠁⢰⡶⠋⠀⣠⠞⠀⢔⡠⠀⠈
⠀⠀⠀⠈⣰⡟⠁⠀⡰⠋⠀⠜⠊
⠀⠀⢠⢠⡿⠀⠀⢮⠁
⠀⠀⠈⣸⠃⠀⡘
⠀⠀⢿⣿⠀⠀⠅⡃
⠀⠀⠀⣿⠀⠰⠂⡇
⠀⠀⠀⢿⠀⠀⡅⢂
⠀⠀⠀⠈⣇⠀⠱⡨⢄⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠘⢦⠀⠱⡘⢦⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠑⠀⠈⠲⣑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠵⠶⠦⠤⠤⠖⠂
⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠀⠄⢨⣟⣈⣹⢙⣏⣛⣉⡛⣯⣙⣋⣉⣋⣹⠋⠉⢉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣽⣯⣉⣿⣿⣋⣉⣭⣉⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⢻⡇⣰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⢦⣹⣼⣷⣣⠬⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡤⠶⡟⡾⡍⢛⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⣧⠙⠿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡛⠛⠿⣿⣿⡿⠻⠿⠿⣽⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⢰⣏⣾⠃⣶⡀⠀⠉⠻⢿⡛⢳⡌⢻⣾⣗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢸⡿⠋⢾⣿⣧⢠⠻⣦⣤⠙⢶⣿⠰⣿⡌⣷⠘⣷
⠀⠀⠀⠀⠀⣴⣿⣿⣫⡴⣷⣿⠿⣽⡙⣿⡲⣤⡀⠀⠀⠙⢿⣦⠀⠀⢸⡇⣾⢻⡽⣿⣼⣧⠛⡸⣇⢰⡿⡏⠙⠡⢟⣴⡿
⠀⠀⠀⠀⣰⣿⡿⠓⣫⣾⣿⡙⢃⡿⡿⢱⢧⣿⣿⣦⣄⠀⠈⢻⣷⡄⠈⣇⢻⣼⣻⡜⢧⢿⠀⡇⣿⣼⣷⡿⠶⠞⠛⠉
⠀⢀⣴⡾⠟⣫⣴⣟⠻⣿⡌⢁⣾⣧⢃⡿⣼⣿⣿⣿⣿⣦⡀⠀⢻⣿⣄⢻⡘⣿⡇⣿⡘⣸⣾⠿⠛⢉⣠⣤⣶⡺⣿⡟⣿⡿⢿⣿⣷⣶⣤⡀
⠀⣾⡟⠀⣨⣷⠶⣮⡕⠈⣠⣿⢸⠇⡼⣹⣿⢿⣿⣦⡙⠻⣿⣄⠈⣿⣿⡞⣧⢸⡇⢿⣿⠟⢁⣴⢞⡏⣽⣿⣿⡟⢿⡻⣥⣶⣸⠷⠞⠛⣿⣿⣆
⠀⣿⣧⢸⣿⡇⢶⣿⠃⢠⡛⣿⠃⣴⡷⠿⣿⣷⡈⠙⠿⣆⢈⣿⠀⣿⣿⣿⡽⣾⡁⡾⢡⡾⢋⡻⣉⣶⢛⣿⢿⣿⢿⡓⡄⣤⣉⠻⢿⣠⣏⣻⣿
⠀⠘⠻⡏⠿⣷⣦⠀⢠⣿⣷⢃⣼⣿⣿⣆⣀⣉⣿⣄⣀⣹⣿⠁⢀⣿⡿⣿⣧⠈⠛⣵⣯⣟⣻⣯⣭⡥⠛⣿⣿⣿⠿⡟⢻⡜⢿⣿⡌⢻⣦⢉⣿⡄
⠀⠀⠀⣿⣄⡀⠀⢀⢞⡿⣡⠾⠟⠛⠋⠉⢉⣉⣉⣉⣉⣉⡉⠀⢸⡿⣏⣻⢿⠀⠀⣹⣷⣪⢭⣭⣭⣴⣿⣿⡿⣿⣿⣯⢿⣇⠀⣿⣿⠀⣿⡛⢾⣿⡄
⠀⠀⠀⠹⣿⣿⣇⡾⠟⠉⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣝⠻⣿⣇⠘⠿⢶⠶⠾⠀⣀⣛⠛⠿⠶⢦⣭⣽⣶⣾⡏⣿⢿⢧⣾⡿⢀⣿⡿⢠⣿⣛⣠⣿⣿
⠀⠀⠀⠀⠈⠉⠁⠀⣠⣴⣿⣿⠟⢉⣤⣤⣤⣉⠻⣿⣿⣧⠘⣿⠟⣠⣶⣶⣶⣿⡝⣯⠙⢳⡶⣤⣈⠙⠻⢿⣷⠃⣼⣆⣿⣧⡾⠟⢡⣾⠹⣇⣽⣿⡿
⠀⠀⠀⠀⠀⢀⣤⡞⡇⡿⢻⡇⠠⣿⢟⣛⢿⣿⣧⠸⣿⣿⡶⢣⣾⠟⢙⣛⠙⢹⣇⣿⢶⣼⣷⣿⣿⣷⢦⡀⠙⢳⡄⣸⣿⣁⣤⡾⣯⣉⣀⣿⣿⠟⠁
⠀⠀⠀⠀⢠⣾⣿⡇⡇⣿⣿⣧⡀⠻⠾⠟⣸⣏⣿⠀⣿⡟⢠⣟⣡⣴⣿⣩⣻⢀⣿⣿⣇⣹⣿⣿⢸⢿⣧⡙⢶⡀⠙⣿⣳⣷⣍⣰⣧⣼⣿⠋⠁
⠀⠀⠀⢠⣿⣿⢸⡇⢻⡸⣿⢻⣿⣶⣶⣾⡿⣿⡿⢰⡟⢠⣿⡟⣿⣿⣿⣬⣥⣾⡇⣿⡟⣿⣿⡏⡘⠈⢿⣷⢏⣿⣆⠈⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠸⣿⣿⢸⣷⠘⣧⠹⣿⣿⣉⣻⣿⣷⡿⢡⢾⠃⣾⢻⡃⠹⡜⢿⣿⣿⣿⣷⡇⠿⣿⣿⢣⣿⣆⢸⢏⢪⣿⠿⣆⠀⠀⠉⠙⠉
⠀⠀⠀⠀⠘⣿⡄⢿⣧⠹⣷⣄⡉⠛⠛⢛⡡⠔⣡⡾⢰⡿⣿⢸⣄⠙⢮⢻⣿⣿⣾⢰⣿⣿⡿⡌⢸⣿⢏⢂⣾⠋⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣌⠻⣷⣬⣍⣙⣋⣩⣥⣶⡿⢿⡇⣸⡇⣿⡧⣩⣥⡈⢧⣿⣿⠇⣼⣿⣿⢷⣿⣀⡿⢣⡞⠁⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⢡⣦⠈⢿⣿⠿⠛⠛⣩⣴⣿⡇⣿⡇⠈⣵⣿⡹⠟⣸⣿⡟⢠⣏⣿⣿⠋⣿⣟⡵⠋⣤⣦⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣸⣿⣠⣿⣧⣤⣴⡾⣻⣿⣿⠇⢿⡇⠀⢹⢻⣿⣾⣿⠟⢀⡞⣸⣿⣿⣴⣿⠟⠁⢸⣿⣦⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠋⠀⢸⣿⣄⣚⣼⣿⡿⠋⢠⠞⢀⣿⢟⣿⠟⣵⣟⢇⣼⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣟⣀⣰⣏⡀⣼⣿⠟⣁⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡤⣀⡚⣣⡄⣴⣶⣿⣿⣿⣶⡴⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣦⣶⣿⡿⣿⣿⣿⠛⢿⣟⣻⣿⣿⢻⠛⠀⠐⢉⣰⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣿⣦⣿⣿⡿⠿⣿⣭⣤⠃⢰⣿⣿⣿⣿⠛⠀⠀⢀⠈⢉⢻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣟⣿⡿⠿⠟⢿⣺⣷⣿⣿⣿⠇⠋⠐⠀⠀⠀⠀⠈⠁⠉⠙⠻⢿⣿⣿⣿⣷⣄
⠀⠀⠀⣾⣿⣿⣿⣟⡹⣟⣭⡖⠀⣶⣼⣿⣿⣿⡟⢻⡡⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⡀
⠀⠀⠈⢩⣷⣿⣽⠿⣿⡟⢁⣤⣾⣿⣿⣿⣿⣿⣷⠏⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣠⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡀
⠀⣴⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣯⣦⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠡⠻⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣿⣿⣿⣷⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢠⣿⣿⣿⣿⣿⡛⣩⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢼⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣰⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢡⡟⠛⣻⣿⣿⣿⣿⣦⣶⣶⣶⣶⣾⣿⣿⣿⣡⣴⣶⣶⣶⣦⣤⣴⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⡟⢀⢆⣰⣄⣠⡚⠁⠀⠀⢀⣉⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⠈⣧⣸⣿⣷⡿⠋⢷⣤⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢻⣟⣟⠛⠛⢳⡈⢿⣿⠟⠁⣁⡈⣿⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠉⠙⢿⣷⣤⣤⠹⡿⣷⣾⠷⢹⣿⣿⠈⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠷⢷⠞⡿⢲⣿⠋⠘⣦⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣟⢁⣠⣼⣿⣿⣿⣷⣿⣽⣿⣿⣻⣻⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⢀⣴⣷⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠶⠾⠿⠿⠿⢦⣤⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡶⠞⣩⣷⣜⡻⠿⠍⠹⠿⣛⣴⣮⡛⢿⣆⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢫⡴⢃⣿⣿⣿⣟⣿⣶⣶⣿⣻⣿⣿⣧⠻⣮⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⡟⣵⣶⣾⡿⠟⠛⠻⢿⣿⣧⣼⣿⡿⠿⠻⠿⣿⣶⣶⡌⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠙⣳⣞⠋⣠⠖⠛⠒⣦⠹⣿⣿⢋⡴⠒⠒⠦⡈⢓⣫⣛⠘⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⢸⡰⣴⣳⡧⠴⠶⠶⠼⣇⢻⠃⣯⡤⠤⠤⠤⣽⡸⣴⡆⡇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⢠⠟⡉⠘⢧⣀⣀⣠⠔⣁⡀⣀⡑⢤⡀⠀⣠⠞⠉⠛⢾⠁⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢿⠸⠭⣳⠀⠈⢁⣴⠞⡁⢱⠁⡙⢶⣍⡉⠁⠀⣾⠽⢆⡇⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⣽⣯⣅⠀⢾⣟⣁⠀⠃⠈⠐⠤⣀⣹⣿⠆⠀⣨⣑⣯⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣜⢿⡻⣦⡀⠈⠄⣖⣀⡠⠀⣀⡠⠅⠀⣠⡾⣫⡝⣵⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⡻⢮⡟⣷⡀⠤⢤⡄⢰⠤⣄⣲⢟⣥⠾⣫⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢶⣭⣋⡉⠯⠰⠆⢴⡤⠟⢙⣪⣵⡾⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠻⣿⣿⣿⡿⠛⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠻⠏⠀⠀⠀⠀⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠚⠲⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠀⠘⠃⠀⠶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠫⣁⠡⠀⣀⠙⢁⡀⠰⢄⡩⠟⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠋⠂⠴⡥⠒⠈⢄⢈⢠⠍⠐⠢⡵⠄⠺⢣⠄⠀⠀⠀⠀⢤⠀⠀⢀⠐⠄⣀⠠⠈⠡⠄⡀⠠⠂⡀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣃⢁⣧⠀⢀⠠⠤⠠⡆⡶⠠⠤⢀⡀⢠⣇⢁⣫⠀⠀⠀⢠⠀⠀⠠⢀⠁⠋⠀⠀⡒⢒⠀⠀⠙⠈⠀⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣺⢃⡝⠀⠃⠉⠀⠄⠛⠣⠛⠃⠄⠈⢁⠃⠈⣅⢸⡂⠀⠀⣀⠀⠀⢑⠂⠃⠚⠀⠰⢧⡿⠄⠠⠓⠈⠐⡈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢽⡄⣡⠂⠠⣇⠒⠀⠀⢠⠀⠀⠘⢂⡧⢀⢂⡉⢸⠅⠀⠀⠉⠀⠀⣉⡄⠀⣆⠂⠀⣀⡀⠀⠂⡹⠀⢠⣉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡌⡌⠔⠂⢉⡀⠠⠈⣌⡍⠀⠀⢈⠁⠒⠌⡌⣟⠀⠀⠀⠘⠀⠀⠠⠐⡀⠠⢄⠀⡔⢆⠁⡠⠄⠀⠂⠂⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⠄⠢⣉⠵⢆⡙⠠⠚⣁⠶⠍⡡⠃⢤⡜⠀⠀⠀⠀⠀⠲⠀⠀⠈⢨⠂⡉⠲⠄⠠⠖⡉⢀⠄⠁⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡀⠔⠊⠙⣠⡘⠉⠐⣅⣈⠴⠃⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠖⠾⠤⠼⠖⠎⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠤⠀⢠⡀⠀⡤⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠚⠀⠈⠃⠀⠚⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠴⠖⠒⠶⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣤⠛⠍⡨⠄⠀⡘⢋⠀⠀⠌⠈⡝⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⡀⠂⢰⠀⠀⠁⠀⠠⠄⠂⡀⠀⠀⠴⠀⠀⠀⠀⢠⡜⠑⠤⢊⣈⠅⢵⣖⢐⡶⠬⢁⡉⠢⠐⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠄⡈⣴⡮⢎⠛⠘⢋⠤⡶⣌⡀⠀⠀⠀⣤⠀⠀⢀⣝⡈⡐⣜⣫⡽⣋⡍⣬⣡⣡⣍⣻⡝⡣⡔⡘⣹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⡘⢠⣨⢿⡃⢘⠛⢀⣷⣏⣬⢐⣀⠀⠀⢀⡀⠀⢐⣏⣸⠁⣤⣄⡝⣇⣀⠍⠩⣄⣨⡾⣇⣤⡀⣇⡱⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠹⠰⠾⡽⠚⠒⡐⠚⠺⡵⠦⠸⠁⠀⠀⠈⠁⠀⠸⣎⢹⡃⣴⡍⣻⡴⠶⠾⡰⠶⠆⣟⣸⣦⡄⣋⣱⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢃⠴⡆⢀⣤⢨⣄⢀⡶⠀⠂⠀⠀⠀⠛⠀⠀⠈⣯⢁⢡⠐⣢⡅⠈⠐⠂⢓⠂⠀⠘⣅⠂⡠⠡⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠁⠔⡠⠂⠀⡆⠀⠢⠐⠄⠁⠀⠀⠲⠀⠀⠀⠀⠐⢣⠢⠓⢍⠣⡈⠻⠟⡘⠟⢁⠘⣋⠐⠤⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠛⡬⣊⠑⠊⠀⢸⡗⠀⠁⠊⢁⣦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢰⠀⠀⡄⠀⢠⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠲⠦⠄⠖⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⢾⠛⠛⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠆⡫⡉⢉⢝⠲⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢠⣶⡜⣷⣎⢣⣶⡄⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣬⣿⢡⣿⣻⡌⣿⣤⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠩⢉⡝⠀⡀⢩⡉⠍⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣀⣮⣴⠀⠀⣦⣵⣀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡽⠞⡳⢜⠳⢎⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠿⠿⠿⠿⣶⠖⠁
⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠰⣯⡈⢧⣆⣰⡼⣁⣼⠆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀
⠙⣧⠀⠀⠈⢷⣌⠻⣿⣷⣿⣐⣻⠉⣧⠉⣶⠁⢱⠘⣧⣴⢗⡟⡹⡅⢩⢟⢻⣻⣦⣽⠒⡆⠉⣴⠉⣼⠁⣟⣂⣿⣾⣿⠟⣡⡾⠁⠀⠀⣼
⠀⠈⠳⣀⠀⠀⠙⠛⠦⣍⣋⣛⠛⠿⠿⠿⠿⣾⣾⣿⢿⡧⣿⣷⠷⢤⡤⠾⣾⣿⢼⡿⣿⣷⡷⠾⠿⠿⠿⠛⢛⣉⣩⠤⠚⠉⠀⠀⣀⠾⠁
⠀⠀⠀⠈⠻⢦⣤⣀⣀⠀⠀⠉⠉⠙⠓⠚⠒⠚⠓⠒⠚⢻⢿⣯⡜⠃⠘⢣⣼⡿⡟⠓⠚⠚⠓⠒⠓⠛⠋⠉⠉⠁⠀⣀⣀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠛⠒⠟⠲⠾⠒⠶⠞⣿⢚⡏⠀⠀⠀⠀⢹⡛⣿⠳⠖⠒⠶⠞⠛⠚⠓⠒⠚⠛⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⡁⣀⣤⣤⣀⢈⡇⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡠⠟⠋⠐⠀⢝⠻⢄⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠛⠛⠛⠛⠁⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠲⠒⡖⢲⠒⠒⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣧⣴⣤⣧⣼⣤⣦⣾⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⢨⣍⢿⡿⣩⡇⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⣍⢷⡄⢊⡓⢠⡾⣨⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⣳⢤⢶⢿⡿⡶⡴⣞⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢋⣙⠦⣶⣶⠴⣋⡙⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠋⡤⠂⠐⣤⠙⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⢟⠁⠙⠃⠀⣻⢽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⢭⢤⡖⢰⡤⡭⠆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣽⣶⡷⢼⣶⣯⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠸⣇⠉⢧⡼⠉⣸⠆⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⣉⡔⢚⠓⢢⣩⡶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣒⣼⠗⠐⠂⠺⣷⣣⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣙⡁⠀⢻⡖⠀⣈⣋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⠻⠟⢻⠟⡟⢃
⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡆⢀⠜⠀⢙⠂⠐⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢤⣄⣨⠀⠀⠄⠠⠚⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⢬⣏⠻⠶⠾⣦⣤⡀⠀⠁⠔⠁⠀⣠⣤⣤⡴⠶⠞⣛⡡⣻⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠉⠈⢫⣢⡌⠙⠳⢤⣅⣰⡏⡹⢉⠏⣹⢉⣉⣀⣠⡤⠖⠚⢡⣠⠟
⠀⠀⠀⠀⠀⠀⠀⡁⠀⢈⠌⠻⣄⣴⠀⢆⠀⢨⠗⢥⢈⡰⣁⠾⠏⠉⢀⢁⢠⣄⣌⠟
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄⠐⠈⠛⠐⢿⠡⣸⡆⣘⢘⢐⣓⠀⣾⡄⠸⠧⠊⠛⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣃⢀⡀⢀⠀⡘⠀⢠⠶⠶⠴⠞⠚⠒⢋⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠸⣈⠀⠀⠀⢸⠀⠆⡀⡀⠉⠎⠸⠀⠀⠀⡀⡅⠀⠇⠀⢀
⠀⠀⠀⠀⠀⠤⢄⠀⢁⠀⠀⠀⠄⢻⡠⠈⠇⢸⠈⠀⠀⠀⠀⠈⢐⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠆⠀⠈
⠀⠀⠀⠀⠸⡠⠈⡆⠈⠀⡄⠄⠀⢀⠄⢚⠀⢸⡀⠘⠙⠛⠛⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠰⠁⠀⠑⡀⠀⢀⠀⠀⢸⠄⠘⠀⢈⠁⠀⠀⠀⠀⠀⠡⠘⠀⠚⠈⢲⠂⣆⠀⡆⣠⢰⣴
⠀⠀⠀⠀⠀⠣⡀⠀⠱⡈⡄⠑⡀⢸⠀⠀⡘⢩⠀⠀⠀⠀⠀⠀⠰⠄⠄⠈⠈⠈⠈⡌⠠⠁⠅⠍⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠈⢗⠸⠀⠸⡀⠄⠀⠰⠀⠃⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠫⠀⠀⢤⡈⢣⡁⠀⠇⢰⠀⡰⢀⣐⣒⣒⣛⣂⣠⠀⠀⡀⢀⢀⠀⠀⠁⠊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢷⠀⠸⣻⠎⢀⠃⠀⠀⠀⠀⠀⢰⠀⢀⡘⠀⠐⠂⡀⡠⢁⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠿⠂⢀⣀⠀⠁⠀⠒⠁⠺⠊⠂⠀⠀⠠⠄⠒⠞⠀⠒⣓⠲⡖⠚⠓⡤⢥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡢⠤⠄⠁⠤⠤⠄⠐⠐⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣶⣶⣤⣤⣶⣶⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠙⢦⠻⣮⣙⡛⢛⣋⣵⠟⡴⠋⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⢠⠹⢚⣶⢶⣶⣶⡶⣶⡓⠏⡄⢠⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⡿⢣⣗⠒⠢⠌⣿⣿⠡⠔⠒⣺⡜⢿⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⡇⡞⣓⣦⣌⣚⡲⢖⣑⣡⣴⣚⢳⢸⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾⣧⢳⡟⠁⠈⣩⢵⡎⣍⠁⠈⢻⡞⣼⡷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⣠⣴⢆⡆⢯⢾⡷⡽⢰⡰⣦⣄⢀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠿⠟⠛⠸⠗⣉⣤⢤⣉⠺⠇⠛⠻⠿⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠿⠷⠒⢿⣫⣛⡽⢯⣛⣝⡿⠒⠾⠿⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠸⠿⡿⠶⢾⡖⠛⣒⣫⣝⣒⠛⢲⡷⠶⢿⠿⠇⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣷⡀⣦⣮⢳⣷⡮⢻⡟⢵⣞⡞⣵⣴⢀⣾⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣬⣝⢮⣻⠇⣀⣀⠸⣟⡵⣫⣥⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣶⣬⣩⡍⢩⣍⣥⣶⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠻⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡄⠀⠀⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⣦⣤⣤⣤⣤⣴⣿⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⣼⠋⠙⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣯⣽⠆⠀⠀⠰⣯⣽⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠋⠙
⠻⣄⢴⣷⠆⠀⠈⠙⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠋⠁⠀⢰⣿⡦⣠
⠀⠹⣆⠁⠀⢀⣄⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠘⣧⣼⠃⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣤⡴⠖⠛⠉⠁⠀⠀⠀⠀⣠⡀⠀⠈⣰⠏
⠀⠀⠘⣧⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⣇⠀⢸⡇⠀⠈⠁⠀⢸⡇⠀⣸⠏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⣼⠃
⠀⠀⠀⠈⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⠾⠷⠶⠶⠶⠶⠾⠷⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠁
⠀⠀⠀⠀⠈⢷⣄⣀⣀⣆⣀⣀⣖⣀⣐⣆⣀⣀⣆⣀⣀⣆⣀⣠⡟⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢻⣄⣀⣲⣀⣀⣰⣀⣀⣰⣀⣀⣲⣀⣀⣀⣀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⢻⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠰⣯⣽⠇⠀⠀⠸⣯⣽⠆⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢾⣿⠆⢾⣿⠆⢾⣿⠆⢾⣿⠆⢸⡇⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠰⣿⡷⠰⣿⡷⠰⣿⡷⠰⣿⡷⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣁⣀⣀⣁⣀⣀⣁⣀⣀⣁⣀⣸⡇⠀⢰⣏⣉⣉⣉⣉⣹⡆⠀⢸⣇⣀⣈⣀⣀⣈⣀⣀⣈⣀⣀⣈⣠⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣧⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⠶⠶⠶⠶⠶⠶⠶⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢯⡽⠇⠀⠀⠸⢯⡽⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⣏⣹⡏⢹⣏⣹⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠹⡿⢿⠏⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠶⠶⠶⠶⠶⠶⠶⠶⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣠⣄⡀⠀⠀⢀⣠⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠾⠃⠀⠀⠘⠷⠾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢻⣟⠛⣻⣟⠛⣻⣟⠛⣻⣟⠛⢻⣟⠛⢻⣟⠛⢻⣟⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣤⣽⣯⣥⣽⣯⣥⣽⣯⣥⣽⣯⣥⣽⣯⣥⣽⣯⣥⣽⣯⣥⡽⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣤⡶⠞⡁⢈⠳⢶⣤⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠿⢿⣶⣿⠏⣴⣿⡇⢸⣿⣦⠻⣿⣶⡿⠿⠟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⠈⠳⢶⣬⡙⣼⣿⠿⡧⢸⠿⣿⣧⢋⣥⡶⠞⠁⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⡇⢸⡆⠱⣄⣉⠛⣋⣥⣦⡄⢠⣶⣬⣙⠛⢉⣠⠎⢸⡇⢸⡆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣸⡇⢐⣚⡛⠻⢿⣿⣿⡇⢸⣿⣿⡿⠟⢛⣓⡂⢸⣇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⢁⣿⡿⠛⠛⠛⠻⣦⡙⢿⣧⣸⡿⢋⣴⠟⠛⠛⠛⢿⣿⡈⠁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠄⠸⠃⠠⠤⠤⢤⣤⣈⢻⣤⡄⢠⣤⠟⣁⣤⡤⠤⠤⠄⠙⠇⠠⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⢠⡄⠀⢄⣀⣀⣀⣄⣉⣁⣜⠇⠸⣣⣈⣉⣤⣀⣀⣀⡠⠀⢠⡄⡇⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣾⣿⠳⠦⣤⡬⠄⣀⣭⣩⡍⡆⢰⢩⣍⣭⣀⠠⢥⣤⠴⠞⣿⣿⡇⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡈⢿⣿⡄⠶⠶⠶⢿⠟⣋⣡⣼⡇⢸⣧⣌⣙⠻⡿⠶⠶⠶⢠⣿⡿⢁⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⡛⠟⢳⣶⣶⣄⢈⣶⠶⢟⣁⣈⡻⠶⣶⡁⣠⣶⣶⡖⠻⢛⣡⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣠⠤⠉⠛⢈⡵⢛⣉⣉⣉⣉⡙⢮⡁⠛⠉⠤⣄⡈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣾⢁⣤⣤⣀⣶⡶⠟⣩⣥⣬⣍⠻⢶⣦⣀⣤⣤⡈⣷⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠻⢾⣿⠿⠟⢫⣴⣾⠛⠁⠈⠛⣷⣦⡝⠻⢿⣿⡷⠟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⣠⡴⣿⣿⢧⣀⠀⠀⣀⡼⣿⣿⢦⣄⣀⣀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣩⠀⠻⣯⡉⠩⡵⢶⣌⡛⠷⠤⠀⠀⠤⠾⢛⣡⡶⠮⠍⢉⣽⠟⠀⣌⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠃⣾⢰⣮⣭⣅⡄⠀⢠⣿⣷⢰⡇⢸⡆⣾⣿⡄⠀⢤⣨⣭⣵⡆⣷⠘⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣿⠂⠥⠶⣦⣤⡶⢋⣭⡵⠾⠇⠸⠷⠮⣭⡙⢶⣤⣴⠶⠬⠐⣿⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⢿⡶⠟⢓⡂⣉⣴⢏⡵⠂⣠⡄⢠⣄⠐⢮⡹⣦⣉⢐⡚⠻⢶⡿⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡄⢸⡿⢛⡛⠋⢸⡇⠰⣿⡇⢸⣿⠆⢸⡇⠙⢛⡛⢿⡇⢠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣰⡟⢰⣾⣿⠗⢀⣿⡇⢸⣿⡀⠺⣿⣷⡆⢻⣆⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡘⣿⣿⣿⣦⣹⡇⢸⣏⣴⣾⣿⣿⢃⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠙⠿⠇⠸⠿⠋⠛⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⡁⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⣿⣷⢍⢴⣿⡶⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⠯⢿⣿⣯⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢧⣷⣶⠜⢼⣾⡦⠙⠋⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⣸⣿⣇
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢘⣠⡟⣆⣛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠉⠉⠉⠹⣾⣾⣿⣿⡿
⠀⠠⢤⡠⠴⡗⠋⠉⠉⠉⠁⣜⣀⣍⣠⣉⡀⠉⠉⠉⠉⠳⡷⠄⣠⠄⠀⠀⠀⣀⢨⠁⠄⢩⢠⡀
⠀⠘⢉⠿⣔⡄⠀⠀⠈⠀⢰⠶⢶⡟⣶⠶⡦⠀⠀⠀⠀⠀⣴⠿⡍⠅⠀⠀⠄⠘⡄⢀⡆⠘⡜⠐⠄
⠀⠀⠀⠀⠁⠃⠀⠀⠈⠀⢸⣿⣿⡄⣿⣿⣟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⠀⢘⣛⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⠀⢿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢶⣌⢋⣴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠭⣍⠉⢉⡭⣅⠀⠀⠀⠀⠂⠷⠖⣶⠒⣶⠒⣧⣀⣸⣿⣻⣿⣀⣠⡗⢲⠖⢲⠖⠷⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣔⡼⢠⠸⣔⡼⠃⠀⠀⠀⠀⠀⠀⣿⠀⠿⠀⢿⣿⣿⣎⢩⣿⣿⣿⠇⠸⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣚⣛⣻⣿⣛⣛⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡘⠪⡒⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⢿⣿⢿⡿⠋
⠀⠀⢄⣠⣠⣠⣀⡀⠀⢸⣃⣴⣿⠀⣼⣷⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢖⣴⡷⠐⠶⠂
⠀⠀⠀⠀⡂⠴⠀⠀⠀⠸⣿⣏⣿⡀⣽⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⡎⠉⠄⠀⣶⣶⡦
⠀⠀⠀⠀⠂⠧⠀⠀⠀⠀⠉⠹⣿⠗⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠐⣦⣤⡖⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠶⣾⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠧⠣⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣷⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⠛⠻⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠉⠻⠿⠉⠉⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣞⠉⢙⡲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢈⠲⣀⡲⣁⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣄⣛⣁⣿⣇⢻⣃⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⡝⠉⠙⡍⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣼⢴⡠⣰⣼⣄⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢖⣛⣕⣍⣃⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡛⠋⠀⢈⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠸⣯⡻⣿⣿⣯⠛⡏⣍⢩⡍⠩⡙⣇⢼⢛⠻⡋⡻⠛⢻⣤⡟⡩⠉⣭⢉⡍⡟⢋⣿⣿⡿⣫⡿⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⠛⠦⢭⣹⣛⡛⠷⠾⠶⠾⠷⢿⣾⣿⢷⣴⡵⢿⣿⢾⠿⠷⠶⠾⠾⠟⣛⣛⣩⠥⠞⠉⢀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⣉⢉⣉⣉⣉⣉⣉⣉⡝⣿⠎⠁⠉⢾⡟⣍⣉⡉⣉⣉⣉⣉⢉⣁⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢩⠋⡏⠀⠀⠀⠈⡇⢯⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡷⢞⠉⢙⠶⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠀⠓⠲⠒⠃⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⡛⡛⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠺⢶⣷⣷⠿⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢬⡋⠽⠍⣫⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣓⣤⢥⣾⣦⢥⣜⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⡢⠶⠦⣞⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠔⣤⡔⣬⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⢠⣈⣀⢰⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣥⣭⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡯⣽⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣣⠈⢲⡎⠠⡃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣳⡆⠘⠀⣶⢋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠁⢄⠄⠙⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠿⠷⠾⠇

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

⠀⠀⠀⠀⠀⣰⣆⢠⣄⠒⠠⠒⠖⠀⢠⡴⡶⠶⣤⡀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢠⡀⣄⢀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⢀
⠀⠀⠀⣶⣤⠛⢹⣸⣿⣷⣾⣿⠆⠀⣿⣿⣟⢿⣻⡇⠀⠘⢧⣆⡁⣿⢠⠀⣨⣷⣿⣿⣾⡴⣀⠀⠠⣤⣌⢻⣦⣽⣂⣸⠄⣠
⠀⠀⠀⣿⠟⠇⢺⣿⣿⣶⣿⣷⠀⠀⢿⣧⣴⡟⣶⡇⠀⠀⠈⠉⢿⣏⡟⠠⢞⣿⣿⣿⣿⣯⠥⠀⣤⣴⣼⣿⠟⢻⣿⣿⡾⢃⣀
⠀⠀⠦⡙⢰⡿⣿⡷⠛⣛⣨⣭⡀⠀⣼⣿⡟⢓⢻⡇⠀⠀⠀⠀⢀⠀⠀⠀⠈⠸⠹⡟⢯⠛⣀⠀⠀⠀⠙⠃⠠⠽⢶⡋⠛⠛⠁
⠠⣴⣶⣾⣾⣿⣿⠷⣿⣮⡉⠉⠁⠀⣝⠿⣿⣿⡿⡁⠀⠀⢀⣾⣿⣷⣷⣦⡀⠀⠀⠀⠀⠞⡽⠦⠀⠀⣤⣴⡀⠀⠀⢠⣴⡇⡀
⠀⠙⢿⣟⣯⣤⢿⣿⠿⠟⠀⠠⣾⣆⠈⠁⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣷⡄⠀⠀⠀⡾⡽⢆⠀⠖⢿⣋⣿⠦⠀⠐⠛⠙⠷
⢼⣟⢿⣽⣿⣾⣷⣿⠗⠀⠀⢈⣉⡂⣶⣶⣶⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⣀⠀⣀⠀⠀⠀⠀⠛⠀⠀⢀⣿⣄⣤⠄
⢠⣾⣭⠋⣼⡼⣯⠛⢬⣧⢰⣿⣿⣿⣿⣿⣿⣿⣆⠻⠿⠿⠯⠭⠭⠽⠿⢿⠿⠿⠷⢘⣿⠈⣻⡃⠀⠀⡴⣄⠀⠛⣿⣿⣿⣿
⠚⠛⣁⣟⡻⣗⣚⣳⣝⡟⠀⣾⣿⡿⣶⣆⣼⣶⠀⣿⣷⡄⣿⣿⠀⠀⢠⣿⣸⣿⡄⢸⣿⠀⣿⡇⠀⢨⠏⡭⠀⠀⢸⣿⣻⡾⢧
⠀⢰⣿⣿⡼⣻⡾⢭⣿⣝⠀⠙⠉⢠⣿⣧⣼⣿⠀⣿⣿⣇⠘⣿⣾⣧⣾⠇⣿⣿⣷⠀⣿⠀⣿⠇⠀⠈⣭⣭⠀⠀⠘⢃⡀⠀⠈
⠀⣾⣾⡏⣿⢏⣿⠝⣻⡟⠀⠀⠀⠀⣿⡏⠉⣿⣸⣿⠙⣿⠀⣿⡏⢻⡿⢠⣿⡏⢻⡆⣿⠀⣿⠀⠀⠀⠈⠁⢶⣄⣤⣾⣇
⠀⠹⣿⣿⣜⢿⡽⡏⠿⠀⢀⣀⠀⠀⠉⣁⣀⣡⣭⣥⣤⣤⣶⣶⡶⣶⡶⢶⡶⢲⣶⣶⣶⣶⣤⣤⡤⠄⠀⠀⣦⣿⣗⣿⢾⣿⠛
⠀⢀⣿⢹⡿⣀⣿⠋⢀⣴⣿⣋⠃⢠⠟⣻⠟⠩⠿⠉⠿⠃⠚⠋⠈⠋⠀⠉⠀⢈⣭⣟⡓⡄⠀⠀⢀⣠⣀⠀⣼⣿⢾⠯⣿⠇⠃
⠀⢠⣿⡟⡱⡞⣿⡄⠉⣩⣭⣉⢁⠠⣤⣤⡄⠀⠀⠀⠀⣿⣭⣕⣲⣄⠀⠀⠰⠟⠋⠉⠿⣿⣄⣄⢼⣿⣿⠑⠏⠉⠛⠛⢻⡇
⠀⣼⣏⢸⣷⢃⡟⠀⠀⣷⣿⣼⣧⣷⣿⣼⡇⠒⣮⡷⠸⠿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣴⣷⡛⣻⢛⠟⣎⢷⣠⢖⡲⡄⢀⡈
⠀⠸⡏⢸⡟⠈⢠⡄⠀⠃⠒⠐⠆⠲⠂⠖⠐⠈⣩⣶⣿⣿⣿⣿⡀⣾⣇⡀⠀⢀⣾⠟⢤⡿⢿⣿⠒⣻⣾⡿⠛⢿⣷⢨⠟⡶⣏
⠀⠀⠀⠀⠃⠀⠹⢿⣿⣟⣛⡻⣦⡀⠀⠀⠀⣼⣿⡻⢽⣛⡿⣿⣷⠙⢢⡤⣤⣞⣿⠛⣻⣷⡾⣏⢙⡿⣽⡿⠀⠸⡿⠀⠀⠃
⠀⣀⣤⣤⠴⡶⢶⢢⢹⡟⣭⣻⢘⣷⣄⠀⠀⣿⣯⣭⣛⡳⢶⣾⡿⠀⣿⣶⠾⢷⣻⣯⢹⡏⢣⣌⡿⣵⣿⠃⠀⠀⠀⣼⢣
⠘⢯⣦⣿⡶⣷⢾⡏⠘⢷⣮⣥⣾⣼⣟⡆⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠘⡏⠀⠘⢮⡻⣿⡿⡿⣋⣾⣿⢧⠀⠀⢠⡰⢶⢧⢶⣄
⠀⠀⢻⡟⣧⣿⣼⡇⠀⠀⠀⠘⠋⠭⠟⠷⠀⠀⠈⠚⠛⠋⠁⠀⢰⠆⠰⠖⠀⠀⠀⠙⠓⠛⠛⠋⠉⡷⣲⠇⠀⠽⠩⠭⠎⠯⠽
⠀⠀⠸⣿⢿⣿⣿⡇⠀⠀⠣⣣⣣⡣⢃⣶⡘⢜⣜⣼⡼⢠⣢⠀⠰⠆⠰⠧⠀⣀⠀⢀⠀⠀⡀⠀⣞⠛⢁⠀⠀⠲⢲⣖⢆⣖⠲
⠠⣤⠀⢹⣿⣿⣿⣧⣄⠀⠀⠑⡕⣡⣭⣭⢟⢌⢊⠞⡰⡱⡱⡱⡀⠀⠀⢀⢾⣯⣰⣛⢀⣻⣃⣚⢏⣰⣻⡀⠀⠱⢡⠭⡼⡬⠑
⢘⣒⠀⣯⢿⣹⣖⣷⡻⠀⠰⠠⠴⠡⠼⠌⠮⠌⠦⠄⠆⠄⠆⠤⠆⠤⠆⠈⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠙⠃⠀⠀⠀⢛⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠻⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⡟⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣦
⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣰⡟⢻⣶⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⣾⡛⠛⠋⣼⣿⣏
⠀⠀⠀⠀⠀⠀⣿⣽⣷⣶⣄⢀⡈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠷⣾⡿⠶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣇⡀⢀⣀⣀⠀⢀⣴⠀⠀⣀⣠⣶⣾⣿⢋⣉⠈⢹⣿⠋⠛⠿⠿⣦⡐⣤⡝⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡎⢻⠏⠻⢿⣿⣻⣄⠈⢻⣷⣾⠛⠟⠛⠛⣀⣀⡘⢿⣾⢿⣿⠇⢀⣀⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⡆⠰⠀⢹⡟⠁⠐⣾⣏⠉⠳⣦⣀⣴⢿⣯⠿⠿⠏⠈⣡⡔⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣴⣾⡏⠙⠻⠟⢻⣷⣶⣿⣧⠁⠜⠃⠀⣰⣶⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⣭⣿⡆⠀⢾⣿⢻⣿⠛⣃⣀⣴⡶⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⢻⣿⣿⣶⣤⡿⠟⠉⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⠟⢿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡟⢀⣄⠀⣼
⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣾⣷⠿⢻⣿⣇⣸⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⣿⠋⠀⠘⢻⣽⣿⡷⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡶⠆⣀⣽⣿⣷⣾⡿⠉⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢏⣽⡿⠋⣿⣆⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡿⠓⠚⣉⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣇⣹⣦⠾⢿⣿⣿⡝⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣶⣿⣶⣿⣿⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⣌⠙⠛⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣿⠶⠶⣟⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢀⣶⠶⠟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠶⠋⣡⣤⡄⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢶⣾⣿⠿⣿⣄⡀⢻⣷
⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠙⠷⣄⣽⣿⣦⡈⠻⣿⣤⡟
⠀⠀⠀⠸⣿⣴⣧⡀⠀⠀⠀⠀⠀⢨⡅⠀⣿⣧⣴⣿⣿⣧⡀
⠀⠀⠀⠀⠻⣿⣿⣿⣦⣄⠀⢠⣤⣿⠃⠠⠟⠋⠹⣿⣿⡏⠁⠀⠀⠀⠀⢀⣴⣶⡆⠀⣤
⠀⠀⠀⠀⠀⠘⢿⣿⠉⠙⣤⡜⠋⠀⠀⠀⣀⠚⠛⣿⣿⣿⠀⣀⣤⣴⣶⣾⣿⣿⣧⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣲⡟⠃⢸⣦⣴⣴⣿⣧⣤⣿⡿⢿⣿⠉⢿⣿⣿⣿⣿⡥⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⡿⠻⣾⣿⣿⡿⣿⣿⣿⣿⣷⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠶⠦⠈⣿⣀⣀⠀⣤⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠄⠀⠘⠋⠛⠃⣤⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣼⡇⠀⠀⣴⡿⠋⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⣷⠖⠀⢀⣴⣦⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠛⠋⠀⢠⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣀⣰⣿⡿⠟⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠘⢿⡿⠛⠀⣠⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠒⢂⣤⣤⠀⠀⢀⣴⣾⣿⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢀⣠⣾⣿⣿⣿⠿⣆⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⣧⠛⠛⠡⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠂⠀⠀⣠⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡞⠛⠿⠆⠀⢀⣤⣴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣀⡈⠀⠀⠀⠈⠛⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠃⠸⢧⣠⣾⣶⣿⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⣈⡀⠸⣿⣿⣿⣿⣿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⢉⣄⠐⠻⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣤⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣯⣼⠻⣿⡀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⢀⣸⡛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠟⠛⣿⣟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠫⣽⣿⣶⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠹⣿⣅⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣿⣿⡿⣿⡿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣿⠏⠉⠰⢿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⢀⠾⠂⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢏⣴⣾⡷⠶⣦⣄⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠈⣠⡿⢃⣴⡟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⣠⣾⣿⣿⠮⢉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⣧⡔⢫⣿⣿⡇⠀⣼⣿⠃
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣆⣼⡿⠛⠋⠉⣠⣾⣿⣧⣤⣄⣀⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣴⣾⣿⡟⣿⣿⣿⡟⣿⣿⣿⣷⣦⡀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⢀⣴⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠻⣿⠀⠀⢀⣿⠟⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡇⠀⢸⣿⢰⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡴⠋⠀⠀⠀⠙⢆⣉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⣠⠔⢆⠀⠰⠢⣀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⣤⣤⡀⠀⣀⣤⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⢟⢛⣛⠻⢿⣿⡿⡟⣛⡛⡻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠀⣤⣀
⠀⠀⠀⠀⢠⣾⣋⣩⡿⣦⣈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⡸⢾⡱⠿⠐⣿⠀⠿⠏⡶⢇⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⣁⣼⢿⣍⣛⣶⠄
⠀⠀⠘⣷⡀⠻⣿⣡⡾⢋⣽⠟⣷⡶⣶⡶⣦⡤⣤⡤⣤⡤⣾⠟⣩⣌⢻⡇⣿⢸⡟⣡⣍⢻⣷⢤⣤⢤⣤⢤⣴⢶⣶⢶⣾⢻⣯⡻⣷⣌⣿⠏⢀⡾
⠀⠀⠀⠈⠳⣤⡈⠙⠷⠿⣯⣾⣯⣴⣿⣰⣿⣡⣿⣡⣿⣰⣿⢸⣿⣿⣼⡇⣿⢸⢰⣿⣿⡌⣿⣄⣿⣘⣿⣌⣿⣌⣿⣦⣿⣧⣽⠿⠟⠋⢁⣤⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⢤⣤⣤⣤⣬⣥⣬⣭⣭⣭⣭⣥⣿⡸⢿⢿⠜⣇⣿⣼⢸⣿⡿⢥⣯⣤⣭⣭⣭⣭⣤⣬⣥⣤⣤⣤⠤⠴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠷⣷⣶⣄⠀⣤⣶⣶⠾⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⢄⡤⣈⠉⣸⠋⣡⢄⠠⣄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠣⣼⣧⠞⣠⠘⣌⠣⣼⣧⠞⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣈⠀⠀⢀⣀⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⠻⠷⠤⠤⣤⠤⠤⠤⢤⡤⠤⠿⠟⣩⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢡⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡌⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⢰⢿⣶⣶⣾⣷⣾⠷⠀⠀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠘⠀⢸⢸⡏⣿⣿⣿⢹⠄⠀⠀⠃⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢸⡇⡏⣿⣿⢸⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⡇⣿⣿⢸⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⣿⣧⡇⣿⣿⣼⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣆⠀⢻⣿⣧⣿⣿⣿⠏⠀⣰⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣼⣶⣤⣈⠙⠛⠋⣡⣴⣶⣧⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣶⣶⣶⣿⣻⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠉⠁⠀⠈⠉⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡴⡂⠐⢦⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⡛⠷⣾⢫⣾⣿⣿⣷⡙⣷⠾⢛⡛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡀⡄⢉⠳⢦⠿⢛⡛⢛⣛⠿⡴⠞⡉⢰⢀⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾⢁⡇⠀⠓⠶⣾⣿⡇⢸⣿⣷⠶⠚⠀⢸⡘⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⣼⠟⠛⠙⠛⢦⡹⠷⠿⢏⡴⠛⠋⠙⠻⣇⠁⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⠀⠁⠀⠉⠙⠒⠦⠻⡆⢰⠟⠴⠒⠛⠉⠀⠈⠀⡈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣾⡷⢬⣄⠈⢉⣛⡛⡃⢘⢛⣛⡉⠁⣠⡥⢾⣷⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⢿⣧⡰⠶⠾⠟⡩⢵⡇⢸⡮⢍⠻⠷⠶⢆⣼⡿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡍⠙⠻⠷⠐⢿⠭⠶⠶⠭⡻⠀⡾⠟⠋⢩⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢰⠋⣡⣀⣠⡵⢟⡋⢙⡻⢮⣄⣀⣈⠹⡆⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠘⠻⠿⢛⣩⡾⢋⢁⡈⡙⢷⣍⡛⠿⠟⠁⠉⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠓⣠⡟⡛⠛⣋⣴⢰⡏⣼⣧⢹⡆⣦⣙⠛⢛⢻⣄⠚⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢁⣴⠋⣡⣶⡿⡿⣡⢠⣾⡇⣿⣿⢸⣷⡄⣌⢿⢿⣶⣌⠙⣦⡈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢸⣿⠸⣿⡇⠣⢁⣹⠿⠋⣥⣿⣿⣬⠙⠿⣏⡈⠜⢸⣿⠇⣿⡇⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠈⢿⣧⡙⠣⠀⠋⠀⡀⠉⠛⢻⡟⠛⠉⢀⠀⠙⠀⠜⣋⣼⡿⠁⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠳⡀⠀⠙⠻⢷⣶⣤⡞⣁⠀⣰⡆⢰⣆⠀⣌⢳⣤⣶⡾⠟⠋⠀⣀⠞⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠹⣇⢿⣬⣿⡇⢸⣿⣥⡿⣸⠏⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣌⣁⡉⠙⠃⠘⠋⢁⣈⣡⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⠀⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡠⣤⣤⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢛⡛⠿⣒⡶⣾⣷⡀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⡻⣾⠿⢸⣿⣧⢿⣵⣷⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢿⣿⣿⣿⠇⣌⢿⣻⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠞⠋⠉⠉⠠⠾⢿⣮⡻⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣠⡾⣱⡿⠿⢿⡽⠇⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢟⡅⣿⣇⠺⠿⠃⠀⠀⣧⣮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣡⣿⣿⣎⢻⣆⠶⠖⣴⣎⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣭⣱⡟⣩⣤⣤⠀⠉⠛⠛⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣧⣙⣿⠃⠀⠀⠀⢀⣠⣤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡏⣉⡻⣿⠀⠀⠀⣴⡯⠛⠉⡟⢯⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⡟⣎⢂⠀⠀⣿⡇⠀⠀⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢹⢸⣶⠀⡉⣷⣄⢀⣷⣾⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⣸⣇⠸⢿⣾⣝⣻⣿⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠛⢫⠝⠚⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠃⠈⠁⠘⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡶⢅⣕⠠⢐⡀⢘⠀⠕⡎⠹⣆⠀⠀⠀⢀⡈⠁⠀⠀⠀⠘⠂⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⣼⢀⠆⢠⠤⢄⡎⣄⠠⢤⡀⠤⡉⡇⠀⠀⠄⠀⠀⡀⠁⠀⣐⣀⠀⡈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⢾⠀⣠⡀⠈⠑⠉⠀⡀⡄⠀⠆⣿⠀⠠⠄⠀⠄⠀⡈⠀⠙⠉⠀⢁⠀⠥⠀⠠
⠀⠀⠀⠀⠀⠀⢻⡉⠤⢘⡀⠀⣈⡀⠀⢈⠁⠄⢱⡇⠀⠀⠂⠀⠉⠀⠩⡀⠨⠅⢀⠅⠀⠍⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠳⡊⡨⢑⢤⡁⢨⠔⡊⢌⣰⠏⠀⠀⠀⠐⠂⡀⠀⠂⠙⢂⡐⠉⠐⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⣤⣞⣢⢤⠷⠊⠁⠀⠀⠀⠀⠀⠈⠁⠦⠀⡀⢀⠀⢀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠁⠀⠁⠈⠁⠰⠀⡀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠫⡝⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⡄⠀⠀⠀⡴⠇⠑⡚⢢⡤⢠⡄⢓⠪⡨⢦
⠀⠀⠀⠀⠀⠀⠤⠀⢀⠠⢶⣖⢙⣘⢁⣶⢦⠀⠀⠠⠄⠀⢸⢍⠠⠿⣟⡥⣬⣭⠬⣻⠟⠴⡀⣧
⠀⠀⠀⠀⠀⠀⠆⠀⠰⣄⣲⣷⣤⢠⣜⣷⣃⡖⠀⠀⠆⠀⣿⢶⢘⣓⢿⣣⣢⢀⣔⡻⣞⡃⡶⢺
⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⢨⡁⣤⢥⡀⡥⠁⠀⠀⠐⠂⠀⢺⠈⠈⢉⡏⠀⣀⣂⠀⢹⡉⠡⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠆⠈⠀⠀⢀⡀⠃⠀⠀⠀⠱⣆⡨⢅⠌⢋⡝⠁⡈⢅⢑⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⡀⠀⡀⢀⡀⠰⠀⠁⠀⠀⠀⠀⠀⠈⠑⠦⡤⣜⣣⣤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣙⣃⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣿⣿⢹⢹⣟⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣿⠿⠛⠛⠛⠻⢿⡏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣭⣬⣐⠀⢐⣠⣬⡝⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠪⠙⠟⠀⠙⠟⡩⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⠀⢤⠀⢤⠀⠚⠳⡀⢀⠲⣤⠴⠂⠃⡰⠛⠂⢠⠄⢠⠄⢠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣇⠣⡸⠶⢬⠛⠻⠀⠙⠶⣄⡂⣢⡴⠞⠁⠸⠚⢡⠴⠾⡠⢃⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣟⣢⢘⣒⢛⢀⢙⢲⡦⠽⠥⣶⠚⢁⢘⠓⢚⣠⣚⣧⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠿⠁⡄⢡⠱⡄⡼⢡⠁⡄⠹⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⢹⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⣦⢠⢇⠈⢀⢦⢠⣢⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠉⠉⠋⠉⠉⠋⠉⢁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠈⢉⠹⣶⣶⠦⢶⣶⡿⢉⠑⠨⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣳⢕⢻⠀⠀⠀⠀⠀⢸⢙⢽⡓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣆⠋⠠⣁⠤⢄⡠⠈⢃⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡉⠉⠛⠿⠟⠋⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣗⡤⠄⣀⡀⠤⣔⡿⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⡤⢍⢉⠉⢉⢉⠥⡀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡄⣸⢀⠆⢇⢸⡠⣤⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠡⠍⠉⠀⠈⠉⠥⠁⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣶⡿⠉⣷⣾⠉⢿⣶⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣧⠀⠐⠻⣧⡹⣦⣴⢏⣼⠟⠃⠀⣼⣷⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⣾⣿⢫⡾⠖⠓⢦⡈⢿⠿⢂⡴⠚⠲⢷⡝⣿⣷⠸⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢸⠙⣈⡌⠀⢀⣀⣤⣬⠗⠺⢥⣤⣈⡀⠀⢡⣡⠋⡇⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⢳⣼⣵⣭⡵⢩⣽⠎⣸⣇⠱⣯⡍⢮⣯⣮⣧⡞⠃⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢐⣭⠹⣟⣴⡎⠱⡾⠿⠿⢷⠎⢱⣦⣻⠏⣭⡂⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠡⣿⣽⡸⣯⢲⣤⢿⣻⡏⢹⣟⡯⣤⡖⣝⢇⣯⣿⠌⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣬⣙⣛⣷⣟⣓⣫⣵⢞⡳⣮⣝⣚⣻⣾⣛⣉⣥⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣙⡛⠋⢙⡫⡷⠭⣚⣓⠭⢾⢝⡋⠙⢛⣋⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⡛⢿⠛⠛⣚⠋⠩⣭⣵⣮⣭⠍⠙⣓⠛⠛⡿⢛⣃⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣀⢴⣴⣝⣯⢿⢾⢻⡟⡷⡿⣽⣫⣦⡦⣀⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣧⣭⡻⣎⡿⠆⡀⣀⠰⢿⣱⢟⣭⣼⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⣷⣤⣝⣋⡍⢩⣙⣫⣤⣾⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⡧⢼⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣷⣮⠻⢫⣶⣮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⢗⣼⣔⢗⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⠭⣛⠿⢟⡫⢕⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣕⠶⣭⡵⢖⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⡿⣿⡟⠉⠉⠉⣩⣭⣭⢉⢩⣭⣭⡉⠉⠉⠙⣿⡿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⣿⣹⡿⣿⡇⠀⠀⠀⡐⠶⢂⡻⢃⠲⠖⠀⠀⠀⠀⣿⡿⣿⣉⣿⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⣿⣹⡟⢿⠇⠀⠀⠀⡿⡻⣿⣧⣿⡿⠻⡇⠀⠀⠀⢿⠟⣿⣽⣿⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⡟⠙⠃⠀⠀⠀⠀⠀⣄⢿⣜⠿⢏⣼⢇⡆⠀⠀⠀⠀⠀⠛⠙⣿⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⣙⢮⡻⣿⡿⣫⢞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣃⣛⣒⣛⣋⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⣉⠭⢍⡩⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡋⠯⠙⠩⠏⡓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢴⢜⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠭⠤⠬⠍⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣒⣒⣒⣂⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣫⣫⣝⣍⣫⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠯⠍⣭⡉⠭⠎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⡃⣩⡁⣛⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⣊⡺⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠵⠿⣛⣛⢷⡝⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠿⠿⠿⠿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⡟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠆⠰⢀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠰⡀⢀⠄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⣀⣽⡿⣿⣿⢿⣯⣀⣀⣀⣠⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢽⣿⣿⣹⣻⡛⢼⣟⡡⣿⡟⢍⣻⡷⢻⣿⣋⣿⣿⡯⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⢻⣷⣦⣌⣉⣀⠖⠛⣿⣷⠟⠾⣀⣉⣩⣴⣾⡟⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠥⢿⣹⣻⣿⣶⣾⡿⢿⣧⣶⣿⣟⣏⡿⠬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⡖⢲⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⠸⣡⣌⠇⢜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠈⠍⠉⠅⠌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠏⠛⠛⠙⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣶⡀⡀⣶⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣊⢡⡌⣑⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⣋⣨⣅⣘⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠭⢭⡭⠭⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣾⣷⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡽⠻⠟⢫⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⢴⡦⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣛⣓⡚⣓⣚⣛⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣧⡀⡤⢄⢀⣴⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢨⠻⡇⢸⠿⡉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠸⡅⢨⠇⣀⣸⡇
⠀⣀⣀⣀⣀⣀⣀⡀⣀⡀⡀⢀⣀⣀⣀⠀⣿⠉⢻⣇⣸⡟⠉⣿⠁⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀
⣿⠉⠉⢉⠉⠉⠉⢽⢉⠉⢋⠉⠉⠉⠙⢷⠋⠀⠈⠛⠛⠁⠀⠙⣾⠋⠉⠉⠉⡙⠉⣉⡯⠉⠉⠉⡉⠉⠉
⢹⡀⠀⠉⡑⠒⠚⠹⣆⠒⠉⠒⠂⠒⠂⣿⡄⠦⢤⢀⡠⠤⠴⢠⣿⠀⠐⠐⠒⠉⠒⣤⠏⠓⠒⢊⠁⠀⢀
⠘⣧⠁⠀⡈⠀⡀⢊⡜⡱⠚⠊⠐⡞⠂⣿⡇⠀⠀⠀⠁⠀⠀⢸⣿⠐⠳⠂⠱⠓⢎⠣⡑⢀⠈⢀⠀⠈⣼
⠀⠘⢷⣄⢀⠔⠉⠉⠂⠑⠁⠀⠐⠁⠃⣿⠃⡆⡀⠀⠀⢀⢰⠘⣗⠘⠀⠃⠐⠈⠊⠐⠉⠉⠢⡀⣨⡾⠃
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠈⠉⠑⠊⠈⠁⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠄⠁⠀⠢⣀⣸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣭⠀⢆⠰⠀⡨⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⠀⠐⠐⠒⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⣠⡀⠀⠀⢠⣆⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢸⡙⠐⠒⠒⠂⢛⡇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⣇⠀⠀⠀⠀⣸⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⢦⠀⠀⡴⠁⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠆⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⡴⠂⠐⢄⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠒⠃⠂⠒⠘⠒⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠸⠇⠀⠀⠸⠷⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣴⣶⠒⠒⣶⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠤⠤⠿⠿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⡉⠠⠀⠲⠶⠶⢖⠌⠄⢉⡛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠐⡂⣨⣽⠿⠦⠴⠾⢯⣍⢐⠂⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣰⣄⣀⣠⣙⣀⣘⣠⣤⣤⣄⣃⣀⣋⣄⣀⣢⣄⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⢀
⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠐⠀⠀⠐⠀⠁⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠦⢤⣄⠀⢠⡞⠁⠀⠈⠙⠓⢦
⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣧⡾⢀⠀⢤⠘⠀⠀⢸⠇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⢷⠦⣀⡀⠀⢸⠇⠈⣠⢂⠚⠀⠀⠊
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠓⢬⡻⡄⠘⠀⢰⠃⠈⢀⠖⠉⠉⠳⣄⡀
⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣷⣤⣤⣤⣄⡀⠀⢀⡌⡜⠀⠀⠀⣠⠄⠀⠀⠀⠉⣇
⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⣹⠟⠉⠉⠀⠉⢀⡈⢠⠇⠀⠐⠛⢒⡢⠖⠀⠀⢠⡇
⠀⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⡟⠀⢀⡴⠋⠁⠀⡙⠁⡀⡀⠠⢤⣀⣀⣀⣀⡤⠟
⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣧⠀⠎⠀⠠⠊⢰⠃⠀⢱⠘⣆⠀⠉⢻⣍⠉
⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠁⠀⠉⠉⢿⠀⠀⠀⠀⢀⣿⠀⠀⠘⠀⠈⠀⠀⢠⣿⡆
⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣠⡶⠄⠘⠷⠒⠒⠻⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠶⠛⠛⠉⠀⠀⢢⠀⠀⠀⠰⠶⠾⠿⠍⠁⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣤⣤⣄⣰⣿⣿⣿⡏
⠀⢸⣿⣿⣿⣿⣿⣷⣀⣀⣀⣤⠖⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⣿⣿⣿⣿⣿⣿⡟⠙⠙⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠰⠦⠴⠋⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠖⠒⠊⢀⡤⠔⢹⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠈⠻⣿⡿⡿⢿⢿⠿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡀⠀⠀⢰⡉⠉⢁⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢆⡈⢷⣆⠀⠚⡷⠿⠿⡿⢿⢿⡿⣿⣿⣶⣄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⢁⡀⢹⡶⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠳⣄⠀⠀⠙⠦⡙⠇⠁⠁⣐⣩⣽⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀⠀⠹⡄⣷⠀⠙⢢⣄⡀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⣠⠴⠒⠂⠀⠀⠀⠶⠀⢀⣀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀⠀⠏⠀⣠⠞⢀⡝⠙⡗⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⣀⣀⡀⠀⢠⠀⠀⠈⠑⠆⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡿⠛⠉⠉⠙⠳⢀⡠⠚⠥⠞⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠤⣌⣙⢦⠙⢦⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇
⠀⠀⣠⣴⣿⣿⠁⢀⠴⠚⠁⠀⠉⢀⣀⣀⠲⣄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣈⣙⢆⡀⠈⠙⠓⠒⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⢀⣾⣿⣿⣿⣿⡀⠀⢀⣀⠄⢀⣎⣁⣀⡈⠉⠻⣄⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠒⠋⢉⡵⠋⣰⡏⣭⡙⠫⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣾⣿⣿⣿⡿⠛⢛⣻⠿⡥⡤⢺⣁⣀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠔⢹⠇⢱⢹⡄⠈⢳⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⡏⠀⠀⠁⣠⢾⠃⡿⡀⠳⣌⠙⠲⠦⢤⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠏⠀⠸⠀⠳⡄⠀⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⡉⠩⠉⠉⠉⢉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠑⢷⢰⡏⢱⣄⠆⠚⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠠⠒⢹⠆⢸⠏⠒⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣄⢳⡀⢠⣊⣠⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⣿⣀⣠⡿⠉⢰⡏
⢸⡛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⡛⠛⠛⠛⠛⠛⣧⡞⠁⠀⠘⠿⠿⠃⠀⠈⢳⣼⠛⠛⠛⠛⠛⡛⣛⠛⢻⠛⠛⠛⠛⠛⠛⠛⢻
⢸⡇⠀⠀⠈⠀⠠⠤⠴⢇⡀⠠⠘⠦⢀⠀⡀⠀⣾⡇⢀⡀⠀⠀⠀⠀⣀⡀⢸⡧⠀⢀⠀⡀⠐⠃⠄⠀⡰⠦⠤⠄⠈⠁⠀⠀⢸
⠸⣇⠠⠄⠐⠣⠄⠀⢀⠰⢢⢀⡀⣀⣀⣀⣀⡀⣸⡇⠈⠀⠋⡞⠢⠹⠈⠀⢸⣇⢀⣠⣀⣀⣀⣀⡀⡔⠖⡀⠀⠠⠔⠂⠠⠀⣼
⠀⢻⣆⠀⠀⠀⠀⢠⡀⢔⢁⡘⠀⠁⠀⣉⢀⡁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢨⡀⣉⠀⠈⢀⠃⡘⣦⢀⡄⠀⠀⠀⠀⣰⠏
⠀⠀⠙⢧⣄⡀⠀⠀⢀⠈⠀⡉⠀⠀⠀⠋⠈⡁⣸⡇⡰⢀⡀⡀⣀⢠⠀⣤⢸⡇⢈⠀⠉⠀⠀⠈⠁⠈⠁⠀⠀⠀⣀⣠⡼⠋
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠉⠐⠃⠈⠂⠁⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⠄⠂⠰⢀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠛⠓⠃⢀⠀⢀⡰⠀⠚⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠉⠆⠀⠐⠀⡀⠐⠋⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⡀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠦⠀⠀⠀⠀⢴⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡟⠛⠉⢠⡄⠉⠛⢻⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⢇⠀⠀⠀⠀⠀⠀⠾⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠚⢇⡀⠀⠀⠀⡜⠃⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠆⠀⠀⠲⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡆⠀⠀⠀⠀⠀⠀⢰⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢠⡄⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡀⠄⠠⢀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣀⠅⡀⢀⠈⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠈⠠⢁⡀⠄⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣽⠆⠀⠀⠀⣷⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⣤⠀⠀⣤⣄⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣬⣯⣯⠀⠀⣽⣽⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠋⠉⢉⣉⡀⢈⣉⡉⠉⠙⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠀⠀⠀⡀⠙⠻⠟⠋⢁⠀⠀⠀⠀⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣀⢀⣴⠿⠿⠐⠂⠿⢟⣦⡀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣄⣀⠀⣀⡘⣀⠀⢃⣠⣤⣤⣄⡘⠀⣈⢃⣀⠀⣀⣤⣀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣉⣌⣹⣅⣤⣉⣩⣯⣁⣼⣟⣽⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣏⣛⣻⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⣿⣿⡧⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠈⣿⡇⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⣿⠃⢈⠀⣠⣤⣴⣶⣦⠀⠀⠀⠈⠰⠋⢀⣠⡴⠛⠀⢹⣧⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⠃⠀⠀⠀⠘⠂⠀⠀⠀⠀⠉⠉⠁⠀⠀⠠⠹⣏⣸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠘⠶⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣽⣆⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⡀⠀⠀⠀⠀⠀⣈⠉⣤⠔⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠈⠉⠉⠓⠊⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣦⣀⠀⠀⢀⣴⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠈⠁⠐⠚⠉⠉⠀⠘⣿⡿⠛⣥⡿⢋⣽⣿⣿⣿⣿⣿⡶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⢠⣾⠟⢀⡾⢻⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢷⣀⡀⠀⠀⣠⡿⠃⢀⣾⠁⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡎⠀⣠⣄⡰⠉⠀⣠⠟⠁⢠⣿⣿⣯⠀⠀⠀⠀⠘⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠁⠉⢁⣰⠃⢤⠀⠀⣴⣿⠁⣿⣿⡆⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠁⠛⣤⠛⠀⢾⠴⠞⠛⠃⣸⣿⣿⣿⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣰⡏⠙⠂⠀⠀⢋⡀⣦⣄⣤⣶⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠀⠀⣼⣿⡿⠛⡷⢦⡤⡈⢠⡀⣴⣿⣿⣿⣿⣿⣿⣧⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⠿⠛⠋⠀⠈⣰⣿⡿⠓⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣙⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣥⣤⡤⠄⠀⣰⡯⣤⣗⠾⣱⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡝⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⢀⠞⠛⠳⢆⣉⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠙⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣀⡴⠃⠀⠀⠀⠀⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠰⠜⠃⠾⠛⣽⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⣱
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠰⣵⢆⡾⠁⠀⠀⠀⠀⢀⣀⡘⢷⣬⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣤⣴⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣼⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠻⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡾⠋
⠀⠀⠀⠀⠀⠠⠆⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠛⠈⢁⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢤⣤⣤⡾⠟⠁⢀⣤⠾⠏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣾⠿⠃⠀⠀⠐⠉⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠶⠿⠏⠁⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣄⢀⠀⠀⠀⠀⡀⣠⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠿⠿⢿⣷⡀⢀⣾⡿⠿⠿⠿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⠟⢡⡴⠞⠛⠓⠮⠓⠚⠵⠚⠛⠳⢦⡌⠻⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⢻⡳⣦⣄⣀⠀⠀⠀⠀⣀⣠⣴⢞⡟⡀⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⢸⡎⠓⠀⡀⠀⡀⣶⣶⢀⠀⢀⠀⠘⢱⡇⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠸⡗⠰⡾⠁⢸⣧⣺⣗⣼⡇⠈⢷⠆⢺⠇⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⣻⡄⣡⠸⡶⠛⠙⠋⠛⢶⠇⣌⢠⣟⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠈⠻⠿⠟⢀⣴⠞⠁⠈⠳⣦⡀⠻⠿⠛⠁⢈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡡⢴⠦⠴⠒⠻⠯⠥⠄⠀⠬⠽⠟⠓⠦⠴⡦⢌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠷⣦⠉⢧⣰⣰⣿⣿⣆⣆⡼⠉⣴⠾⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡑⢭⣛⡉⢉⣛⡭⢊⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⢻⠘⣇⣸⠃⡟⠏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠉⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢢⠀⠀⢀⠖⠀⢰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡃⠀⠀⡄⠀⠸⠀⠀⣙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠈⠍⠹⠶⡒⠋⢉⠙⡒⠶⠏⠍⠔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢂⠜⢲⠭⠍⠉⠓⠶⠛⢉⡩⠭⠖⢤⡐⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠰⡁⢾⠆⡇⡤⠒⢄⢀⠰⡷⢨⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣀⠈⠶⢊⣀⠀⠀⠸⣀⠑⠖⠁⣠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢠⡴⠋⠀⠀⠀⠫⣄⠀⢐⠈⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⠜⠶⠍⡀⠀⠀⠀⠀⠀⠀⠵⠖⠩⡁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣂⠀⠙⠣⠀⠀⢠⠞⠉⠀⣰⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡒⠌⣑⡒⠠⡇⠀⡼⠀⣐⣊⠤⣒⠜
⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⣀⣀⣀⣀⠤⢐⡢⠭⠉⡭⠭⢭⢩⠉⠉⠁⣀⣙⠣⠀⠛⣁⡈⠈⠉⢙⢁⠭⠭⠍⣉⠥⢔⡂⠤⣄⢀⣀⣀⣀⣀⠠⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣰⡀⠯⠀⠠⠘⠄⠀⠠⢺⡀⠀⢀⠁⠈⡀⠀⢸⠁⠘⡃⠀⢸⡘⠄⠀⠠⠇⠀⠀⠱⢀⣧⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠠⠖⠉⠀⠀⡞⠋⠛⠒⡚⠛⠛⠛⠑⠐⠁⠀⠀⠑⠐⠃⠀⠀⠙⠀⠈⡗⠙⠋⠛⠒⠙⠙⢓⠀⠀⠉⠂⠄⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⣠⠁⠀⠀⡄⠀⡎⢉⠉⡁⠀⠀⠀⢊⠁⢉⢱⠀⣇⠀⠀⠘⠃⠀⠀⠀⠱⣄⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡔⠒⠉⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⢋⠀⡁⢘⠀⠀⠀⡇⢈⠀⣹⠀⢻⠀⠀⠀⠘⡄⠀⠀⠀⠀⠁⠒⢲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⢀⠔⠁⠀⠀⠀⡜⡇⠀⠐⣤⢠⡜⠀⠀⠀⢣⡤⣤⠆⠀⡈⢃⠀⠀⠀⠈⠦⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠤⠤⠠⠤⠾⠠⠰⣄⡠⠦⠤⢦⣀⣀⣀⡰⡦⠴⢄⣴⠇⠠⠳⠦⠠⠤⠤⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⣠⣥⣤⣴⣼⠀⠀⠀⣧⣦⣴⣬⣀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠊⡠⣒⡢⠙⢦⡀⠀⢀⠜⢁⣔⡂⡄⢡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢜⣿⣟⠀⢀⠜⠛⠆⠀⢬⣻⣿⡘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠳⣈⡁⣁⠔⡫⠒⡶⠒⡕⢄⣁⣈⡠⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠉⣇⠘⡢⠃⢀⠷⡀⠱⣞⠁⡌⠉⡂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠟⠷⠿⡷⢾⠧⠦⢼⠶⡾⠷⠞⢮⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣘⠃⠀⠶⢸⠀⠀⢸⠀⠴⢀⠛⡸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢌⡚⠵⢻⣮⣤⢤⣤⣾⠓⠌⣊⠰⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠒⠂⠀⣀⠐⠒⠂⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡏⡐⡤⠈⠿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀⠀⠀⢠⡆⠀⠀⠀⣤⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠗⠡⠐⢈⠉⠉⢩⠂⠠⣌⢚⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢂⡀⢴⠀⠀⢨⣀⣀⣸⠅⠀⢨⠜⢀⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⣌⡘⢧⡀⣘⠁⠀⢸⣂⢀⠜⣉⠄⠀⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢹⠄⠈⡏⠲⣶⠊⠉⠀⢀⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⠸⣆⠀⠣⠤⠙⠤⠆⢀⡼⠒⠒⠒⠒⠺⣄
⠀⠀⢀⣀⢀⡀⢀⡀⠀⣀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⣀⠀⢀⢀⡀
⠀⠀⠘⠃⠀⠐⠊⠙⠃⠛⠉⠛⠛⠃⠀⠛⠛⠃⠈⠒⠛⠒⠓⠖⠓⠂⠀⠀⠀⠀⠀⠀⠀⠒⠛⠖⠓⠚⠓⠊⠀⠀⠀⠀⠀⠀⠀⠛⠛⠊⠿⠓⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⢀⡴⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠠⢤⣀⠄⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⣞⣿⣺⣿⡿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣯⣿⠃⢇⣩⣶⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣾⣿⣰⢿⣻⣿⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠙⢛⡃⠁⣻⣇
⡟⠒⠀⠀⠀⠠⣾⣁⣿⣿⣿⣿⣿⣹⣇⣶⠶⡏⢰⡿⢧⡛⡷⠿⢿⠀⣿⠟⣿⣹⣦⡿⡾⢻⢿⡽⣭⡿⣟⠂⠄⠠⣜
⠹⣆⠀⢀⡠⠚⡹⢹⢁⡇⡏⡙⢸⢹⢋⡏⡏⡇⢸⣷⣧⣾⣄⡛⣪⡇⡇⣼⢸⠈⡇⡇⢹⠸⡈⡏⣇⠳⡄⠉⠲⣄⡠
⠀⠀⠙⠣⠤⠾⠁⢞⣸⣠⠃⡇⣿⣸⢸⣸⡇⣇⢸⣃⢻⠿⢿⣃⣺⡃⣇⢿⢸⡄⣧⣷⢸⡄⠧⠱⠼⠶⠜⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠉⠉⠀⠈⠉⣹⢧⣿⣂⣺⣴⣤⣿⡍⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢫⠀⢰⡉⡟⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣧⢽⣀⣼⣤⡟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣛⢮⡿⢝⡭⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣬⣵⣾⢿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣟⣭⣼⣿⡛⢷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠐⠢⠬⠍⣁⣉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠍⣸⣷⣾⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡎⣴⣶⣶⣎⢳⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣼⡟⣿⠟⣿⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⣿⡏⣛⡋⢹⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⡀⢹⡁⢸⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠛⠳⣏⡷⠛⠓⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡕⢮⡠⢖⣿⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⢻⡏⣶⠿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠐⠲⣶⣖⠚⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⣙⣓⠒⠒⠚⢛⡛⢷

⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣟⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⠛⠻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⣿⣯⢿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⣤⣬⠨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣋⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⢻⣿⡉⠀⠀⣉⣄⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣍⣿⣭⣏⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢌⣁⡈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣿⡏⠂⢈⡽⠛⠛⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠍⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣿⠀⠈⡌⢠⣷⡆⢑⣾⣿⡄
⠀⠀⠀⡀⡀⠀⠀⠀⠁⠒⠲⠿⠛⠒⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⡟⠋⠉⢀⢰⡟⠀⠀⠉⠑⠨⡻⡟
⠀⠀⣨⠇⠁⠀⠀⢰⠀⠀⠀⠆⠀⠀⡇⠀⠸⣦⠀⠀⠀⠀⠘⠋⠈⠛⠛⠒⢲⡶⠐⢻⣶⣶⠇⠀⠀⢴⡄
⠀⠨⡁⠀⠀⠀⠀⢨⠀⠀⠀⢠⠀⠀⠹⠠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣬⡿⣿⣾⠚⠉⠙⠦⠀⠀⣾⡇
⠀⠀⠀⠢⢀⣤⠀⢀⠀⠀⠀⣠⠤⠠⠤⠐⠀⣀⡜⠀⠀⠀⠀⢠⣤⣶⣿⣿⡄⠘⣿⣦⡀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠸⡿⠒⠀⠀⠀⠞⠹⠶⠀⠠⣶⢿⡧⠂⠀⠀⠀⠀⠈⢿⣿⡇⠈⢿⠀⠈⠓⠙⢦⣄⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡶⠚⣛⡛⠙⡛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢩⣻⣿⠁⢸⡿⠉⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢰⡎⣠⠹⣍⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⣰⣇⣀⣸
⠀⠀⠀⠀⢤⣤⣤⠀⢠⢄⡠⢠⡤⣀⢀⣄⣤⠄⠀⣤⣤⡄⣠⣄⢶⣭⢭⣤⡭⣥⡶⣠⣄⢠⣤⣤⠀⠠⡤⢠⡀⣀⢤⡄⢄⡠⡄⠀⣤⣦⡤
⠀⠀⠀⠀⠀⡴⠾⣫⡌⣓⠬⣒⠬⣻⠏⣿⢟⣢⡤⣼⣥⣾⢍⡙⠈⣃⡄⠾⣠⣨⡁⢋⡩⣷⣬⣧⢤⣔⡻⣿⢹⣟⠥⣒⠥⣚⢡⣟⠷⢦
⠀⠀⠀⠀⠀⠀⠘⢉⡾⣻⣟⣬⣑⠢⢍⣓⠪⠝⣃⣹⠟⢡⣾⣿⣄⠘⡧⠀⡾⠃⣠⣿⣷⡌⠻⣏⣘⠫⠕⣚⡡⠔⣊⣤⣻⣟⢧⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢹⠏⡾⣰⢮⣍⡑⣒⢒⠨⠬⠯⠭⠽⣶⠦⠀⠴⣶⠯⠭⠽⠥⠅⡒⣒⢘⣩⡰⣆⢷⠹⡏⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠹⠃⡟⠼⢻⢸⠟⢧⡴⢚⣻⣟⣟⡳⢦⡤⠻⡇⠟⠇⠻⠘⠏⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢲⠀⡖⠲⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣒⢚⣀⡓⣒⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣥⣼⣿⣧⣬⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠞⣹⣛⣛⠳⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⢼⣭⡅⠤⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣤⣼⣿⣧⡤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢶⣦⠉⣴⡶⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢈⠻⠛⠿⡁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢃⣓⣀⣚⡘⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⢋⣭⣭⣭⡙⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠖⢲⢠⡖⠰⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠾⠈⠷⠤⠤⠼



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