Birthday card Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⠸⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠇⣿⡂
⠀⠀⠀⠀⠀⠀⢠⠖⣐⡋⠁⣸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣇⡈⢙⣂⠲⡄
⠀⠀⠀⢤⣴⣴⡴⢰⣦⢿⣷⠗⣶⣶⠈⣭⡭⠩⠩⠍⠭⢩⡍⠍⠭⠩⠍⠍⢭⡭⠍⠍⠭⢩⣭⠁⣷⣶⠻⣾⡿⣠⠆⢦⡦⣦⡤
⠀⠀⠀⠴⣶⡦⢁⣠⣽⠟⢁⣴⣍⣙⡴⠻⣿⣶⣾⣷⣽⢶⡼⠖⠀⠀⠐⠲⢿⡶⣯⣾⣿⣿⣿⣶⣋⣩⢦⠈⠻⣯⣄⡈⢴⣶⠦
⠀⠀⠀⠀⠀⠤⣿⣯⢸⣿⣏⢹⡿⠟⠀⠀⠀⠉⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⠀⠻⢿⡎⣸⣿⡇⣽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠆⣬⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⠰⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡟⠩⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⡻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢟⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣦⠱⣫⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⡏⣬⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡍⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢙⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⣹⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣏⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⣱⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣎⢐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢆⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⣨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠄⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠠⡇
⠀⠀⠀⠀⠀⠰⣶⣟⢰⣿⡏⣹⣷⣄⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣠⣾⣏⢹⣿⡆⣳⣶⠆
⠀⠀⠀⠤⡿⠗⠋⠹⢪⣤⠙⠳⣛⣙⠧⣴⣾⡿⣿⡯⢷⡭⢷⠤⠀⠀⠀⠤⡾⠯⡾⢽⣿⣿⣷⠶⣋⣛⡿⢋⣤⡗⠏⠉⠚⢿⠤
⠀⠀⠀⠞⠻⠺⠳⠰⠟⣿⣽⠦⠿⠿⠀⠛⠃⠒⠘⠀⠂⠘⠛⠂⠂⠐⠐⠂⠚⠓⠐⠂⠂⠘⠛⠀⠿⠿⡤⢿⣿⠻⠆⠞⠗⠟⠳
⠀⠀⠀⠀⠀⠀⠘⠦⠹⣍⠀⣹⣶⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⣶⣏⠀⣩⠟⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⢁⣶⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣶⡈⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣞⡽⣳⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⡥⢴⡖⠻⢍⠻⣾⣵⣷⣾⣿⣇⢀⣀⠤⠤⢀⡀
⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣥⠏⣔⡩⣬⡗⡄⡃⢸⡾⠟⢿⣿⣽⡟⠀⠀⣀⡀⠈⠲⠗
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢄⢨⡙⣩⠇⡜⣧⠎⠆⣠⣤⠈⣉⡃⢠⠞⠉⠉⠱
⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠚⢳⣤⣙⣭⣍⡩⠜⣡⣾⣿⡛⠁⠺⡤⠈⠇⣰⣷⣀⡴⢁⡄⢠⣋⠉⢆
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠉⣈⣁⣪⡓⠶⠶⣿⣟⣏⣼⣽⡗⡿⠂⣀⠘⠦⣀⣀⠤⠛⠤⣉⣉⣀⡤⠀⠠⡀
⣿⠀⢸⡇⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⢩⣏⣀⣈⣉⡧⡙⢦⣿⢍⠚⢭⣶⠞⢣⡘⢂⡕⢀⡉⢀⠎⢉⢙⠀⠀⠀⠧⣴⠀⣽
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⣌⣯⣃⡾⢠⣇⡜⢹⣷⣿⡏⢀⣤⣀⠛⠁⠀⠏⣰⢹⠀⠈⢻⡆⠀⠀⠀⢢⣤⢳⠂⠴
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⢿⣤⣉⣉⣽⡀⣠⡾⢿⣿⠻⢟⡭⠽⣦⣀⣀⣀⠠⠊⠀⠀⠊⠀⡔⠉⠉⢧⠈⣎⠓⢤⠄⠤⡀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⢻⡵⢻⣯⢝⣪⡟⠘⢿⡘⡹⣿⣿⡇⠀⠀⠀⠀⠀⢰⠀⠀⢣⡀⠚⠧⢀⠟⠃⠧⠩⠂⢹
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣻⣷⣾⠁⠀⠀⠉⠙⠛⠿⠇⠀⠀⠀⠀⠀⠈⣳⣄⣤⢈⠗⠈⠀⢴⡉⢢⡀⠀⢘⣠⣤⣤⡄
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⠇⣈⠂⠃⡾⠦⡄⠈⢁⡔⢟⣿⣿⣿⠁
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡓⣿⡹⣏⠀⠻⣷⣴⢝⣷⢼⢦⣸⣹⡾⠫⣽⠇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⢮⡿⠋⢙⣋⣬⡙⢿⣗⢿⡎⢜⣿⣿⣿⣯⣄⣀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡿⢀⡟⢀⣀⡀⣀⢀⡀⡀⢀⢀⠀⡀⠀⠀⠀⠀⠑⢿⣵⢃⣴⣍⡐⡎⠆⢹⠟⢉⠿⠭⡉⠱⡷⢫⣩⣿⣷
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⣾⠓⡾⢡⡏⣼⢡⢏⡼⣿⢣⡟⡞⣰⠏⠀⠀⠀⠀⠀⠀⢻⢦⡨⡿⢚⣇⠼⣴⣀⡥⣔⣒⢶⠶⡷⡛⢍⡿⠁
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠈⠃⠈⠁⢩⡟⠈⢱⠏⠉⠀⢱⠏⠀⠀⠀⠀⠀⠀⠈⢌⠳⢍⣁⠠⠋⣼⡍⢼⠁⣿⠝⡵⢠⡟⠚⠋
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢲⣦⣀⣀⢠⣤⣆⢠⣸⣡⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠹⠀⢧⣈⡶⢮⡭⢷⢷⣳⡀
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠣⠜⠙⠃⠚⠊⠓⠛⠛⠑⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡞⠓⣶⠂⣻⡿⠿⠇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⣿⠀⠸⠷⢶⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡷⠶⠿⠀⢸⡇
⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠿⠶⠶⠶⠾⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇
⣶⣶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠤⡄⠀⠀⠀⠆⢀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣀⠀⠉⠀⠁⠭⠘⢠⣦⠂⣤⠀⠁⣠⣤⠄⠰⠆⠰⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣤⠀⠈⢻⠟⠂⠐⠠⣶⡆⢲⡦⣥⡞⢻⠀⠀⠹⠏⠃⠀⣤⠀⠀⠘⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡉⠁⢐⠪⠂⠀⢰⠄⢨⣀⡅⠐⣠⠷⢠⣴⠌⣙⡷⠆⠀⠙⡍⡤⡹⠓⠀⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⢆⠎⣆⠀⠴⠀⡀⠀⠀⠐⠃⡂⠳⣸⣛⠒⠘⡆⣸⠁⣠⣾⠄⠈⢁⠀⠇⢀⠀⠙⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⢀⠀⠀⠐⠀⡿⣆⠀⠁⣀⣁⢀⠋⠛⠀⠀⠘⠏⠀⠀⠀⣀⣀⠈⠀⣰⢿⠐⠂⠀⠀⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠀⡡⠑⢀⣀⣤⠇⣘⠛⠋⣿⢋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡙⣿⠛⠛⢃⠸⣤⣀⡀⠊⠄⠀⠠⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⡆⠰⣀⠡⠜⠿⢥⣀⠘⠿⠃⠘⠷⣄⠘⠃⠀⣿⣼⡇⣾⠀⠘⠃⣠⠾⠃⠸⢿⠂⣀⡬⠿⠣⠌⢅⠆⢰⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠄⠀⠈⠁⠃⠀⠀⠶⢹⡇⢰⠋⠓⡚⠛⠛⠀⠀⣯⢹⡇⣿⠀⠀⠙⠛⠓⠒⠙⡆⢸⡏⠶⠀⠠⠀⠈⠁⠀⠨⢠⠁⠀⠈
⠀⠀⠀⠀⣠⡄⠠⠈⠍⡚⠀⠦⠀⠀⠀⠈⢴⠄⣷⠏⢐⡦⠡⠄⠙⠀⠀⣿⢸⡇⣿⠀⠀⠋⠠⠌⢴⡂⠹⣾⠠⡆⠁⠀⠀⠀⠴⠀⢒⠨⠁⠄⢠⡄
⠀⠀⣤⠀⢃⡘⠂⢠⡄⠁⢰⠤⠤⡆⠀⠀⠀⠠⠉⠀⡸⠊⠁⠀⠀⠀⠀⣿⢸⡇⣿⠀⠀⠀⠀⠘⠑⣇⠀⠉⠀⠀⠀⠀⠰⠤⠠⡄⠈⢠⡤⠐⢃⡘⠄⣤
⠀⠀⠀⡙⣈⡁⡁⢠⣤⡀⠴⢵⣢⠥⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠛⠘⠃⠛⠀⠀⡄⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠬⣔⡮⠦⢀⣤⡌⢁⢈⣁⣋
⠀⠀⠀⠉⢁⠙⠇⢈⠁⠀⡀⠀⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣾⣾⣦⣾⣴⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠁⢀⡀⠈⡁⠸⠋⡈⡙
⠀⠀⠀⠈⠶⠆⣳⢉⠾⠅⠤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠿⠿⠿⠿⠿⠿⠿⠾⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠤⠨⡷⠉⣚⠠⠶⠁
⠀⠀⠀⠀⠀⠀⢉⡛⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢰⣄⡀⢀⡀⣠⣤⣠⣦⣄⣄⡀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢛⡉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣭⣿⡿⣿⣿⣿⣟⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⣠⡄⢀⡀⠀⣀⣀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣿⣷⣶⣀⣿⣿⣾⣿⣿⣿⣿⣾⣧⣿⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠘⠾⠋⠟⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢠⣄⢠⠄⡄⡁⡤⡀⢠⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠘⠀⠃⠃⠃⠃⠉⠃⠛⠘

⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⣻⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣟
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠠⠆⠈⢱⠌⠁⠦⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠞⢩⢋⡜⠀⡀⠀⠀⣀⣠⠀⣀⣠⢀⠀⠀⠀⠀⠀⢀⣼⡡⠃⢀⠃⣀⣀⣠⠇⣰⣁⠀⠀⢠⠃⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠈⠋⠸⠁⠸⠅⠧⢰⠃⠜⢰⠃⠜⠸⢆⡇⠀⠀⠀⣺⠅⢸⠇⠶⠀⠃⠀⠦⠀⠏⠸⠰⠄⠻⠀⠯⠸⠄⠷⣺⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠇⠀⠀⠾⠔⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣭⣽⣽⣯⣿⣭⣭⣯⣬⣭⣦⣭⣿⣭⣵⣾⣧⣭⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠦⢀⠲⠆⡀⠶⠂⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣽⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣯
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣾⣿⡴⠂⠲⣾⣿⣼⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢿⡀⣀⠀⠀⠀⠀⠀⠀⢠⡈⣿⠁⣼⣏⢹⣟⣿⢉⣿⡄⢹⡏⣠⠀⠀⠀⠀⠀⠀⢀⡀⣸⠿⡁
⠀⠀⢻⢷⣄⢠⣤⡀⠀⠈⠀⣝⣿⠂⡀⠀⠀⢠⡀⢸⣷⢷⡉⢿⡟⢙⡋⣃⠙⣿⠏⣱⢷⣿⠀⣠⠀⠀⠀⡀⢾⣟⡅⠈⠀⠀⣠⣤⢀⣴⢿⠃
⠀⠀⢈⠢⣻⡆⢎⠻⡆⢶⣦⡀⢈⣿⡁⠀⠀⢸⡇⣸⣷⣿⡿⢶⠜⣿⣻⣿⡟⢶⠶⣿⣷⣿⡀⣿⠀⠀⠀⣹⢏⠀⣠⣶⠆⣾⢋⠆⣾⡣⢊
⠴⣛⣛⠙⠃⢙⣿⠷⣻⣔⣜⣿⠈⠁⡳⣜⡆⠀⢹⠟⣫⣥⠉⣀⣁⠻⢇⣹⢃⣁⡈⢡⣭⡛⢿⠁⠀⡞⡴⡃⠉⢸⣟⣄⣼⠷⢿⣟⠁⠛⢙⣛⡷
⠀⠀⠀⠀⣶⠟⠋⢀⣤⣿⠋⠙⣶⣄⡉⠻⡇⠀⠏⠀⠼⢋⣶⡽⠏⠠⡤⡥⠉⠿⣱⣏⠻⠄⠈⠇⠀⡿⠋⢁⣴⡞⠍⢻⣦⣄⠈⠛⢧⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠛⠉⠀⠀⠁⠳⠌⠀⠀⠀⠸⠃⠁⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠀⠈⠴⠃⠁⠀⠈⠙⠓⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⢰⠠⠁⠀⡀⠰⢀⠀⠀⢀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠨⠸⢰⠡⢊⠡⠂⠁⡇⠀⠀⠀⠸⠀⠇⠄⠁⠄⠰⠀⠠⠘⠈⠘⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠐⠦⣤⣄⠛⠳⣦⣀⠠⠔⡟⠑⠀⠀⣀⢸⣧⡆⠀⢀⡀⣀⠀⠀⣦⣿⠀⡀⠀⠐⠙⠂⠀⢀⣠⠶⠛⢃⡤⡴⠖⠀⢀⡄
⣀⣀⢀⡀⢋⠻⣦⡀⣨⣽⣷⣾⠋⠀⠶⡾⠇⠀⢧⡀⢽⣧⠍⡾⠧⢌⡭⣉⠤⠿⡎⢥⣿⠅⣠⠇⠀⡿⡶⠆⠈⢻⣶⣿⣭⠄⣠⡾⢋⠁⣀⣀⣀
⠉⠓⠶⠾⣖⡴⢻⢋⡟⢠⣴⡟⢠⣢⠎⠑⠁⢀⡞⣿⣶⣯⣴⢀⠄⣿⣤⢿⡖⣄⢰⣬⣵⣾⡟⣆⠀⠑⠉⢦⣠⠘⣷⣄⠸⣏⢻⠳⣔⡾⠶⠖⠋
⠀⠀⢠⣫⣾⢣⣥⡿⠁⠛⠉⣤⣤⠻⠆⠀⠀⢸⡇⢸⣏⣿⡟⣫⡝⠿⠟⠾⠟⣭⡛⣿⣏⣿⠀⣿⠀⠀⠀⠾⢣⣤⡌⠙⠃⠹⣧⣧⢻⣮⣣
⠀⠀⠿⠋⠁⠈⠀⠀⠀⡠⢠⡔⠯⠃⠀⠀⠀⠈⠀⢸⠏⣏⠶⣿⡿⢦⣶⣴⠾⣿⡷⢎⡏⢿⠀⠈⠀⠀⠀⠀⠫⠗⣤⠠⡀⠀⠀⠉⠀⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⠄⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⣦⣹⣧⣼⣿⣾⣤⣺⣡⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣷⣿⣿⣍⠉⢈⣽⣿⣶⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⡉⠀⠈⣹⡿⠙⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣧⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⢠⣐⠀⠀⠀⠀⢀⠀⠠⠀⡤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠤⠀⠀⠄
⠀⠃⠐⠀⢈⢈⠀⠈⠀⠀⠐⠄⠋⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣞⣉⡛⠀⠘⡅⠀⠀⡀⠀⠀⠀⠐⠀⡀⠀⠀⣀⠀⢄⠀⠀⠄⠄⠀⠀⠀⢈⠀⠆
⠀⠠⠀⠀⠀⢂⠀⠀⠀⠀⡀⠠⡀⠡⢤⠄⠀⣀⠀⠉⠀⠀⠀⠀⠈⣴⠧⢈⠙⡃⠀⠈⠀⢀⠀⠀⠀⠠⠈⡄⠀⢠⠂⠁⠀⡠⠰⡄⠀⠀⣀⢀⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠈⠉⡄⠀⢀⠀⠀⠀⠀⠀⠀⠐⠮⡈⠐⢩⠀⠘⠀⠁⠀⠀⣀⠀⠀⡀⠀⡀⠀⠆⠁⣘⠃⡀⠁⡘⠀⡅⠀⠁⡄⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡀⠈⡀⠈⠀⠠⠀⠀⠀⣀⢀⡀⠀⠇⠀⠄⡀⠘⡀⠀⠠⠐⠀⠁⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠅⠐⠀⠀⣀⠀⠀⠉⢀⠀⠀⠀⠦⠠⢠⠄⠀⠀⠂⠀⠠⠈⠀⠀⠀⢁⠀⠀⡠⠀⡀
⠀⠁⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣇⠎⠀⢀⠀⠀⠠⠀⡀⠀⠀⡀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠈⣁⣀⣠⣀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠈⠄⢀⡀⠐⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢄⡠⣦⠀⠄⠢⠁⠀⠀⠤⠄⠸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠄
⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢲⠀⢲⠀⡠⢤⡀⢀⣀⣀⠀⣀⣀⡀⢀⡀⠀⡀⠀⠀⢶⠖⢲⠀⣝⠀⣀⣀⡀⠴⣷⠄⢹⣀⡀⠀⢀⡀⣿⣠⢤⡄⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠛⢻⠀⡔⠚⣗⢸⠋⢙⡇⣿⠉⣻⠈⢧⣠⠏⠀⠀⠘⠗⠛⡄⣸⠀⣿⠉⠉⠀⡇⠀⢸⠉⢹⠴⠋⢉⡏⣰⠒⢿⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠀⠛⠀⠈⠃⠙⠋⠙⢸⡟⠋⠀⣿⠛⠁⢠⣨⠏⠀⠀⠀⠘⠓⠀⠁⠛⠁⠛⠀⠀⠀⠙⠃⠙⠀⠘⠃⠑⠋⠓⠈⠛⠉⠃⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢰⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠊⠀⠀⢀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠠⠈⠀⠀⠆⠑⠀⢀⠀⠀⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠈
⠀⠀⢂⠀⠀⠤⠐⠀⠀⠀⠀⠀⠋⠰⢄⠀⠙⠀⠀⠀⠀⠂⢀⠀⠀⡀⠀⠀⠒⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⢰⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⡀⠀⠁⠐⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⠢⠑⠤⢀⣀⡀⠐⠁
⠀⠃⠀⠀⣉⢘⠁⠀⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢁⡂⠁⠀⠐⢓⡈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠆⠀⠈⠀⠠⠄⠀⠠⠀⠀⠀⠀⠈⠉⢢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⡀⡀⢀⢀⠄⡀⠈⠄⠂⠀⠀⠠⡀⢀⠀⠐
⠐⠄⠡⠀⠄⠀⠂⠀⠀⠀⠀⠀⢃⠀⠀⠃⡸⠀⠀⠀⠀⠤⠐⠒⠀⠈⢡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢦⠔⠇
⠀⠀⣤⠀⠀⠀⠀⡠⠀⠁⢀⠀⠀⡱⠂⠀⠀⠀⣀⠀⡈⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀
⠀⣀⠀⠀⠀⠀⠀⢰⠀⢀⡅⠂⡰⠃⢀⠀⢀⠹⢥⠌⠀⠀⡁⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠂⠐⢀⠀⠀⠀⠄⢠
⠈⠧⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠴⠠⠰⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣴⡆⢠⣶⡴⠀⢀⣄⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣻⠋⣥⣮⡙⣿⠛⠊⣉⡺⣿⢋⣴⡳⣯⢾⣁⢠⡀⠀⠀⠰⡖
⠀⠀⣾⠛⠛⠛⠛⠛⣿⣏⢛⡟⢉⣼⣉⣀⠺⠉⠀⠈⠂⠑⠈⠂⣨⣤⢿⡙⡆⣄⠰⣆
⣤⢤⣿⡤⡤⠤⠤⡤⣿⣹⣻⢮⣽⣷⣪⣍⠋⢸⡅⢠⡖⣠⠒⣠⠂⢠⣴⠋⣳⢾⡇⢙⡤
⣿⠀⣿⠀⠀⠀⠀⠀⢹⣧⣴⣷⣬⢻⡩⠉⣶⣬⠿⢄⠸⢯⠩⣛⢲⣉⠁⠉⠀⠒⠋⠀⣷⡀⠀⠀⢀
⣿⠀⣿⠀⠀⠀⢀⣴⣿⣦⡙⢏⣥⣿⡶⢂⣍⡺⣯⣌⠶⢂⡀⠈⠁⠉⠁⠀⠀⠀⠒⠲⢼⡓⡆⠀⢸⠃
⣿⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⠇⠈⠟⠻⠀⠀⠀⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢳⡑⡇⢙⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⢉⣹⡇⢸⡄⠀⠀⠀⢠
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡻⡞⣄⠀⠾⠴⠀⢠⡻⡿⣠
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⢻⠇⣸⢃⣀⡀⡀⢀⢀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠐⠻⠇⡘⠛⣣⡞⢰⡌⠋⠃⡸⠟
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⢁⢰⡟⢰⢇⡞⣼⢱⢏⣾⡞⡸⢻⢣⡏⠀⠀⠀⠀⠀⠐⣶⢺⣧⠮⣼⣻⣟⣧⠵⣤⣿⣶
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠈⠀⠁⠀⡏⠈⢼⠁⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠑⢏⣰⣿⣄⢍⡹⣁⣼⣦⡹⠎
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⢿⣡⡤⢰⡾⣄⣤⣧⣤⣤⠄⠀⠀⠀⠀⠀⠀⣅⡙⣿⣁⣿⣹⣄⣻⠛⣰
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠋⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠙⢿⠋⢻⡏⠋⢿⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢺⠀⢸⡇⠀⠀⠁
⣧⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⣿⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⢿⠶⠾⠃
⣿⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣾
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡉⢄⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣿⣦⠙⠛⠿⣷⣤
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢸⣿
⠀⠀⠁⠀⠀⣀⣀⠠⠔⢲⠊⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⢶⠖⠛⠉⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠛
⠀⠀⢢⠀⠃⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⣀⣠⡴⠆⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠉⣄⠽⡰⢣⡜⣹⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⣁⠂⣘⡴⢷⣨⠄⣼⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠑⣀⢤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡖⠃⡤⣀⠨⠄⠸⠁⠁⣡⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠈⣠⠤⠖⠣⠀⠀⠀⣠⣤⣈⠡⢴⣣⠿⣶⣯⠈⣀⠀⠀⡀⢚⠙⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⢭⢘⣹⣄⠀⣓⣤⠝⠶⠉⢻⡈⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠉⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⠀⠀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢠⡌⣷⣂⢸⡇⣿⢶⡾⢿⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡇⢸⢦⣱⡘⣏⠛⠑⠂⠀⠁⠨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⡌⠏⠁⠉⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣇⠀⣀⡀⡠⡀⡖⢾⠾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡇⠹⡄⡿⢳⣷⠿⢻⡍⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠀⠈⠀⠀⠈⠇⠀⠁
⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⣛⣯⠽⠶⢲⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⣞⣛⠩⠅⠒⠛⠉⠁⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠿⢿⡶⠶⠶⠿⠶⡶⣶⡶⢤⡤⣤⣤⣤⣤⣤⣼⣼⣧⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠒⠺⠇⠀⠀⠀⠀⠙⠃⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣁⠀⠈⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢢⡀⢠⣄⣀⣆⠀⣰⢦⠀⣏⡽⠀⣯⠗⠘⢦⡞⠀⠀⠀⠀⠀⢀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠋⠉⠙⠀⠏⠉⠃⠑⠀⠀⠃⠀⠀⠘⠀⠀⠀⢀⢠⠀⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⢀⡀⣀⣄⣀⣤⠦⢠⢰⡀⡞⠲⡄⣰⣜⠢⣼⠈⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣍⣼⡈⢥⢱⡾⣅⠈⣇⠸⠋⠧⠹⠴⠛⠋⠙⠂⠉⠀⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⢯⡤⠟⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠎⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠜⠁⠀⠀⠀⠀⠀⢰⡆⢺⣆⣿⡀⣿⢈⣏⠀⠀⠀⠀⠀⣴⠒⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠐⢲⠀⠀⠀⠀⠀⣸⣷⢸⣿⣛⣧⣿⣿⣿⣄⠀⠀⠀⠀⠈⠳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⠏⠀⠀⠀⠀⣞⠉⠉⠉⠉⠉⠉⠀⠀⠀⣈⠇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠉⢹⠃⠀⠀⢸⠉⠶⠊⠒⢆⣠⠔⠒⠋⣹⠀⠀⠀⠀⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡏⡀⠀⠀⢸⡇⢄⡀⠀⠈⠁⠠⢐⡨⣿⠀⠀⠀⠘⢇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⣽⠀⠀⠛⠶⠦⣥⣤⣭⣥⡴⠞⠋⠀⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⣰⠃⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠾⠷⠶⠦⠤⣤⣤⣧⣤⣭⣒⣤⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⢈⠀⠒⠐⠂⠒⠐⠂⠒⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⡀⢸
⠀⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸
⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⢸⠀⡂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸
⠀⠀⠀⢸⠀⡅⠀⠀⠀⢠⠃⢀⠂⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⣆⡀⠀⠀⡀⠴⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⢸⠀⠆⠀⠀⠀⢸⠀⢸⠠⠡⠇⡞⡰⢸⢠⠐⠁⣇⠀⠀⠀⠀⡇⠈⢔⠀⠀⡄⢨⠐⢀⠈⠁⡆⠏⠜⠰⡀⠀⠀⠂⢸
⠀⠀⠀⢸⠀⡃⠀⠀⠀⠈⠀⠀⠀⠀⠀⡏⠀⠛⠀⠀⠀⠇⠀⠀⠀⠀⠁⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡁⢸
⠀⠀⠀⢸⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⣼⡆⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢠⡀⣠⡄⣠⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢸⠀⣿⡄
⣼⣿⠇⣸⡄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣼⡀⢿⣿
⡙⣽⣿⢿⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣸⢿⣿⡝
⡇⢉⣤⣾⡟⡂⠀⣠⣴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣤⡀⠀⡛⣿⣦⣌⠁
⠀⠘⠛⢻⣾⣷⢊⡀⠉⠓⠻⠇⠀⠀⢀⠀⣴⡀⣠⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⣰⡄⢀⠀⠀⠀⠿⠓⠋⠁⣈⢰⣿⣾⠛⠛
⠁⠀⣀⣀⡤⣴⡾⠟⢣⡀⠀⣠⣠⢰⣿⠰⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⣿⡷⢸⣧⢠⣠⡀⠀⣠⠛⠿⣶⡤⡄⣀⡀
⣎⡍⠀⠀⣵⣿⡇⣀⢴⣿⣇⠙⠟⢹⣿⡇⢙⡡⣩⣶⣶⣤⠀⠀⠀⠀⠀⢠⣶⣶⣮⡁⡙⠁⣿⣿⠙⠟⢁⣿⣷⢄⡀⣿⣷⡇⠀⠈⣍
⣠⣑⣤⠞⡛⢶⡿⣝⢸⡇⠈⢦⠀⠀⠨⢠⢞⣥⣿⣯⣅⠀⠀⠀⠀⠐⣦⡀⣼⣿⣿⣧⣝⢦⠈⠀⠀⢀⠎⠈⣿⢑⡹⣷⢞⡻⣦⣜⣩
⣯⠀⠙⢻⣶⢼⣃⢌⢹⡇⣀⡨⢣⠀⢾⣛⣿⠋⠉⡟⠉⠑⡄⠀⠀⣦⡹⣧⣿⡿⠋⠙⠋⣁⣻⢆⢠⠫⣄⡀⣿⢋⢄⣻⣴⣶⠛⠁⢨
⢿⣧⡤⢾⠁⡊⡿⠛⠚⢋⣍⣻⣾⡷⢿⣿⣤⣤⡄⢿⢯⣝⡹⣲⣄⠘⣗⣩⣶⠞⢀⣠⢤⡼⢿⠷⣿⣾⣋⣍⠛⠚⠻⡏⡁⢹⠦⣤⣿
⠁⣹⣧⡿⣻⠋⣣⣀⣤⣾⣯⣄⡀⣿⣮⣿⣿⣿⣇⢘⠉⠙⢿⣄⡿⠦⡵⢶⠲⠤⣬⣿⣻⣷⣥⣹⡇⠀⣬⣿⣦⣄⣠⡋⢿⠿⣧⣾⡁
⣴⣏⡿⡃⢼⡏⠉⣽⣿⣟⣿⣿⣿⣿⣿⣧⣟⠃⠀⠀⠳⢲⠋⣭⣀⣤⡿⠊⠳⣭⣶⠿⡿⠗⢤⣽⣅⣀⣿⣟⣿⣿⡍⠉⣿⡀⡹⣭⣷
⣸⣟⣥⣮⣾⣅⣀⣈⡽⣿⠷⠈⣣⣾⢿⣧⣶⠎⣩⣷⡾⣿⠉⠸⣿⣿⣿⢇⣠⢾⣿⠿⠀⠀⠀⢻⣀⡋⠰⢿⡿⣏⣀⣀⣽⣮⣬⣜⣿
⣉⣛⣯⣭⣾⣿⣧⣽⣁⣀⣀⣤⣋⣀⣼⣛⣁⣀⣰⣯⣬⣼⣷⣀⣼⣙⣟⣋⣙⣾⣁⣀⣀⣶⣀⣀⣈⣣⣄⣀⣀⣹⣥⣿⣿⣮⣽⣟⣋
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⣳⢌⣭⡅⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣷⣶⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⡄⠀⠀⡤⠄⠀⠠⠠⡀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠘⠙⠀⠀⠋⠀⠀⠘⠉⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣴⠖⣦⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣶⣶⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⠀⠀⠀⢰⣶⡄⢸⣷⡄⠀⡄
⠀⠀⠀⠀⣰⣿⡟⠁⠀⣿⣟⡔⢁⣴⡿⠀⣿⡆⣠⡁⠀⣴⠶⣾⣿⠓⣿⣿⣠⣤⡀⢀⣴⣦⣿⡟⠀⣴⣿⢿⡀⠀⢸⣿⠇⣾⣿
⠀⠀⠀⠀⠛⠿⠀⠀⢠⣿⣿⣴⣿⠟⠁⠀⣶⡅⠈⡟⣷⡦⠀⣿⡏⢠⣿⣿⢻⣿⠇⣾⡟⢱⣿⠇⢸⣿⢁⣾⣿⠂⣾⣿⣰⣿⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⢉⣷⣴⣿⡇⣰⢣⣿⡇⣰⣿⡇⣼⣿⡟⣼⣿⣠⣿⣠⡿⣿⡴⠻⣧⣼⠻⠿⠞⠙⠛⢻⣿⠋
⠀⠀⠐⠀⠀⠀⠀⠀⣼⣿⣰⣈⣴⣿⠟⠹⣿⡶⠁⠘⠿⠷⠙⠿⠞⠉⠛⠃⠈⠙⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡿
⠀⠀⠀⢀⣤⣤⠀⠀⣿⣿⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠟⠁
⠀⠀⠀⠸⣿⡿⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⢠⠀⠀⠀⢴⠀⠖⡀⠐⢢⠇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠰⠦⠀⠀⠀⠀⠙⠀⠀⠓⠀⠘⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠉

⠈
⣳⣂⠀⠠
⢉⡹⢀⢔⣶⣀⠀⠀⠀⣠⣤⣄⣀⣖⣁⣼⣷⣾⣯⣼⣿⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣻⣲⡂

⠀⠀⠀⠀⠀⠀⢸⣇⠻⣿⣿⢏⣽⡷⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠢⠄⠀⠀⠓⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣠⡿⡿⣾⠷⠿⣏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣀⣀⠀⢀⠀⠐⠧⠂⠀⠤
⠀⢀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠁⠈⠙⠂⠀⠀⣶⠾⣉⡻⣳⢆⡀⠀⠐⢨⡶⣹⣠⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⣧⣮⣝⡷⠇⠀⠳⣍⣿⣚⣿⡏⠁⣀⣠⣄⣀⠀⢤⡄
⣀⢉⣰⣏⢳⡄⣀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠞⠷⠟⠀⠀⠀⠈⠁⢹⡥⠶⠆⢠⢥⢯⢄⡽⠧⠀⠘⣦⣤
⢭⡿⣝⡆⣿⢳⡆⢻⣋⡭⠜⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣼⡟⣾⠀⠀⠘⢴⣿
⣩⠧⢲⣽⡿⢺⡇⠘⠏⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⣶⣿
⠶⣾⡵⣪⡄⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠖⣀⠀⢐⠆⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠐⠁⠈
⠾⣷⣎⣝⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢶⣿⣉⣟⣛⣷⣄⡄
⠻⠆⠺⠏⠀⠀⠀⢀⡤⠀⠀⢠⣄⠀⠀⠀⠀⠀⠠⢿⣿⡟⣿⣿⡟⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠆⠻⣿⣷⣤⠾⠟⠳⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠈⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣶⠵⠀⠐
⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠄⡐
⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣼⣶⣦⣤⠄
⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣫⠟
⠀⠉⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣃⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⣠⠀⠀⠀⠀⣤⠘⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠖⡎⠔⠡⡄⣠⢤⢀⢠⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⠒⠚⠠⠗⢀⡞⣀⣰⡎⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠔⠁⠀⠀⠀⠄⠀⠠⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣶⠄⠀⠀⠀⠀⢰⠀⡴⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⡊⢉⢃⡄⣤⡤⢈⠋⣴⡧⠀⠴⠁⢠⠄⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠘⠓⠀⠘⠊⠀⠃⠙⠂⠃⠓⠓⠛⢓⣙⢒⠮⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢼⡟⣳⡆⢘⡃⣀⣀⢀⣤⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⢰⡟⠻⣦⢻⣆⡿⠀⠀⢸⣟⣹⡷⣸⣧⣿⠉⢸⡟⢡⡿⠚⣶⠀⣠⣄⣴⠆
⠀⠀⢠⣄⠀⣴⠖⢿⡌⣿⣀⡿⠘⣷⠾⠋⢀⣿⠇⠀⠀⠈⠉⠉⠀⠈⠉⠁⠀⠈⠛⠘⠃⠀⠿⢸⣇⣨⡿⣠⡶⢦⣄
⢰⣦⡼⠿⣦⡹⠶⠞⠋⠸⡇⠀⠀⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠻⢦⣾⠃⣾⢂
⠀⠙⣷⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠘⠃⠉⠀⠲⠀⡤⠊⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⢈⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄
⢀⡀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⣠⠄⠄⠀⠀⡍⠈⠄⠀⠀⠀⣀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠾⣡⠅⠀⠀⠀⠀⠀⠀⠠⠠⢄⠀⠀⠀⠀⠙⠂⠃⠀⠀⠀⠉⢄⠀⠀⠀⡄⠠⠀⠐⠂⠈⢧⠀⠀⠀⠀⢀⡶⠃
⠀⠀⠀⠀⢘⠈⡑⠂⠀⠘⠲⠂⠀⢠⠄⣤⠀⠀⠀⣀⠰⡎⠃⠜⠋⠑⠲⠐⠲⢀⡁⠂⢀⠀⡖⠤⢒⡖⠈
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠃⡤⠘⠀⠀⡎⠀⠀⡘⠠⠀⡀⠀⠀⠀⢢⣀⡁⠂⠈⠀⠘⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠒⣀⢠⠀⢤⠀⠀⠀⢠⠊⠁⡠⠂⠑⠀⠢⢧⡀⠀⠀⠀⠀⢱⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠁⠆⠈⠀⠁⠚⢦⠀⠀⠈⠄⠎⣀⠀⠀⠀⠀⠀⠑⠂⠤⡐⠄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢲⡀⠉⠀⠀⠀⠀⠀⢤⡀⠀⣇⠠⠤⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢈⠁⡦⣀⠀⠀⠀⠀⠈⠀⢌⡤⠃⠈⠛⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢰⡷⢄⣍⡛⠢⢀⠀⠋⡌⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⢣⠌⠀⡏⣁⣤⠈⠒⡧⡀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠦⣀⣀⣇⣈⣹⣄⠀⠡⣥⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⢇⠀⠤⣼⠧⠈⠀⠘⠋⠀⠀⢿⣳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⠓⠊⠁⠀⠙⠈⠋⠉⠛⢆⠀⠉⠛⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠃⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡟⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡥⢉⣠⠖⠦⣬⠨⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠑⢀⡄⢀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣧⡀⠀⠀⠀⠘⠙⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡗⠈⠁⠀⠀⠀⠀⠀⠁⠉⠣⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠋⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡳⣞⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⢿⣤⣉⣉⣤⣿⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⣀⣤⣀⠀⠀⣸⢧⡈⠓⠤⣏⠀⠀⣀⣤⣀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⡇⠀⠈⠉⠉⠹⣆⠉⠲⢤⡏⠉⠉⠁⠀⢸⡂⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡖⠒⠋⠀⠀⠀⠀⠀⠀⢯⣑⣂⡼⠀⠀⠀⠀⠀⠀⠙⠒⢲⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠙⢦⣄⠀⠀⠈⠧⠤⠴⠒⠒⢦⠀⠀⠀⠀⡴⠒⠒⠦⠤⠼⠁⠀⠀⣠⡴⠋⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣇⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠈⠑⠶⠖⠋⠁⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⣸⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡟⠓⠚⠙⣆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣰⠛⠓⠚⢻⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢿⡀⠀⠀⠘⣆⢀⡴⠛⢦⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⡴⠛⢦⡀⣰⠃⠀⠀⢀⡿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠁⠀⠘⢧⣀⣠⡞⠁⠀⢳⣄⣀⡼⠃⠀⠈⠉⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢦⣀⣀⣤⣄⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣠⣤⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⣰⠞⠛⣦⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣴⠛⠳⣆⠀⠀⡼⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠸⣆⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠀⠙⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄⠀⠀⢀⣾⠻⣧⡀⠀⠀⣠⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢈⣿⠀⠀⢸⣇⣀⣽⠇⠀⠠⣿⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⢀⣉⣛⣉⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⢸⣿⠉⣿⠀⠀⠀⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣀⣠⣼⣿⠀⣿⣤⣄⣀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢿⣇⣸⣿⠉⠉⠹⣿⣤⣿⠉⠉⠉⣿⣄⣸⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣌⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣡⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣯⠉⠛⠛⢻⣿⠛⠻⠿⠟⢻⣿⡟⠛⠛⢉⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⠷⣦⣴⠟⠻⣷⣤⣀⣤⡾⠛⠷⣦⣴⠾⠃⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⡈⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠉⣁⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡟⠛⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠟⠛⢻⣯⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⠛⣷⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⢠⣾⠻⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⠷⠶⠾⠋⠈⠻⣶⣤⣤⣤⡾⠟⠈⠛⠷⠶⠾⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⢸⣧⣼⠀⣼⣷⠀⣿⢹⡆⣿⢹⡎⢷⣴⠏⠀⠀⣿⣽⡇⣿⢸⡏⣷⠉⣿⠋⢸⣧⣼⡇⡟⢻⡆⣸⣷⡙⣧⡾⠁
⠀⠀⠸⠇⠹⠰⠟⠛⠇⠿⠋⠁⠿⠋⠁⠀⠿⠀⠀⠀⠿⠾⠇⠿⠸⠟⠿⠀⠿⠀⠸⠇⠹⠃⠷⠾⠳⠟⠛⠧⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠤⠤⠤⡀⢠⠔⠒⠒⢤⡀⡠⠤⠠⢤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⣀⡤⢄⡀⣰⣋⣀⡤⠽⠖⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠓⠾⠥⢄⣈⣱⡄⣀⠤⢄⡀
⠀⠀⠀⡞⠁⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠘⡆
⠀⠀⠀⣧⠒⠋⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠓⢦⡇
⠀⠀⠀⡇⠀⠀⠀⠀⣷⠊⠉⠉⠑⣄⣠⠔⠒⠦⡀⠀⣠⠤⢤⡀⢀⡤⠖⠒⢤⣀⡔⠉⠉⠉⢲⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⣀⣀⠴⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡏⠀⠀⠀⠈⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡷⢄⣀⣀⠔⠁
⠀⠀⠀⠀⠐⡅⠀⠀⠈⠢⠤⠤⠖⠙⢆⡀⠀⣀⡼⢧⠀⠀⠀⣠⠿⣄⠀⠀⣠⠞⠑⠤⠤⠴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠳⡄⠀⠀⠀⠉⠉⠁⠀⠀⠉⢒⠊⠁⠀⠀⠉⠉⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡗⠒⠊⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠙⠒⠒⡇
⠀⠀⠀⠀⠀⡟⠢⢄⣀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠖⠉⠀⠀⠀⠈⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⢀⣀⠤⠚⡇
⠀⠀⠀⠀⣠⡏⠒⠤⣈⡉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠋⣉⡠⠔⠊⣧⡀
⠀⠀⠀⢰⠁⡇⠀⠀⠀⠉⠉⠒⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠀⡇⢹
⠀⠀⠀⠈⠢⣈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢊⡡⠊
⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠚⢉⣉⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⣖⣒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣖⣒⡶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠭⢿⠉⠉⠉⢹⠯⠭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠦⡄⠀⠀⠀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⢀⡟⠀⠀⠀⠀⠘⠄⣀⣴⠇⠀⠀⠀⠀⠠⡊⠉⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢠⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣧⠀⠀⢃⢾⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡟⠀⠀⢣⣾⠟⠿⠶⣶⡀
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠠⣒⣦⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠢⠀⠐⠂⠉⠀⠀⠀⠀⠀⢁⠤⠖⠛⠁⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠍⠻⠿⡁⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠄⠀⠐⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⢸⡧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠀⡅
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣼
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠰⡄⡐⠘⡄⠀⠸⣿
⠀⠀⠀⣇⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢸
⠀⠀⠀⢹⣶⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⠋
⠀⠀⠀⠈⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⣼
⠀⠀⠀⠀⡟⠔⠀⠀⠂⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣰⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⠐⠀⢀⣀⡀⠄⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⡟
⠀⠀⠀⠀⠸⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⠔⠂⠁⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡏⠛⠐
⠁⠀⠀⠀⠀⠀⠺⠗⣣⠘⢸⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠞⠉
⠀⠀⠀⠀⠰⠀⠀⠀⠈⠛⠢⢄⡁⠙⠛⠳⠶⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠈⠉⠒⠲⠤⣄⠀⠈⠈⠉⠉⠑⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⢸⢚⡲⠄⡄⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠙⡟⠂⢠⣀⢂⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣤⣀⣀⣀⣀⣈⣀⣀⣭⡶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠉⢉⡉⠉⠉⠉⠁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠁⠠⠤⠀⠀⠀⠤⠄⠐⣀⠀⠀⠂⠐⠀⠀⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⠀⣀⠀⠀⠄⠀⠐⢄⢖⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣧⣴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣁⣀⣀⣤⣤⠶⠞⠛⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣤⣤⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⡀⠄⢂⠀⠡⠂⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠍⠀⠀⠈⢵⡄⠈⠐⠢⢦⣶⣄⣀⣀⢀⡀⠀⠀⣀⢀⣀⠀⣤⠴⣖⡞⢀⠀⠀⠀⠀⠘⣡⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠱⠀⣀⣋⠀⢠⢙⠃⢠⠀⢼⠉⠷⢶⠀⡀⠠⢐⠃⠀⠊⠙⠂⢠⠀⠐⠤⠌⠀⢀⠀⣀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡷⠧⠉⠒⠄⠁⣄⡀⠂⠈⠀⠠⠀⠀⠂⠀⠙⠀⠁⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠂⡙⠃⠢⠐⢉⡂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣇⡀⠀⠀⢀⠐⠒⠄⠈⠁⢀⠐⡀⢠⠀⠀⠀⠐⠀⠐⠀⠀⠀⢤⠦⠀⡄⠀⠀⠀⢐⣤⣶⣶⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⠛⠻⣶⣦⣤⣤⣄⡂⠀⠀⠀⠀⡉⠀⠑⠂⠀⠀⠀⢈⠀⠀⠀⣀⣠⣤⣦⣴⣶⣿⡿⠛⠋⠁⡐
⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⠀⢬⡀⠀⠍⠉⠛⠻⠿⢿⠿⠿⢶⣶⣶⣶⣶⣶⣿⣿⡿⠿⡿⠟⠛⠛⠉⠉⢁⠀⢈⠀⠄⠊⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠈⢻⡀⣀⠀⠀⠀⠀⠉⠒⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⡤⣆⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠒⠃⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⡖⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢧⡤⢤⣀⣠⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⢀⡦⣄⡞⠲⠾⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠒⠈⠉⠉⢛⠋⠉⠷⢞⢹⡶⠎⠳⢶⠉⢲⠋⡙⠛⢋⠛⠁⠉⠠⠤⠤⠤⠤⠀⣀
⡇⠀⣀⠠⠀⠀⠒⠈⠉⠉⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠄⠂⠘⢀⠀⢀⡘⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢠⢀
⡇⠁⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⠤⡦⠀⠀⠀⠀⢠⠄⠰⡀⠀⠀⠩⠄⡆⠠⠣⠈⡃⠀⠐⠀⡠⠀⠀⣀⠐⡄⠀⠶⣀⠀⣀⢀⠀⢀⡀⢀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠀⠤⠬⢀⠤⠄⠀⠀⠐⠁⠀⠀⢀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠐⣨⠂⠀⠘⣈⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠀⠘⠠⠒⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑
⠏⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⢄⣠⠴⠚⢉⡀⠙⠒⢦⣀⡠⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⢁⣤⣶⣄⠀⠙⣦⣾⣿⣿⣷⣆⡜⠁⣠⣤⡀⠈⠳⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡰⠃⠈⣵⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠞⠉⢀⡴⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢋⡱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠉⢀⠔⠋⢠⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⢋⡔⣈⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠏⡀⢠⠎⢸⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠤⠖⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⠲⢤⣁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠈⡞⠁⠤⠚⢡⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⡇⢲⠀⠈⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⡿⡀⣇⠀⣀⡤⠊⠀⢀⠜⠋⡰⠉⠻⢿⡿⠿⣿⡿⠛⢿⣿⢿⡿⣿⠟⠋⠰⢈⠙⢧⠀⠊⢀⡜⠀⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⢾⡦⣄⣀⢀⣰⠃⢀⡴⠃⡟⠀⠀⢻⠞⠁⢠⠏⠀⠙⢦⡾⠁⢀⡰⠃⢸⠀⠀⣇⣀⠀⣀⡠⠞⣡⠋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⢬⣁⠹⣄⠀⢀⠔⠁⠀⢀⣾⠐⠚⠁⠠⠃⠀⠀⣧⡀⠈⠀⠰⠃⠀⣠⠏⠉⠉⢁⡠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⡀⠀⠀⠈⠑⠺⠷⣶⣶⠖⠒⠋⠘⠦⣀⣀⣀⣀⡤⠞⠀⠉⠒⠲⠶⠖⠚⢁⣠⠤⠒⠉⠀⢀⡠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠚⠋⠉⠁⢀⡴⠒⠒⢀⣞⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠙⠒⠒⠒⣞⠉⠉⠓⠦⡀⢀⣀⣠⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠒⠂⠀⣮⣀⣀⡠⠞⠀⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠙⠲⠤⠤⠖⠻⣄⡀⠀⠉⢓⣠⠖⠉⠉⠉⠃⣀⠜⠡⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣀⢛⡦⢄⠀⣀⣀⣀⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠚⠛⢇⣀⣭⠙⠤⡶⠆⠸⢉⣵⡐⠲⠗⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠖⣂⠄⠀⢁⡀⠀⡀⢀⠀⡀⣤⠄⡤⠤⣢⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠤⢬⡕⣴⣆⡿⠁⢈⢰⠴⡇⣉⣣⣇⣰⠀⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠶⡒⣄⡀⣫⠈⢉⢁⢸⣆⣀⣏⣉⣉⣀⣤⣭⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣁⠒⠤⠤⣌⣉⣈⣂⠉⡙⠉⠉⠈⠉⣉⣉⣠⣥⠴⠞⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣉⡸⣂⠤⣠⡄⢤⣈⡩⣉⣉⣉⢉⣉⣠⢁⠄⢰⡆⠚⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡌⢒⠛⠛⠲⠨⢤⣼⣤⣙⣁⣼⣀⣹⣌⣧⣭⣭⣲⠟⢟⢛⣹
⠀⠀⠀⠀⠀⠀⣀⣠⣸⠧⣄⠉⠃⠙⠓⠖⠶⢲⡤⡬⣀⣩⣭⣥⣤⣤⣽⡴⠶⠶⢛⢋⣩⣀
⠀⠠⡀⠒⠐⢅⠀⠀⠙⠲⢄⣁⠘⠙⠼⠶⠤⢤⣤⣨⣄⣄⡤⣤⣤⣤⣔⣦⢴⠶⠟⣋⣹⠏⠉⢓⠅⣀⠂⠄
⠀⠀⠀⠁⠐⠀⠠⠄⠀⠀⠀⠀⠉⠀⠂⠠⠄⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠶⠒⠒⠉⠁⠀⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⢹⠁⠀⠀⠀⡏⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⢄⠀⠀⡠⠤⠀⢀⡀⢀⡀⠀⠀⢀⠀⣠⠲⡄⡠⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⠇⢸⠀⢰⠃⠀⠒⠋⡇⡏⠘⠀⠀⡏⠉⠁⠀⠧⠇⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⢤⠼⠀⠀⠀⢠⠃⢹⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠀⠳⠴⠃⠀⠀⠀⠀⠀⠀⡏⠉⠓⠦⣀
⠀⠀⠀⠀⠀⢀⣞⠁⢰⠉⡳⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢞⠉⡦⠈⡳⡀
⠀⠀⠀⠀⠀⠸⡌⠂⠀⠀⠀⠀⠀⠀⠀⠉⠩⡙⠓⠒⠒⠒⠒⠒⠒⠒⢋⠍⠉⠀⠀⠀⠀⠀⠈⡠⠚⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⢢⠀⠀⠀⡀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠇⡜⠁⢸⠀⠀⠀⠈⠋⠀⢱⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⢀⠀⠀⠀⣼⠵⠤⣄⠀⣴⡸⡀
⠀⠀⠀⠀⠀⠈⢲⠃⠀⠸⡄⢀⠆⠀⠀⠀⣼⠀⠀⢀⡀⢸⠀⠀⡇⠀⠰⠛⣆⠀⢀⡇⠀⠀⠘⠚⢹⠃⢣
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠊⠀⠀⠀⠀⢹⠀⠀⣼⠐⠁⠀⠀⢧⣠⠇⠀⣿⠀⠈⡇⠀⠀⠀⠀⠸⣆⡼
⠀⠀⠀⡠⠤⡴⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠀⢈⡗⢦⠤⣄
⢀⣠⠞⠧⠴⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠘⠦⠼⠳⣄
⡏⢯⠀⠀⠀⠀⠀⠀⣙⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣒⣋⠀⠀⠀⠀⠀⠀⡽
⠘⢆⡓⢤⣀⠀⠀⠐⢅⡨⠂⠀⠈⠉⠉⠓⠒⢒⣶⠶⠶⠶⠶⠶⠶⣶⡒⠒⠚⠋⠉⠁⠀⠐⢅⡨⠂⠀⠀⣀⡤⢚⡱
⠀⠀⠙⠲⢬⣙⠓⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣉⣉⡉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⢉⣉⣉⡤⠤⠖⠚⠋⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁
⠀⠀⠂⢠⡀⢀⠀⠀⠢⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦⣤⡶⢠⣀⣀⠀⠀⠀⠀⢀⠀⠀⡀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽
⠀⠄⠐⠉⠳⢎⠀⢀⡆⠀⠀⠀⠀⠀⠠⠹⠌⠀⠔⠀⠀⠀⠀⠀⠈⠐⣗⣰⢩⢿⣉⡈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠆
⠀⢤⠀⠐⠣⠄⠃⠡⠀⠀⠀⠀⠀⠀⠀⡆⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠈⠀⢠⡤⠊⠀⠀⠀⠀⠀⠠⠀⠀⠤⠁⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖⠋
⠀⠀⢀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢆⣀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⢄⠀⠂⠠⠀⠀⠀⠀⠀⠀⠤⠷⠰⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢖⡀⢏⠃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠀⠀⠀⠇⠠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠐⠣⠖⠀⠀⠀⠆⠀⠀⠀⠀⡨⠁⠁⣀⡄⠈⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠠⢤⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡉
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠂
⠀⠀⠀⠳⣄⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠛⠀⢰⠀⠀⠀⡄⠄⠀⢀⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠐
⠐⠎⣠⠔⠙⠀⠏⠁⠀⠀⠀⠀⠀⠀⠂⠐⠒⢀⠀⠂⡄⠀⠀⠀⠀⣧⠀⠀⢣⡼⠋⠢⠀⡀⠀⠀⠀⠀⠀⠀⠙⠣⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠲⠄⠘⠀⠂⢠⠀⠀⠀⠀⠀⠀⠃⠸⠀⠉⠀⠀⠀⠀⠀⢈⠑⠲⢡⣴⠶⠂⠀⡀
⠀⠀⠀⠃⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠈⡇
⠀⠀⢦⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⠀⠀⠐⠐
⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⡀⠤⣐⡖⣲⠤⠚⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡴⠉⢨⣧⣌⣀⡠⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠙
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠠⠿⠍⣤⡽⠃⠀⠀⠀⠀⠁⠀⠐⠰⠃⠙⠈⠁⠀⠀⠀⠀⠀⠈⠆⠀⠃⠛⠒⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⣀⠜⠁⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⢸⡇⠐⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠒⠐⠂⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⠂⠐⠀⢂⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇
⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡇
⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⡇⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠠⠄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⢸⡇
⠀⠀⠀⢸⡇⠄⠀⠀⠀⢸⠁⠘⠁⠊⡏⡼⢨⠴⢃⠆⠃⢘⠀⠀⠀⠀⡿⠀⡆⠀⠃⢰⢀⡇⠆⡀⠍⡐⢰⢠⠁⠂⠀⠀⠰⢸⡇
⠀⠀⠀⢸⡇⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⡏⠁⢸⠈⠀⠀⡎⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢘⢸⡇
⠀⠀⠀⢸⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇
⠀⣰⡆⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⢀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⢰⣆
⣰⣿⡇⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠁⠈⠋⠈⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡇⢸⣿
⠙⣻⣿⣿⡁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⣿⣿⣟
⡇⠉⣩⣼⡿⠄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⢿⣧⣍⠉
⢁⠘⠿⢿⣵⣧⠐⡉⠙⠷⠾⡇⠀⠀⠀⠀⣠⡄⢀⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡀⢠⣄⠀⠀⠀⠀⢸⠷⠼⠋⢉⠀⣼⣮⡿⠿⠧
⠂⠀⠀⢉⣈⣠⣼⠿⢦⡀⠀⢀⣀⢀⣾⡀⣿⣧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⢀⣷⡀⣀⡀⠀⢀⡴⠾⣧⣄⣁⡉
⡴⢊⠉⠁⣣⣾⡇⢀⣠⣷⡆⠙⣿⢸⣿⡇⠙⠏⢛⣡⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣬⡛⠹⠋⢸⣿⡇⣿⠋⢰⣾⣄⠀⢸⣷⣜⠈⠙⡑
⣙⠻⣆⡴⡿⠌⡵⡫⢼⣿⡘⣆⠘⠀⠙⠁⡼⣋⣿⣟⡋⠉⠁⠀⠀⠀⣤⡈⢩⣿⣿⣿⣙⢧⠈⠋⠀⠁⡰⠣⣿⡯⢙⢮⠩⠿⣦⣠⠟
⣟⠁⠻⢭⣔⣹⡧⡈⢺⡇⠀⠈⢦⠀⣰⠖⣾⠟⠛⣿⠛⠳⡀⠀⠀⣤⡹⣿⣿⣿⠟⠻⠟⠃⠳⣄⠀⣴⣁⠀⢸⡗⢉⢼⣏⣢⡽⠟⠉
⣿⣄⣀⣼⠋⠼⣿⠾⠼⠗⠚⠶⣾⣦⣽⣿⣍⣀⡀⢽⣴⡲⢒⠤⡀⠸⣿⢘⣯⡥⠂⠀⢀⣨⣿⣯⣶⣷⠶⠛⠺⡧⠷⣿⠛⠙⣧⣀⣠
⠊⠻⣇⣾⣦⡶⢇⠀⣀⣸⣟⡉⠈⣷⣜⣿⣾⣿⣇⠸⡊⠻⣾⡉⣼⣆⣘⣭⡍⣄⣘⣿⡿⣮⣜⡕⡾⠁⢉⣻⣇⣀⠀⡸⢺⣴⣷⣸⠟
⣠⢞⣻⠇⣹⡷⠛⢻⣿⡿⣿⣿⣷⣾⣿⣯⡻⠟⠉⠀⠷⢶⡞⣻⠁⢀⣱⡬⢷⣴⣪⣭⣿⣷⢍⡻⡇⠀⢸⣿⢿⣿⡟⠛⢶⣇⠼⣟⡳
⣻⣿⢓⣕⣽⡇⠀⠙⣟⣿⣿⠑⢟⣹⣿⣏⣯⡴⠒⣦⣸⣾⠒⢻⣿⣿⣿⣦⠀⣸⣿⣷⠊⠀⠀⢿⡏⠳⠋⣿⣿⣻⠋⠀⢸⣦⣪⡘⣿
⠻⠿⡿⡛⣽⣿⣆⢻⡏⠋⠁⢀⡾⠋⢱⡿⠛⠁⢈⡝⡉⣘⣧⡀⢙⡿⣿⠷⠻⣤⠟⠁⠀⢠⡀⠀⠑⢲⡀⠈⠙⢸⡟⣰⣿⣯⢻⣿⠿
⡶⣶⢾⠿⠿⡿⢿⠿⢷⣾⣿⣿⣷⣶⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣿⣿⣶⣶⣿⣿⣶⣶⣾⢿⡿⣷⣾⡿⣿⡿⣿⡿⡷⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡎⠀⠇⠀⢀⠔⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡌⠙⠒⢼⠠⠐⠛⠠⡟⢀⣔⡿⠒⠒⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠡⡀⠀⣠⠏⠸⠁⢈⡒⢢⡀⠘⣄⠀⠁⠀⠀⠀⠀⠘⢏⠉⠁⢈⡸⠁⠑⣏⠈⣧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⣱⡯⠣⢴⡆⠙⡤⠸⠊⢙⣶⣿⣷⣶⣄⠀⠈⠀⠀⠸⠶⣈⣁⠴⡄⢴⠁⠈⢦⢠⡯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢤⣾⠑⢦⢸⠀⠋⢁⡔⠛⣾⡿⣺⣘⠽⢼⡽⣦⣄⢤⡧⢊⡥⢖⠛⠃⠀⠱⠀⠣⡀⣁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⡇⠀⠀⠀⠀⠀⡰⢻⡿⠒⣤⢞⣿⢿⢷⣷⣲⣏⢏⢱⣳⡿⠼⠒⠛⠲⠧⢄⣠⠁⠉⡤⠐⢇⠈⡦⢜⠉⠓⢤
⠀⠀⠀⠀⣠⠊⠁⠐⠀⠱⡀⠀⠀⠀⢠⡀⠀⠀⣼⣯⠮⣗⣏⠿⣻⣟⣿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠓⡄⠸⠣⣀⡸⠈⠃⠀⠱⡀
⠀⠀⠀⡸⠁⠀⠀⠀⣀⡀⠈⠑⠒⠒⠟⠳⢄⣀⣿⣟⣿⣿⢎⣸⣛⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠛⠶⠚⠁⠀⠀⠀⣀⠀⠇
⠀⠀⠀⡇⠀⠀⠃⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⢿⣻⣮⣾⣿⠿⠃⠸⣏⡒⠄⢒⣒⣒⠦⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠪⠤⠷⠀⠀⠀⡄
⠀⠀⠀⡼⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡈⠉⠉⠀⠈⠀⠉⠢⣕⠢⣄⠀⠀⢠⡇⠀⠀⠤⠄⠀⠀⢀⠔⡇
⠀⠀⠀⡇⠈⠳⡌⠀⠄⠀⠠⠤⠀⠀⢀⣀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠙⠲⠭⠿⠟⠁⠀⠀⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⡇⠀⠀⠈⢦⡀⣀⢀⡀⠀⠠⠌⢉⡀⡀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⡰⠆⠠⠀⠀⠈⠁⣀⠤⠒⠒⠊⠁⣰⢻
⠀⠀⠀⠘⣄⣀⡀⠀⠀⠀⠀⠈⠒⠒⠒⠦⡀⣁⣉⣀⣁⢀⣀⠈⠀⠉⠀⠁⠒⠂⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡿⢦⡀⣰⠿⠛⠛⠉⠨⡇
⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠀⠀⠄⠊⠁⠈⠁⠀⠉⠀⠀⢀⡾⠁⠠⠀⡇⢻⡀⠄⢀⠔⠁⣧⣀
⠀⠀⣠⢴⠈⠣⣉⡇⠀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⢒⢶⣄⣀⣀⣀⠀⠀⣾⠀⠀⠀⠀⡇⢸⣢⠐⠀⠀⠀⡧⠈⠓⣄
⢀⡔⠁⣸⠀⠀⠈⡇⠠⡟⢘⠥⡂⢙⢿⣷⣄⠀⠀⠀⠀⠀⣠⠖⠏⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⡧⠀⢿⠀⠀⣀⠠⡷⡏⠀⠀⠀⢀⣠⠃⠀⠀⠈⢦
⡜⠀⠀⠈⣦⣄⠀⠑⠚⠀⠉⠀⠛⠐⠀⠨⢿⡆⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠃⣿⢠⠞⠛⠉⣻⠀⠀⠀⠀⠈
⡇⠀⠀⠀⡯⠘⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡎⠀⠀⠀⢀⣇⣸⠎⠀⠀⠀⣹
⢳⠀⠀⠀⠓⢦⡀⠙⢿⣦⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⡇⢀⣠⠞⠉⠉⠁⠀⠀⢀⡴⠉⠀⠀⠀⠀⡸
⠀⠳⡀⠀⠀⠑⠉⠢⣀⠉⠛⠿⠷⣦⡤⠒⠶⣾⠀⠀⢷⣤⣤⣤⣤⡀⠀⠀⣀⣤⣤⡤⠞⠋⠉⠓⣏⠀⡸⠁⠁⠀⠀⠀⠀⢀⠴⡪⠊⠀⠀⠀⢀⡔⠁
⠀⠀⠈⠢⣄⠀⠀⠀⠀⠉⡒⠤⣀⠀⠀⠀⠀⢸⡀⢀⡎⠀⠉⠉⠙⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡀⠄⡪⠁⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠁⠀⠉⠔⠒⠠⢬⡅⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠆⠁⠀⠁⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢄⣀⡀⠀⠀⢸⠁⠀⡧⠋⠁⠈⠩⠟⠭⠬⠬⠛⠋⠀⠈⠙⠀⠀⠁⠀⠀⠀⢀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⡏⠀⠀⢸⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠜⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢄⠠⠊⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠁⠠⠐⣂⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡀⢀⢈⠉⣀⡠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⠃⠉⠀⠀⢀⢠⢄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⡐⢀⠁⢀⠥⠼⡁⢄⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡗⡌⢄⡤⢾⢉⠉⠉⠑⡓⠀⠀⠘⡦⢀⣲⠃⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⠈⣉⣁⣈⣂⣀⣀⣒⡀⠀⠀⠀⠉⠠⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠤⡀⠀⠀⠀⠠⡀⢀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠒⠤⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠐⠈⠁⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠐⠒⠂⠀⠤⠤⠀⠀⠀⠤⠤⠀⠒⠒⠒⠂⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢠⣓⡄⠀⠀⢀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠇⠀⠀⣿⣩⡇⠀⠀⢿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣭⡇⠀⠀⣟⢩⡇⠀⠀⣟⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⡇⠀⠀⣟⢥⡇⠀⠀⣟⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇⠀⠀⣿⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣴⡇⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠆⠒⠛⠛⠓⠀⠉⠉⠉⠉⠉⠁⠉⠛⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡖⠉⢢⢀⡴⡄⡎⢸⠀⢸⠁⢸⠀⡇⢡⠀⡎⠀⢱⢠⠒⠀⢴⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⢸⠈⡇⠓⠂⢸⠀⠸⠀⢼⠀⢃⠼⠀⡇⠀⣆⢈⠀⠓⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠁⠀⠀⢨⠀⣸⠃⠈⠒⠂⡇⠀⢸⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠤⠤⠆⠒⠒⠒⠚⠛⠉⠀⠉⠉⠈⠁⠒⠚⠒⠂⠤⠤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠒⢤⠀⢀⣀⢀⡊⢦⠀⡰⠋⢱⡀⡎⠱⠀⢠⠊⠑⡄⢀⢤⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠇⠀⢰⠀⢂⠸⣠⠆⠘⠀⢃⠀⢘⠃⢣⢀⠀⢣⠀⠀⡇⢸⠐⠤⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣄⡸⠀⠀⠀⡇⠀⠸⠀⠹⣀⡸⢸⠀⠈⡄⠀⠣⠞⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠀⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⠀⢠⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡜⠒⡄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠈⠲⠤⠍⣐⣒⠒⠐⠲⠆⠀⠀⠤⠤⠤⠄⠀⠀⠐⠶⠒⠒⣒⣒⡩⠤⠖⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠬⠭⠍⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⠉⠭⠥⠤⠤⠐⠒⠂⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣤⢠⣤⣤⡄⣤⡄⢤⣤⣤⠴⣤⣠⣤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣼⡯⣿⣇⣿⡇⠜⢻⣿⠄⠟⠀⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠃⠘⠛⠛⠃⠙⠛⠛⠁⠀⠘⠛⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢠⣶⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⡿⠀⠀⠻⠦⢤⣿⢻⠃⢻⡇⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠸⠁⣴⢷⡆⠀⣾⣯⠃⠀⡾⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⠀⣴⠀⢿⡜⠀⢀⣿⠏⠀⢰⠇⠀⡀⠀⢠⣾⢻⡟⠀⢠⣾⣿⡇⢀⣼⡟⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡇⣿⣸⡟⢀⣼⡟⠀⢨⣏⠀⢠⡿⠀⣼⡇⢠⡿⢣⣿⡃⠀⣿⣿⣿⢡⠎⣽⡷⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢰⡏⠸⣧⠎⢸⡇⡠⠋⠻⠄⠋⣴⡼⢻⠁⣸⠷⠋⠸⣇⠜⠛⠃⠿⠋⠀⠈⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣸⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠗⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠄⢠⣤⢤⣄⠀⢠⣤⠀⣠⡄⣤⡤⢤⣠⣤⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢰⡿⠀⠀⢹⣿⠟⠡⣿⡃⣸⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠙⠛⠛⠁⠀⠀⠘⠋⠀⠀⠛⠓⠋⠈⠛⠂⠛⠁





⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠙⢦
⠠⠀⠀⠀⠀⠀⠌⠀⠀⢀⠀⠄⠀⠀⠐⠂⠄⠀⠀⠀⠉⠀⠄⠠⢘⡀⢀⠄⠀⠀⠦⠀⠀⠀⣀⣀⣸⣀⣀⠀⣸⡇
⠀⠀⠀⠁⠀⠀⠀⠈⢉⡉⠀⠀⠀⠀⠈⠀⠈⢄⠀⠶⢦⣘⣴⡔⢁⡠⠖⢒⠂⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠉⠀⠉⢈⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢰⣀⢀⣉⠭⠤⠄⢿⡉⠉⠻⠭⠭⠭⠤⠤⠤⠄⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠠⠉⢐⢀⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠈⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠠⡆⠄⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠑⠶⠄⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠑⣆⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣱⠤⠨⠥⠃⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠆
⠀⠀⠀⠠⠒⠈⠂⠀⢤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠈⠀⠄⠀⠠⢀⠀⠄⠀⠀⢴
⠀⠀⠀⠀⠒⠂⣧⡴⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠂⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠐⠀⠞⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠈⠈⡋⠈⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡂⣲⣤⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠠⠤⡧⠠⡦⡄⠠⣤⠬⢤⣄⠀⠀⠀⠀⠀⠉⠤⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢀⣴⢃⣄⣀⣀⣀⣀⠀⣄⢲⣄⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣴⢀⣼⣷⠾⣟⣛⡛⠙⠛⠚⠛⠙⣛⣛⡿⢦⣿⣄⢰⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣼⡿⠿⠟⠶⠶⠶⠍⠙⠃⠀⠀⠀⠛⠉⠱⠶⠶⠞⠿⠷⣿⣄⢻⡆
⠀⠀⠀⠀⠀⢀⢀⣀⣤⣷⡿⣤⣭⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢫⣍⡻⣬⣷⣄⡀⡀
⠀⠀⠀⢀⡄⠒⠘⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠂⢠⡀
⠀⠀⠀⢉⣴⡅⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣦⡉
⠀⠀⠀⠘⣛⣱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣎⣻⠃
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢠⡚⡇⡆⡤⣄⡤⣤⢤⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠋⠻⠂⠹⠊⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⢀⣿⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢠⠠⢐⠦⣀⣆⣄⣠⠀⠀⠀⠀⠀⠀⣦⠈⣷⡀
⠀⠀⠐⢦⣿⣴⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠸⣦⣿⡴⠂
⠀⠀⠠⣤⣍⡻⣰⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣆⢟⣩⣤⠄
⠀⠀⠀⠀⠉⠙⢿⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢰⡿⠋⠉
⠀⠀⠀⠀⠈⠙⠾⣷⠃⢻⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡟⠘⣾⠷⠋⠁
⠀⠀⠀⠀⠀⠻⢷⣬⣄⣞⢰⣦⣀⡞⠉⣻⠿⠦⡀⠀⠀⠀⠀⠀⠀⢀⠴⠿⡟⠉⢳⣀⣴⡆⣻⣠⣥⠶⠛
⠀⠀⠀⠀⠀⠀⢰⡦⠾⢻⣿⠻⣦⡍⣲⣆⠀⢀⢷⢠⠟⡝⢯⠻⡐⡦⡀⠀⣰⣖⢩⣵⠟⣿⡟⢷⢴⡆
⠀⠀⠀⠀⠀⠀⠈⢷⣵⡀⠙⣷⠜⠉⠀⠙⠁⠈⠻⣁⣔⣴⣦⣣⣀⠟⠁⠈⠋⠀⠉⠣⣾⢋⢠⣮⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢻⡁⠳⣄⢀⣥⠤⠂⠤⢟⠉⣉⣻⡿⡿⠤⠀⠤⣤⡀⢠⠖⢈⡟⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⢀⣈⠀⠈⠀⠂⠀⡰⠛⡩⢏⠛⢆⠀⠀⠀⠁⢐⣁⡀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠒⠀⠀⠉⠉⠉⠀⠀⠉⠉⠋⠠⠀⠂⡀
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣟⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⡄⠀⠀⠀⠀⢠⠃⢆⢣⠀⠀⠀⢀⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡆⢱⠀⠀⠀⠀⢯⢸⢸⢸⠀⠀⠀⢸⢠⠱⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⣄⡜⠀⠀⠀⠀⠈⣻⣿⢿⡄⠀⠀⠘⣼⣾⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⢲⡀⠀⠀⠀⡞⠛⢩⣼⠃⠀⠀⡴⠻⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⢸⡇⠀⠀⢸⣴⣿⡗⣿⠀⠀⠀⣷⣰⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢚⣿⡇⣀⡀⢈⣿⠦⣌⣏⠀⣀⠀⢸⣿⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠶⣤⣶⣾⣿⣻⡏⠭⠛⣿⣿⣭⣿⡯⣑⠢⣿⣿⣭⣿⣿⠿⣋⣿⣷⣶⣶⡴⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⢾⣿⣷⣿⣛⣛⠋⠉⠉⠉⣸⡧⢐⣫⣧⠀⠀⢰⡗⠠⢍⣿⠀⠀⠀⣿⣈⠤⣿⠉⠙⠛⠛⠛⣷⣶⣽⣟⣛⣳⣆
⠀⠀⠀⠀⠀⢾⣷⢻⣽⣶⣿⣭⣭⣿⣶⡞⠲⣮⣩⣭⣭⣥⣤⡶⢮⣭⣛⣋⣭⣴⡶⢦⣭⡿⡿⢭⣴⡞⣛⣛⠺⣿⣷⣴⡟⣿⢻⡿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⣚⣿⡸⣿⣿⣿⣿⣾⣽⣶⢶⣾⣿⣿⣶⣮⣻⢯⣯⣭⣿⣶⣿⣯⣿⣷⣭⣿⡿⣿⠿⢿⣿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡯⣽⣽⠿⣿⣿⣿⣮⣿⣯⣿⣾⣿⣯⣽⣿⣽⣿⣿⣟⣟⣫⣾⣯⣿⣷⣿⣷⣷⣿⡿⣿⣻⣿⣟⡾⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡷⡏⣵⠟⣿⣿⣿⣞⣭⡭⢿⣟⣯⣿⣿⣟⣯⣭⢯⣟⣿⣯⣷⣿⣿⣷⡿⠞⢾⣿⢿⣿⢫⡷⣿⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⣸⠇⠀⢹⡟⣿⠉⣿⡝⣹⠟⠉⣿⣯⡿⠁⠹⣟⣿⣿⠿⣿⡿⢡⡟⠀⠀⠀⢻⣏⢃⡾⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠀⠀⠘⣷⣻⡿⠃⣴⠏⠀⠀⠉⠉⠁⠀⠀⢿⣭⣿⣠⣿⠇⣼⠃⠀⠀⠀⠀⠙⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣘⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠟⢁⣴⡟⠀⣀⣀⣀⣠⣤⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣫⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠩⠻⣯⡛⠿⠗⢒⣺⣾⠶⢾⣖⠾⣿⣿⠿⢟⣫⡶⠞⠛⠻⢮⣟⣟⣩⡴⠞⠉⠉⣇⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠶⣻⣄⣀⡀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠉⠓⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣠⡶⠿⣟⣷⣄⣀⡀
⢀⣠⠴⠞⠋⠉⠉⢿⡟⣽⢿⣯⣟⢛⣶⡶⢦⣤⣤⣄⣤⣤⣀⣤⣤⣤⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣻⣭⣽⣿⣿⣿⡿⠋⠉⠉⠛⠶⢤⣀
⣾⣧⣄⡀⠀⠀⠀⠈⠻⠾⢿⣽⣿⡿⡷⣿⣿⣷⣷⣿⢿⣿⣫⣴⣶⣮⣿⣿⣛⣿⣭⣴⣦⣽⣷⡾⠿⣶⣾⢿⣻⣿⣵⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽
⠈⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⠈⠛⠿⠿⠻⠷⡿⠿⣿⣯⣿⢾⣿⣿⠿⣯⣭⣽⡽⠿⣿⡿⠟⠛⠛⠛⠛⠛⠉⠀⢀⣀⣀⣀⣤⣤⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠲⢄⣠⣤⣶⣤⣤⠔⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣇⣀
⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⢻⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠹⡈⠉⠛⠒⣦⡄
⠀⠀⠀⠀⢸⠳⠦⢤⣀⡀⡞⠀⠀⠀⠀⠀⠀⢀⣨⠧⣤⣤⣠⡼⣀⡀⠀⠀⠀⠀⠀⠀⣧⠴⠚⠉⠁⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⢳⣀⣀⣀⣤⣴⣾⠋⠀⣰⠃⠀⠈⢣⡀⠉⠹⣶⠦⠤⣤⣴⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⣤⣀⣀⠀⠀⠀⡏⠁⠀⢸⡼⠁⠀⢠⠧⢤⣠⠤⠖⢣⠀⠀⠘⢆⠀⠀⣿⣀⣠⠴⠒⢻⠁
⠀⠀⠀⠀⠀⡇⠀⠈⠉⠛⠲⡧⢤⣠⠞⠀⠀⢀⡏⠀⠀⡇⠀⠀⠈⢧⠀⠀⠈⢷⠚⣿⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠯⢴⡆⢀⡾⠦⢤⣀⣇⣠⠤⠖⠛⢦⢠⡖⢤⡧⣻⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠷⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢻⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠳⠤⣄⣀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⣠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠣⢤⣀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣨⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⡇⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡷⠀⠰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠘⣶⡂⠀⠀⠀⠀⠀⢀⢹⡟⣹⠻⡿⡿⢻⡙⣿⢁⠀⠀⠀⠀⠀⠀⣲⡞
⠀⠘⡷⣄⢤⣄⠀⠁⣵⣷⣀⠀⠀⡄⢸⣾⡌⢿⢛⣙⣛⢻⠏⣼⣾⠀⡄⠀⢀⣰⣷⡅⠁⢀⣤⢄⡴⡟
⢀⣠⣬⡟⣤⣝⡇⠳⣦⠰⢧⣀⠀⢻⣼⠿⠞⠓⢹⡾⣿⠑⠻⢿⣿⣬⠃⢠⣠⠗⢠⡶⠃⣟⣥⡼⣯⣤⣀
⠈⠉⠀⣠⠞⠁⣸⡿⠻⣄⡐⠻⠁⡘⠁⡿⣣⡷⠂⣁⡃⠲⣧⡻⡇⠙⡀⠹⠓⣀⡼⠻⣿⡀⠙⢦⡄⠈⠉
⠀⠀⠀⠀⠀⠉⠁⠐⠋⠁⠀⠁⠳⠀⠀⠀⠋⠁⠀⠀⠀⠀⠉⠃⠀⠀⠰⠃⠁⠀⠉⠓⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠨⠂⠁⠅⠀⠀⠉⠘⠀⠐⠐⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⡀⠀⣤⣀⠠⠤⣀⠀⠠⡔⠀⠀⠀⣆⡀⠀⠀⠀⠀⣀⡆⠀⠀⡐⡤⠀⢀⡤⠤⢀⣠⡄⠀⡀
⢀⡀⠀⠙⢳⣄⣬⠷⣶⠋⠰⣾⡄⢱⡀⢿⡍⠿⢄⡭⣁⠼⠏⣽⠇⣰⠁⡼⡶⠈⢳⡶⢯⣄⣴⠛⠁⠀⣀
⠀⠉⡉⣷⠋⣡⠇⡶⠋⢰⣏⠈⠀⡾⢻⣿⣾⡴⣼⣷⣿⡴⠼⣞⣿⢻⡆⠈⢈⣷⠈⠳⡆⢧⡉⢳⡏⡉⠁
⠀⠰⠿⠋⠘⠁⠀⡀⡩⡿⠀⠀⠀⠃⢸⢻⠣⣾⡦⣥⡥⣾⡦⢹⢻⠀⠃⠀⠀⠸⡯⡁⡀⠀⠙⠈⠻⠶
⠀⠀⠀⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⠀⠀⣸⣧⣽⣶⣿⢷⣾⣥⣿⡄⠀⠀⠀⠀⠀⠀⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⡷⠄⠴⣿⢿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠋
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠻⣦⡀⠀⠈⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⠤⢤⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠶⠶⢬⣿⣦⡀⠈⢣⣱⠀⠀⠀⠀⠀⢀⠜⢀⠔⠉⠀⠀⢠⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠠⣄⣈⠉⠛⠶⢤⣨⠤⠶⡦⣄⠔⣃⣔⣁⠠⠤⠤⠴⢥⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠂⠠⠀⣀⠉⠉⠉⠉⠁⢸⣤⠀⢰⡃⠬⡁⠤⠤⠤⠤⠤⠤⢀⠈⢳⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠦⢬⡒⠖⠒⠂⠉⠉⠉⠩⠙⠛⠿⠷⠾⢇⡀⠈⣧⠐⠲⢤⣤⣀⠀⢠⠟⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⠉⢻⠈⣇⠠⠤⠤⠤⢄⣻
⠀⠀⠀⠀⠀⠀⠤⢺⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠉⠐⠒⠠⡔⠊⢹⠀⢸⠲⣤⣀⣀⣠⡟
⠀⠀⠀⠀⢠⢂⣀⣼⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢠⠏⠀⢸⠀⠀⠉⠉⠁⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⢸⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⢄⡀⡇⠀⠀⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣞⣠⢤⡀⢠⠇⠀⠙⡇⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢳⡼⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡇⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⠀⠀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡇⠀⠀⡇⠀⠀⠘⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡔⠀⢠⠁⠀⠀⡇⠀⠀⢀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠦⣄⡀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⢸⠀⠀⠀⣠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠤⠌⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡸⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⠀⠀⡇⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠃⠁
⣿⣟⢻⡟⠿⡿⠻⢟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⣠⣾⣶⣿⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣿⢛⠉⡉⢀⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠿⠿⠿⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣀⣀⣸⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣽⠀⣬⠀⣤⡄⡴⣶⣄⡴⣶⣄⣦⣀⣶⠄⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒⡿⡻⣿⠛⢿⢋⠙⠿⢋⠙⠿⡛⡟⡙⣿⢿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣴⢿⡇⣿⣿⠟⣿⣿⠇⢹⣿⠏⠰⣿⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⡁⠀⠋⡄⢸⠀⢀⣤⠀⢀⣼⠆⢀⣼⣃⠀⢈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠛⠻⠘⠃⠂⠀⠀⠃⠀⠰⢟⠁⠀⠀⢨⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣤⣤⣧⣼⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⡗⢻⣿⣿⣿
⠀⠀⠀⣶⣇⣆⠀⠰⠀⠀⠶⠦⣶⡴⢦⣆⡆⠰⣦⡛⢰⡰⡄⣢⣡⡐⠂⠀⠀⣿⣿⣿⠃⠸⢻⣿⣛⣿⣿⡍⣿⠹⢻⡟⠿⣻⣏⠙⣤⡟⢟⣿⠿⠟⢯⣿⣿
⠀⠀⠀⣿⡤⡟⠀⢭⡆⡶⠶⠄⣿⢨⡅⣿⢇⡤⢪⣅⠠⠿⡄⠸⣧⠀⠀⠀⠀⣿⣿⣿⠀⢻⢰⣷⠆⣿⢉⢉⡫⠘⡒⣿⠀⠹⣋⢕⢾⡗⣘⢻⡗⠘⣾⣿⣿
⠀⠀⠀⠭⠟⠻⡆⣻⡇⣻⢞⠁⣿⣼⡯⡿⢰⠆⠀⢸⣤⣴⣷⠀⣿⠀⠀⠀⠀⣿⣿⣯⣂⣤⣄⢿⠀⣿⢀⣠⣷⠀⠇⣖⣸⠈⣿⣿⡆⡇⠙⠸⣿⠀⣿⣿⣿
⠀⠀⠀⣭⣦⢾⠇⢺⣯⣿⢹⢆⢙⣟⡃⠶⢸⣲⣶⠞⣝⡆⠿⡆⢛⡄⠀⠀⠀⣿⣿⣿⡂⢛⢡⣾⠁⠙⢰⣧⡿⡆⢰⣿⣹⢠⣿⠛⣴⡻⣹⣠⣿⠤⢿⣿⣿
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠉⠁⢀⣤⡪⠉⠀⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⡿⠻⣿⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⣠⣶⣿⣿⣿⡆⠈⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⠟⠁⠀⠀⠀⢻⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣿⠗⠀⢀⡀⢿⣿⣿⣿⣿⡇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⣼⣿⡿⣷⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢿⣿⣿⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠏⠉⠑⠀⠀⠉⠢⡀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠤⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⣀⣀⡀⠀⠀⢤⡈⢦⡀⠀⠀⡞⢀⡠⠂⠀⠀⠀⠀⢈⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠉⠲⣤⣙⢦⣳⡒⡞⣠⠛⣁⣤⣤⣶⠶⠶⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡽⢶⣦⠤⣤⣤⣤⣿⣿⣿⣥⣍⣹⣷⣟⣋⡁⠀⣀⣀⣀⡠⢼⣃
⠀⠀⠀⠀⠀⠀⠀⡏⠓⡶⠋⠀⠀⢀⡤⠖⠋⡩⠋⠙⠛⠻⣟⠛⠻⠭⣉⡉⠀⠀⠀⠀⢢⠝⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠞⠁⠀⢀⣼⣿⣷⣶⠮⢄⣀⠀⠀⠀⠀⠑⠢⣀⣀⣤⣵⣤⡀⠻⠃⠇⠠
⠀⠀⠀⠀⢀⡴⠚⠕⠀⠀⢠⣾⣿⣿⣿⡿⠀⠀⠈⠛⠲⡦⠔⠒⠉⢹⠉⢉⠙⣿⡇⠀⠀⠸⣴
⠀⠀⠀⠀⠉⠉⢉⡿⢀⣴⠿⢿⣿⢻⣿⡇⠀⠀⠀⢈⣾⡇⠀⠀⠀⢸⠀⠈⠀⠘⡇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⣾⠵⡿⠃⠀⠀⡟⢈⢿⣿⠶⣤⣀⡀⣪⡇⠀⠀⣀⣸⡇⠀⠀⠀⣿⣄⠀⣶⡄⣣⡀
⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⡆⠈⡞⡟⠀⠀⠉⠛⢿⡷⠖⠛⠉⠘⡇⠀⠀⢀⠈⠻⣦⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠀⠁⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⣿⡀⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⢀⣴⣾⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⢄⡀⠀⠨⡇⠀⢀⣀⡤⠧⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠷⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⡏⢰⠆⠠⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⡇⠋⠀⠀⠀⠀⢀⣴⣿⠟⢛⣉⡙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⢿⠘⠁⢀⡏⠀⡾⣰⣿⠟⠠⠞⠛⠉⠛⠆⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠆⠀⢀⣤⡀⠀⠀⠀⣼⠁⢰⠇⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠏⢠⣿⠀⠀⢿⡅⢹⠀⣀⣰⡏⢀⡿⠀⠛⠀⢸⠇⠀⠀⠉⠀⠀⠀⠀⣼⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢀⣾⠷⣄⠐⠈⠛⢾⡌⠀⣿⠋⣹⣣⣦⠀⣀⡿⢀⣤⡀⢀⠀⣠⠀⢠⡟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⡇⠘⠃⠀⢹⣆⡇⢀⠇⡿⢰⡟⠀⣿⢣⡟⡼⢩⡇⣯⢾⣡⣇⡴⣿⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣿⠁⣴⠗⠀⣸⠿⣇⡜⢸⢣⢸⣇⠀⠋⢸⡇⠷⠁⠉⠀⡈⠀⠉⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣀⣠⡟⠀⠉⠀⠘⠃⠀⠙⠂⡀⠘⠇⠀⠀⢀⣀⠀⡴⠚⢹⠇⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⣉⠉⠀⣄⠘⣿⡄⠀⣴⡆⠀⣿⠀⠀⢀⢠⡏⠙⠸⣅⣴⠟⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⣿⠀⣿⡇⡄⢻⡇⢀⡏⣴⢰⡟⠀⣿⡄⣀⣀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⢸⣿⠀⢹⣷⡇⠘⣷⠚⡇⢿⠾⣅⢄⡼⣿⠉⠹⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⣿⠀⣾⠘⠆⡼⢹⠀⠀⠀⠀⣰⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢀⡏⠀⠀⠑⠋⢀⡀⠀⢠⡏⠀⣠⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠞⠁⢀⡆⣠⠀⠈⠀⠀⠈⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡏⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⣐⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀⡄⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢟⣋⣿⣿⣷⡀⠀⠀⠀⢣⠀⠄⡁⡀⡄⢄⡀⢐⠃⠀⠀⠀⠀⠙⠈⠉⠁⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡘⣿⣷⣶⢟⣽⣿⡾⠞⠃⠀⠀⢰⡆⡆⣶⠰⢂⢴⣞⣆⣮⢲⠀⠀⠀⠀⡀⢀⢀⡀⡀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢹⡄⣿⠙⣗⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠈⠃⡇⢸⠀⡇⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⡄⢸⠆⠿⠘⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⣨⠄⠀⠀⠀⠀⠁⠈⠀⠁⠁⠈⠀⠁⠀⠀⠈
⠀⠀⠀⢀⡤⠾⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣂⣀⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠉⠈⠀⠀⠐⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡨⢐⠠⠌⠀⠀⠀⠀⣤⠤⠭⣥⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⢡⠒⣈⠀⣀⢀⢀⢠⡀⣘⡛⣛⣛⣛⠂⠀⠀⠀⠀⠠⠄⠀⠂⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣥⢅⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠿⠸⠘⠺⠃⢇⠒⠲⠶⠆⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⡄⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⢭⣭⠉⠋⠀⠀⠀⠀⠀⡴⡈⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠐⡗⠃⠂⠐⠀⠀⠀⠀⠀⠀⡀⢀⢠⣸⠇⡤⡃⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠠⠀⠐⠿⠭⠔⠤⠤⣴⣾⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠁⠓⠒⠃⠋⠀⠀⠀⠀⠀⠀⠐⠐⠂⠁⠒⠀⠊
⠀⠂

⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⣤⡁⠀⠀⠀⠀⡀⠀⠄⢠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠈⠂⠀⠐⡀⠑⠀⠀⠀⠀⢲⠉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣰⣂⣈⡅⠀⠑⠀⠀⠀⡀⠀⢀⠀⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠤
⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⠐⢄⣀⠦⠂⠀⡄⠈⠉⠀⠀⠀⠀⠀⣾⠂⠄⡉⠀⠀⢁⠀⢀⠀⠀⠠⠄⢰⠀⠀⠀⠈⠀⣀⠂⢆⠀⠀⢀⠀⡄⠀⣀⠁⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠄⠀⢀⠀⠀⠀⠀⠀⠀⠐⠦⣈⢐⢲⠀⠃⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠰⠈⠀⠉⠄⠈⡄⠁⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠁⢀⡀⠀⠀⠀⠂⠀⠀⠀⠄⠤⡀⠘⠀⠂⠰⠀⠡⡀
⢀⠀⠀⠰⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠁⠈⠀⠠⠀⠀⠀⠄⠠⠀⠀⠐⠂⠀⠆⠀⠈⠈⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠃⠀⠄⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠐⠀⠀⠀⠀⣅⡤⣴⠄⠂⠀⠀⠀⠤⠀⡀
⠀⠀⡀⠀⠐⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢦⠐⠇⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠂
⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠄⠠⡄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠘⣇⣸⡅⠔⣓⣆⠰⡦⢤⡀⣶⠤⣄⢠⡄⠀⡄⠀⠀⢹⢉⡱⠀⠦⢠⣤⢤⡜⢻⠛⠀⣧⢤⡄⢠⠤⣼⠰⣚⣦⠀⢤⠀⢠⠄
⠀⠀⠀⠀⠀⢠⡇⠸⣇⢮⣉⣿⠨⣇⣠⠇⣿⣀⡼⠀⢱⡼⠀⠀⠀⣨⡀⠀⢤⣧⢀⣇⠀⠀⢸⣄⢠⡇⠀⣇⢇⣀⣼⠸⣍⣹⡄⠈⢧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⣿⠀⠀⠘⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢈⢢⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⢁⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃
⠀⠀⠢⢀⡀⠁⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠨⡄⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠠⠀⠀⠠⠀⠄⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠱⠀⠀⠀⠊⠠⠀⠄⠀⡀⠀⠈⠀⠒⠀⠁⠀⠀⢀
⠀⠀⠀⠒⠂⠂⡀⠙⠒⠂⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐
⡀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠁⡆⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠁⠐⠐⠀⠂⠊⠐⠀⠂⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⣄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢢⡄⠀⠂⠀⠠⠀⠠⠀⠀⠀⠂⡄⠘⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠒⠂⠀⠀⠀⠀⠌⠁⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡎⠀⠀⠀⢰⡓⡂⠀⠀⠀⠁⠀⠂⠀⠀⠄⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠠⡀⠘
⠄⡀⠀⠀⠀⠀⠀⠁⠁⠂⠀⠎⠀⠐⠀⠈⠀⡉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⡀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢷⣦⠀⠀⣠⡾⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣼⠏⠀⣰⡟⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⡄⠐⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡴⢶⣿⠅⣠⡾⢳⡆⢀⣾⡗⢺⡆⣰⣿⠖⣷⠐⣿⡟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣼⡇⢰⡏⡰⣿⢀⣼⣯⣰⡿⢡⣿⣥⣼⠏⢰⡟⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⢧⠀⠀⠻⢧⠈⠉⠀⠉⢹⡏⠈⠉⠀⣾⠃⠉⠁⠀⣈⣉⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢿⠁⠀⠀⠸⡏⠀⠀⠀⣿⣭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠀⢀⣤⠀⠀⣀⠀⠀⣠⠀⠀⠀⠀⠀⠂⢿⡧
⠀⠀⠀⠀⢀⣠⣴⣶⡶⠶⢤⠀⠚⢛⡛⠛⠒⠶⠶⢤⣾⣏⣴⣟⣁⣀⣀⣿⠆⢠⡿⠀⠀⠀⠆
⠀⠀⠀⠀⠸⣏⣰⣟⣀⣠⡼⢀⣀⡘⠃⣴⡦⠀⠀⣾⠃⣼⠏⣉⣭⡛⢋⣡⣤⡿⠁⠀⣠⣤⣤⠀⢀⣴⠆⣠⡄
⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⡆⢨⡟⠁⣠⢟⣿⠂⣸⠏⢰⣿⠞⣽⠋⣼⠋⢁⣿⠁⢀⣼⠟⣠⡟⠀⣾⠃⣴⡟
⠀⠀⠀⠀⠠⣿⣅⣠⣤⠞⠁⠺⠷⠚⠁⢿⡵⢾⡟⠀⢼⠃⠸⠧⠔⠷⠶⠛⠳⠶⠟⠻⠖⠹⠷⠚⠿⢎⡿⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⣠⡾⠃⠀⣈⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⣻⣿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠂⠀⠀⠀⠀⠀⠀⠀⠳⣶⣤⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠒⠒⠛⢲⡴⠚⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢄⣸⠇⠀⠰⣶⡀⠀⣿⣤⣠⠴⠋⠉⠉⢳⢀⡴⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢤⠏⠀⠀⠀⠀⠉⠲⣤⢄⠈⠉⠀⣿⡞⢢⠀⠀⠀⢀⣾⠇⣀⣤⣀⠀⡇
⠀⠀⠀⠀⠀⠀⣾⣦⡄⢀⣀⣸⣴⣠⢀⠀⢠⣶⣶⣮⣯⡭⠄⣼⢟⠛⡽⢀⡀⣐⣼⣿⣿⢷⡶⣿⣿⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣟⡶⠚⠛⠿⣿⣟⡀⢸⣿⣧⣷⣻⣯⢹⡯⣢⢼⣷⠟⠋⠉⠀⠉⠙⢷⣷⣿⢚⠍⠀⠉⣆
⠀⠀⠀⠀⠀⠀⢀⣞⡁⢀⡠⣠⢾⡿⡿⡿⣮⣿⣹⣿⣏⣿⣿⣞⣵⣿⣿⣽⡆⠀⠀⢀⠀⠀⣟⣥⢥⡀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠸⣯⣻⢮⣍⡏⠈⠛⠺⠼⠼⠚⢛⣛⣿⣾⣿⣿⣿⣿⣟⣵⢁⣴⣧⣒⣠⣴⣷⢿⣽⣧⡚⠁
⠀⠀⢀⣠⠤⠖⣪⣿⣟⣛⣻⠀⡸⣟⡿⠛⠛⠉⠉⠉⢛⣿⣿⣿⣿⣿⣧⠉⠉⠉⠙⢿⣿⣛⣛⠋⠉⠉⢉⣉⣷⢶
⢰⠺⢥⣀⡀⠈⠁⠈⠻⢿⣿⣄⣙⣈⣇⢄⠀⠀⠀⠀⣾⠿⠛⣹⢿⣾⣾⢀⢄⠄⡄⡼⠳⠤⣄⣠⡴⠚⣫⡿⡡⣿
⣿⠀⠀⠀⠉⠙⠒⢤⠞⠉⠉⠉⠏⢛⢷⣾⣄⣇⣆⠀⣿⣿⣼⣛⠿⠾⠓⠿⠿⣾⠛⠏⠉⠀⠀⠙⣗⢕⠍⢜⢍⣿
⡧⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⣴⣯⣉⡙⠉⠙⠛⠛⠟⠉⠀⠀⣀⡤⣴⡞⡩⣧⠀⠀⢔⠅⠀⢻⡣⡪⡢⣲⡟
⢧⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠒⠦⢤⡠⡴⠚⡋⡯⡫⣫⢮⣺⣿⠀⠀⠣⠊⠄⢸⣗⣵⣟⡿
⠀⢸⠿⢷⣦⣤⣀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⢶⢎⢮⢎⢖⢕⢕⢕⣿⠀⠀⣠⡠⠆⣼⡫⠪⡶⡇
⠀⢸⠀⠀⠈⠉⠻⢷⠀⠐⣤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣵⠕⠑⢁⡂⣰⣽⣿⣿⠠⠚⠁⠀⠀⣿⢕⣴⢾⡇
⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⢶⢦⣤⣀⡀⠀⣿⣫⣪⣮⣾⢾⢟⢕⢽⡇⠀⠀⠀⠀⠀⣿⡎⡱⣹
⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠙⢻⡿⣫⣝⣕⠕⡱⡣⡺⣻⡇⠀⠀⠨⡂⠀⢻⢟⡴⢿⣄⡀
⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢸⣯⡪⡺⣣⡪⡪⢊⢞⢽⡇⠀⠂⠙⠄⠀⢸⡾⣱⣿⣿⡁⢁⠀⠠
⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣟⢔⢔⢝⢝⠕⡵⡱⣻⡇⠀⢈⢂⠄⠀⢸⣝⣯⣾⠒⠒⠀⠀⣀⡀⠁
⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡧⡣⡻⡣⡫⡪⢊⢞⣽⡇⠀⠀⠫⠊⠀⣸⡿⠟⢈⣉⠉⠋⠀⠐⢒⡒
⠀⠙⠛⠶⣤⣄⡀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⢎⢊⢜⢕⡵⡕⣻⣿⡇⠀⢀⣠⣴⡿⢛⠋⠁⠉⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠈⠙⠻⣄⣦⡄⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣟⡵⡱⡫⡪⢪⣾⣿⣿⣧⠾⠟⠋⠀⠀⠀⠀⠠⠤⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠶⣆⣷⣄⡀⠀⠀⠀⠀⣯⣮⢺⣞⣵⣟⡛⠓⠒⠂⠀⣙⠋⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠗⠶⣤⣄⣿⡵⡟⠉⠀⠤⠤⠀⠈⠉⠉⠁

⠀⠀⡄⠀⠀⠀⡇⠸⣿⣷⡌⢢⡁⠠⣄⣠⣿⣀⣩⠀⠘⢎⢣⡻⣄⠠⢿⠆⠀⠀⢀⡏⣾⢘⠀⠀⠀⠈⠓⡄⢀
⠀⠀⠳⣤⠿⠂⠀⠀⣿⡇⢿⡄⢹⡀⢸⣧⣴⡟⠁⠘⠓⠈⣦⢳⡼⣦⠀⠀⠘⠀⠸⡇⣿⠛⠀⠠⠤⣀⣴⣻⠈⢇⡠
⠀⠀⠀⠐⠃⠀⠀⠀⣿⣷⠘⣿⠀⣧⠈⠰⣶⢍⡶⠀⠀⠀⠀⣬⡁⣩⡀⠀⠀⣤⣄⣦⢿⡜⣧⡀⠐⠚⠛⠁⠀⠈
⠀⠀⠯⠇⣈⠀⠀⢀⣿⣿⠀⡌⠁⠈⠂⢰⣿⡆⠙⠚⠢⠞⠦⠔⠀⠙⠇⠠⠀⢿⡁⠙⠟⠛⠨⠁⣀⡤⠦⠀⠀⠀⠈⠁
⠀⠀⠐⠾⣠⠀⠰⢀⠉⠛⠸⣿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠛⠚⠉⠁⣇⠀⠰⠀⠘⠂
⠀⠀⢰⡀⡧⢳⡎⡨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠙⠒⠂⣤⠾⢃
⠀⠀⢇⢟⡧⢈⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠔⢂⠀⠈
⠀⠀⣰⡁⠄⡎⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣷⠀⠶
⠀⠀⢩⠁⢠⣇⡀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⡈⠀⠈⡄
⠀⠀⠀⠀⠀⠻⣮⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢩⠯⠂⢤⠀⠀⠐
⠀⠀⣧⠀⠀⠷⠌⠻⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣓⡌⠀⠱⠄
⠀⢠⣷⣦⢀⠀⠀⠀⢀⠄⠀⣦⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠋⠐⡎⠁⢀⠀⠀⣤⠀⠦⠶
⠀⠘⢧⡀⠸⠆⣠⣀⢂⠔⠉⠑⠋⠀⢀⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡶⠋⠘⠂⠀⠀⠀⠠⠟⠀⠹⠀⠟⠛⠂
⠀⠀⠰⠟⠄⠂⢿⠨⣸⠀⠀⠀⡴⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢼⠻⠷⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠘⠊⠀⣀⢸⡆⣿⠀⠀⣒⠎⢉⠘⠳⢀⣀⠀⠈⠁⢂⠀⠀⠈⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⢠⠞⠂
⠀⠀⣷⠿⡦⢉⡼⡰⠋⠀⠀⠌⠀⢿⠿⠆⠉⠤⠁⠀⢀⡀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠀⠘⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⣾⠟⠛⢿⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⢻⣦⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠋⠀⠀⠀⠈⢷⢳⠀⠀⢾⡇⠀⢀⣴⠟⠁⠀⣠⡶⠟⠹⠄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⡟⠁⣀⣀⠀⠀⠀⠈⢧⢣⠀⠀⠀⣠⣟⡁⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⢻⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡾⠿⠛⠻⠿⣶⣄⠀⠈⢿⣧⡶⠿⣛⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡇
⠀⠀⠀⢀⣀⣠⣤⣴⣶⠾⡄⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⢠⠏⠾⠿⠟⣻⡇⠀⢠⣴⣤⣄⣤⣤⣤⣤⣴⣶⣷⣤⣀
⠀⠀⠀⡟⠿⠿⠿⠷⣶⣦⣽⣷⣶⣤⣤⣤⣤⣤⣤⣴⣿⣾⣷⣶⠗⣿⠋⠀⠺⠿⠿⠟⠻⢿⣿⣉⣭⣭⣭⣤⣬⣿⣿⣿⣿⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⢉⣽⠟⢉⣼⢛⡽⠋⠁⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠉⠉⠉⠉⠉⢹
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢠⡟⢁⡾⠁⠀⠀⠀⠀⣷⠈⢳⡄⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣷⣤⣤⣤⣄⣀⣀⣀⡀⢠⡾⠁⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠈⣧⢀⣀⣀⣀⣤⣾
⠀⠀⢀⡈⠉⣿⠛⠛⠛⠛⠿⣿⠏⠀⠀⠀⠘⠀⢰⣃⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠸⠟⠿⠿⠻⡟⠛
⠀⠀⠘⠇⠀⣿⠀⠀⠀⠀⢰⢏⣠⡾⠟⠀⠀⢀⡏⠙⠛⠿⠿⣿⣶⣦⣿⣴⣾⣿⠿⢣⠀⠀⢠⣄⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡟⠉⠀⢰⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠁⠀⠀⠘⡀⢀⡞⠙⢧⢀⡞⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⢧⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢃⡞⠀⠀⠘⡿⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣦⣤⣄⣀⣿⢀⣀⣤⣴⣶⣿⡿⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡀⠉⢳⡀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢏⠹⣷⡄⢳⡀⠀⠀⡼⠁⢀⡤⠞⠋⡷⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠙⢿⡌⢧⡀⣸⠁⢠⡞⣀⡤⠊⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠬⠷⢶⣤⣤⣼⣈⣉⣉⣀⡞⠋⠁⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠉⠉⠉⠉⠙⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣀⣀⠀⠀⠀⠀⡤⠀⠀⠀⢀⡤⠤⢤⣀⣀⣀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠉⢣⡀⠀⠀⡀⠀⠀⢠⠏⠀⠀⠀⠙⢦⠀⠀⣽⠀⠀⠀⣀⡤⠴⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⡏⢀⣴⠲⡀⠀⣧⠠⠤⡇⠀⠀⢸⠀⠀⡏⢹⣦⠈⣧⣀⡇⠀⣠⠞⠁⠀⢀⣀⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠙⢦⡀⠀⠀⢸⠀⣾⡏⠈⠁⢠⡇⠀⠀⡇⠀⠀⠈⢧⡀⠀⠈⠻⣧⢸⣸⠇⣰⠃⠀⣤⠞⠉⢩⠛⠄⡿
⠀⠀⠀⠀⠀⠀⢸⡇⢠⢟⠙⠓⠶⣄⠀⠙⣄⠀⣼⢰⠟⠀⢀⣴⣋⡠⠴⠚⠳⡖⠲⠦⠾⢝⣶⣤⣀⡙⡆⠿⠶⠇⢀⣾⡡⠴⠊⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠉⠲⠤⢬⣷⡀⠘⠛⣉⣼⠴⠚⠋⠉⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠉⠉⠟⠐⠒⠒⢾⠤⣠⣤⣤⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣤⣀⣤⠤⡟⠊⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡸⠀⠀⠀⠈⠉⠉⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠁⠀⠀⠸⡀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⡆⠀⠀⢀⡀⣀⠤⠔⢺⡄⢀⡀⠀⠀⣰⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠹⠈⠉⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠹⠀⠀⠀⠀⠗⠒⠠⠤⠄⢀⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⡀⠤⠐⠀⠉⢣⠀⠀⠀⠈⣄⠀⠀⡀⠠⠄⠒⠈⢧⠤⠄⢀⣀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠘⡍⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⡞⠒⠒⠒⠠⠤⠄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠤⠐⠒⠉⠁⠘⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡈⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣨⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣸⣤⡤⠖⠚⠛⠓⠶⠤⢴⣤⣀⣀⣀⣏⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣀⣠⡤⠼⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠉

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⠶⠶⠶⠶⣤⡀⢀⣤⡴⠶⠶⠶⢦⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠛⣇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⢷⢸⡏⠀⠀⠀⠀⠀⠙⡆⠈⣧⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡏⠀⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⢰⡇⠀⠀⠀⠀⢀⣰⠇⠀⢿⡀⠀⠀⠀⠀⣾⢻⠄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣀⣸⣧⠀⠀⠀⣾⣤⣤⣼⣷⠆⠀⣿⠶⠦⠶⠶⠞⠋⠀⢸⡷⠶⠴⠶⠶⠋⠁⠀⠀⠸⣇⠀⠀⠀⣼⠃⣼
⠀⠀⠀⠀⠀⠀⡿⠛⠛⠋⠉⠉⢹⠁⠀⠀⣼⠃⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡼⠃⠀⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⠀⠀⠘⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠻⠀⠀⠀⠀⠀⠀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⠴⠋


⠀⠀⠀⣠⢀⣤⣤⣄⠀⠀⡄⢀⣀⣤⡤⣤⡀⠀⢀⣀⣀⣤⣠⣤⣤⣤⢀⡄⠀⠀⠀⣠⠀⡶⠶⢤⣀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⠉⠀⠀⣸⠇⠀⡇⢻⠁⠀⠀⢀⡇⠀⠈⠉⠁⣿⠀⠀⠀⠀⢸⠃⠀⠀⠀⣾⠠⡇⠀⠀⠈⠳⣆⠀⠀⢠⡏⣧⠀⠀⠘⡄⠀⠀⠀⢰⡿
⠀⠀⠀⣿⠤⠤⠾⠓⢤⠀⡇⢸⣀⣠⠴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⢹⠀⠀⣞⣀⣸⡄⠀⠀⢧⠀⠀⢠⠏⡇
⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⡇⢸⠉⠳⣤⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⠛⠙⠉⠉⣿⠀⡇⠀⠀⠀⢠⡟⠀⣸⠁⠀⠈⣧⠀⠀⠈⠳⡤⠏⠀⡇
⠀⠀⠀⣿⣀⣀⡤⠞⠃⠀⡇⢸⡀⠀⠀⠉⠳⢦⠀⠀⠀⢹⠀⠀⠀⠀⢺⠀⠀⠀⠀⣿⠀⡇⠀⢀⡴⠋⠀⢠⠇⠀⠀⠀⠸⡄⢇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠿⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢦⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠋




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣆⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣠⠴⣤⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⠖⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣿⣿⣿⣿⣽⡇⠀⠀⠀⢸⢹⣿⣧⢠⠞⠁⣴⣾⡇⠀⠀⢠⣿⠿⣿⢷⡄⣼⡥⢞⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⡿⣷⣿⣼⣯⣛⠷⣿⠀⠀⠀⣿⣼⡟⢻⣿⣶⣿⣿⣿⡇⠀⠀⢸⣷⣾⣿⣿⢻⠇⠴⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠿⣦⣙⣿⣿⣝⢳⡏⠀⠀⠀⡿⢿⣿⣾⣿⣿⣷⢉⡟⠀⠀⠀⠘⣧⣾⣿⣿⣿⣦⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢷⣦⣉⠉⠛⠿⡿⠁⠀⠀⠀⢻⣿⣿⣷⡙⢿⢷⠞⠁⠀⠀⠀⠀⠹⣿⣿⠟⡫⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣬⣿⣷⣦⣰⠁⠀⠀⠀⠀⠸⣿⣿⣿⣇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠻⣤⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⡀
⣿⣿⣿⣿⠟⠻⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠷⠦⢤⣶⣿⣷⣤⣤⣤⠀⢰⡄
⣿⣿⣿⣿⡇⠀⠸⡗⢭⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⣿
⣿⣿⣿⣿⡇⠀⠀⠳⠀⠈⠲⡀⡾⠀⠀⣄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡟⡀⠁⠈⠉⠉⠁⠺⠇⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠡⠈⠒⢲⣤⡶⠶⠂⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠁⠁⠀⠉⢣⣀⡤⠴⣄⠈⢹⡿⠿⠛⠪⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠛⠻⣿⡇⠀⠀⠂⠀⠒⣷⣄⣀⣀⡈⠁⠙⡄⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⢰⣿⣿⣷⣶⣦⡰⠊⠀⢻⣿⣿⣿⣷⣶⠀⠀⢠⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⠤⠝⢿⣿⣿⡿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡏⠙⣆⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡀⠈⢱⢊⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⢻⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢀⣨⡉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⠉⠉⠉⠉⠈⠉⠉⠁⠉⠀⠉⠈⡉⠁⠀⠀⢀⣷⣿⣿⣷⣄⠀⢀⠄⠉⠦⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠛⣿⣿⣿⣿⠏⠉⠀⠀⠀⡆⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⢀⠀⣠⠄⣤⠔⠛⠛⠛⠻⠂⣀⣀⣴⠛⠑⠆⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣿⡀⠀⢀⠀⠀⢀⠈⠁⠈⠀⡁⠈⠀⠁⠀⠈⠓⠄⢶⢴⣶⡶⢏⡟⢏⠛⢛⠯⣓⡀⢸⣿⠛⠛
⠀⠀⠀⠀⣿⡇⠰⠁⣰⢃⡣⡄⠆⠌⠼⠐⠄⠬⠔⠆⢦⠆⠀⠀⣾⠈⣷⢸⠻⠖⠲⠦⠰⠆⠨⢿⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠲⣼⣏⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣼⡿
⠀⠀⠀⠁⠻⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠁⡄⠒⠒⢄⣀⡀⠀⢂⠀⠀⠀⢀⣐⣀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠁⠀⠀⠋⠟⠒⠀⠈⠃⢀⡀⠀⠉⢹⠛⠥⣀⣀⣀⣀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢶⣤⡈⠍⠓⠚⠒⢀⡀⣉⢉⠁⠀⠄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⣰⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢉⠲⣄⠀⠀⠀⠬⠟⢎⣀⠀⢀⠅
⠀⠀⠀⢀⡞⠀⠀⠀⢀⠇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡼⠀⠀⠀⢀⣌⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤⣀
⠀⠀⠀⣁⠀⠀⡀⠈⠀⠀⢠⠃⢰⠁⡞⠀⡏⢀⠇⣼⠀⡝⢸⠁⡞⠀⠀⠀⠠⢀⡇⠁⢄⣀⡀⢀⡠⠂⠂
⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠁⢠⠃⠀⠀⠀⠰⠃⠀⠀⠀⠁⡸⢸⠐⠖⠘⠍⠉
⠀⠀⣼⢠⠄⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡠⠂⢠⠃⠙
⠀⠀⢉⡞⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢐⠀⠀⡞⠀⡀⡀
⠀⠀⢸⠁⢤⡀⠀⠠⠀⠀⠀⣸⠀⡼⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠹⠯
⠀⣠⠃⠆⠀⡈⢠⠆⢰⠐⢢⠇⢰⠗⡴⢀⠆⣸⠁⡔⢠⠆⢰⠂⡖⠀⠀⢠⠀⠀⢠
⠈⠁⠉⢉⡉⠀⠈⠁⠈⠀⠈⠀⠈⠀⠁⠈⠁⠈⠀⠁⠈⠁⠈⢠⠃⠀⠀⠀⡄⠀⠀⠁⠈
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠥
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣒⢦⣤⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰⣁⢱⠀⠀⠀⢠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⢠⣟⡇⠀⠀⠠⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣴⣲⡤⣼⣓⣧⣤⣤⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣶⠖⢿⣿⣇⠉⠋⠀⠻⠭⠽⠀⣨⣝⣿⠿⣿⠦⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠛⠋⠀⣼⣓⣛⣶⠀⠀⠺⠀⠀⣼⢯⣛⣿⡄⠀⠀⢿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⣠⣦⡅⠘⠛⠁⠀⡴⣶⣦⠀⠈⠙⠛⠛⢡⣤⣄⠠⠏⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢇⢠⣤⣤⣝⠿⠃⠀⠸⠆⠀⢿⣟⠝⠀⠀⣤⠀⠀⠯⠽⠿⠁⣤⣴⠚
⠀⠀⠀⠀⠀⡤⣖⣟⣿⣿⣿⣿⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⣦⢀⣿⣿⡀
⠀⠀⠀⠀⢸⣽⢻⠓⣾⣿⣿⣿⡀⣿⣿⣿⡇⢀⣷⣶⡄⠀⣿⣧⣼⣷⣤⣿⣿⣿⣿⣿⣽⢷⣦⡀
⠀⠀⠀⢀⣾⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣝⣿⣷
⠀⠀⠀⠈⣿⡍⠛⢇⣀⢤⡿⣥⣿⣿⣿⡿⣿⡋⠙⣿⣿⠟⢏⣋⠽⡿⠻⢤⣸⡀⠀⣾⠟⢻⣿⣽⠃
⠀⠀⠀⠀⠘⢿⡦⣴⡙⠺⠷⠜⢿⣿⡿⢶⣿⣷⣶⣿⣿⡠⢹⢫⣸⡷⠤⠞⣵⠎⠉⠉⣁⠤⣪⠏
⠀⠀⠀⠀⠀⠀⠙⠢⣍⣓⠲⠤⣤⠖⠦⣀⠉⠁⠀⠀⠎⠙⢛⣛⣉⣀⣠⡤⠴⢒⣊⠭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠿⠯⠭⠭⢭⣉⣉⣉⡭⠭⠭⠥⠴⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠘⠶⣦⣤⡀⠈⢿⡆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠀⠀⠀⠀⠀⠙⠻⣷⣌⢿⡿⠛⠛⠛⠛⠻⠿⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⣿⣷⣶⣤⣤⣤⣤⣤⣬⣿⣿⣿⠿⠿⣶⣦⣠⣤⠶⠟⠋⠉⠙⠻⢷⣦⣤⣀
⣤⣤⣶⣶⡿⠿⠟⠛⠋⠉⠁⠀⠈⠉⠉⠛⢿⣯⣍⢻⣿⡏⠀⠀⠀⠀⠉⢿⣆⣀⣠⣤⣤⣤⣤⣤⣴⡿⠛⠻⢷⣦⣄⡀
⣿⡟⠻⣶⣤⡀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠾⠟⠛⠉⠛⢿⣿⣄⠀⠀⠀⠀⢀⣿⣏⣉⣉⣉⡉⠉⠉⠛⠻⢿⣦⡀⠀⠉⣛⣷
⣿⡇⠀⠈⠙⢿⣷⣶⡶⠟⢻⣏⣉⡀⠀⠀⠀⢀⣀⣴⡿⢹⡿⠿⢶⣶⣶⣿⣿⠟⠛⠉⠙⠻⣷⣄⠀⠀⠀⢹⣿⡾⠟⠋⠹
⣿⡇⠀⠀⠀⠀⣿⠻⣷⣦⣿⡟⠛⠿⠿⠿⠿⠛⠛⢉⣴⠟⠀⢀⣾⠿⣄⢸⣿⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⣿⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⠀⣾⣏⣀⣬⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⣧⣀⣠⣤⣶⠿⠛⣹⡟⠀⠀⢠⣿⡿⠟⠛⢹⣿⣿⣦⡀⠀⠀⠀⢀⣠⣾⠟⠁
⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠿⠟⠛⠻⣿⣾⠿⣿⡇⠀⠀⠘⣿⡆⠀⠀⢸⣿⠈⠻⠿⣿⣷⣿⣿⠛⠁
⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⢻⣧⠀⠀⠀⠹⢷⡀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿
⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠈⢿⣧⣠⣤⣶⣾⠿⠆⢸⣿⠀⠀⠀⠀⠀⢸⣿
⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⢸⣿⠄⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⣿⡄⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⣷⡀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠻⣷⡀⠀⣿⡀⠀⠀⣿⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠙⣷⡄⣿⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⣿⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣠⣴⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢸⣿⠀⣀⣤⣴⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⠿⠛⠉
⣦⣶⣤⣶⣤⣤⣦⣶⣶⣶⣶⣤⣴⣶⣼⣿⣯⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣦⣤⣶
⣿⣿⣇⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣫⣍⡀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣥⡀⠀⠀⠀⠀⠀⠀⣀⣩⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠑⠚⢿⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⣻⠳⠾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠶⢾⠀⠀⠀⠀⠀⠀⡏⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⣿⠲⠦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣀⣸⠀⠀⠀⠀⠀⠀⡿⠢⣄⣀⣯⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⣿⠀⠉⠒⢿
⠀⠀⠀⠀⠀⢀⡴⠢⣤⣀⠀⠀⠀⣀⣀⣀⣿⣦⣄⣀⣸⣄⣤⣤⣤⣄⠀⡿⢢⣤⣤⠷⠤⣤⣀⠀⠀⣀⣿⣄⡀⠀⣸⠀⣀⣀⣤⣀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⢳⣴⠛⠉⠉⠉⠉⠑⣦⡝⠋⠁⠀⠀⠀⠈⢻⣧⡞⠉⠀⠀⠀⠀⠉⢧⡞⠉⠀⠈⠙⢿⣿⡞⠉⠁⠀⠈⠙⣦⠞⠉⠉⠉⣷
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠷⣄⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠀⠉⠛⠲⠤⠴⠚⠋⠉⠓⠤⠤⢄⣤⠤⠞⠋⠙⢦⣀⣀⣀⣀⡤⠞⠻⢤⣀⣀⣠⠞⠉⠓⠦⠤⠴⠋⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⣄⡀⠀⡇⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡼⠋⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⠀⠈⠻⣄⣠⠶⠛⠋⠉⠉⠉⠛⢶⡄⢀⡴⠚⠋⠁⠀⠈⠉⠻⣆⣠⠶⠊⠙⠋⠑⠶⣄⣠⠶⠚⠛⠛⠛⠛⢶⣜⡶⠞⠋⠙⠶
⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠟
⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼
⠀⠀⣟⠉⠉⠓⠚⠋⠙⠶⢤⣤⣤⣤⣤⡤⠖⠲⢦⣤⡀⠀⠀⠀⣀⣤⡴⠖⢶⣀⠀⠀⠀⠀⠀⣀⡤⠾⣄⡀⠀⠀⠀⣠⠞⠳⣤⣄⣀⣠⣴⠏⠀⠙⠒⠒⠚⠉⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠑⠒⠶⠖⠊⠉⠀⠀⠈⠉⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡞⠛⠛⠳⢦⡀⠀⢀⣀⠤⠤⠦⠤⣤⡀⠀⢀⣀⠴⠶⠶⠖⠶⠦⣄⠀⠀⣀⡴⠆⠛⠛⠓⠶⢦⡀⠀⣠⡤⠤⠤⢄⡀⠀⠀⢀⡤⠶⠶⠶⠦⣄⠀⢀⡤⠦⠤⣮
⣯⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠙⣦⡼⠋⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠈
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠲⠶⠤⠤⠶⢦⣄⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⢀⡜⠛⠶⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠉⠛⠓⠶⠶⠶⠞⠛⠁⠀⠈⠳⠆⣀⣠⣠⡴⠞⠋⠈⠛⠶⠦⠤⠶⠛⠁⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⡇⠀⠀⠀⠀⠀⠀⡾⠈⣧⠀⠀⠀⠀⠀⠀⠀⡾⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⡿⠀⠀⠀⠀⠀⠸⡇⠀⣽⠀⠀⠀⠀⠀⠀⠰⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣦⠀⠀⠀⣿⠀⠀⠀⢠⣾⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣧⣀⣀⣸⣿⣿⣁⣀⣠⣿⣀⣀⣀⣸⣿⣿⣀⣀⣀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣄⡀⠀⠀⣀⣄⡀⠀⠀⢀⣴⠶⢦⡀⠀⢠⡾⣶⠀⠀⣰⠶⣦⠀⠀⣠⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡼⠋⠈⣿⠀⢠⡟⠈⢷⡀⠀⣾⠃⠀⠈⢿⣄⣾⠁⢸⡇⠀⣿⠀⠹⣦⣀⡿⠹⣦⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣄⣼⠃⠀⢸⡇⠀⣿⠀⠀⠀⠀⠉⠁⠀⠈⣿⢰⡏⠀⠀⠈⠉⠁⠀⠈⠻⠞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⢷⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣶⢠⣄⣤⢤⣠⢤⣤⣠⠄⢰⢤⣸⣠⡤⣦⢰⢤⣀⣤⡆⣤⣤⣄⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠋⠛⠋⠹⠛⠰⠏⠀⠘⠛⠉⠉⠀⠙⠘⠈⠉⠛⠉⠛⠃⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⡠⠀⡄⡦⡄⢀⡀⢀⡀⡀⢠⡄⡆⠀⢤⠆⣠⠄⢰⢀⡤⢤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡤⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⡉⠉⢹⠐⡁⠀⠀⢨⠃⠀⠑⢈⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡀⠀⠈⢳⣀⣈⣼⣿⣦⡴⠁⠀⢀⠔⠋⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠬⠵⢦⡎⠁⠀⠙⡟⢻⣡⠔⠊⠉⠐⠢⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡽⠀⣀⠧⢄⣠⠔⠣⡞⠛⠛⠻⡖⠢⣄⠀⠉⣢
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⢰⣕⡋⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡇⠳⠚⢹⣀
⠀⠀⠀⠀⠀⢰⠣⢜⣄⣤⣷⣾⠴⢳⣸⠀⠀⠀⠀⠀⡇⠀⠀⡠⢓⡢⣇⣠⢔⣵⡒⠲⡵
⠀⠀⠀⠀⡟⢻⢦⣼⠿⠇⠻⣦⡤⢮⠭⠷⢦⢀⣠⣤⠧⠒⠒⡷⣇⣭⠷⡟⢲⣶⣛⣫⠜⠓⠒⠤⢤⣀⡀
⠀⠀⠀⠀⡇⢸⢸⠁⢸⡏⠉⠀⡇⢸⡀⠀⢸⡼⢋⣿⠍⢱⠖⢿⠮⣷⢮⠟⠉⢉⣢⡍⢻⠗⠖⠋⠉
⠀⠀⠀⠀⡇⢸⢸⠀⢸⣇⠤⠤⠧⣮⣬⣝⠉⣱⣋⣻⡥⠼⠦⠼⣀⢸⢸⠉⡏⠁⠀⢸⠸⡆
⠀⠀⠀⢀⡧⢼⢸⠀⢸⢑⠶⣶⠲⠯⣧⠾⠭⢶⠼⢦⠕⠒⠒⠒⢻⣾⡸⠀⡇⠀⠀⠘⢦⣱⡷⠂
⠀⣀⣤⣾⠉⠒⣿⡖⣼⠓⠊⣸⠠⠄⠀⠤⠤⢼⠀⢸⠦⠴⠒⢲⡎⠘⠁⠀⡇⠀⠀⠀⢸⠀⡏
⠀⡇⠈⠉⠑⢻⢻⠿⡟⡟⢻⠃⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⣣⠤⠒⠁
⠀⣅⠀⠀⠀⢸⢸⠀⡇⡇⢸⢀⠀⠀⠀⠀⠀⢐⡇⢸⡀⢀⠀⠼⠣⢀⠀⠀⡇⠀⢀⠠⠚⠈
⠀⠀⠈⠉⠒⠚⠼⠀⡇⠗⠚⠁⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠒⠗⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣟⣛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣼⣿⡿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠋⣿⡇⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⣤⣤⣼⣷⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⡿⠛⠛⢿⣦⣴⡟⠉⠙⢻⣦⣄⣀⣀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠉⠉⢹⣇⡀⢀⣼⡏⢿⣆⠀⠀⣸⡿⠉⠉⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣤⣽⣿⣿⣋⣀⣈⣻⣿⣿⣿⣥⣤⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⡿⠿⠟⠋⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠁⠙⢿⣿⣿⣶⣶⣶⣶⣿⣿⠟⠛⣿⣿⣶⣶⣶⣿⣿⠏⠈⠻⣿⣿⣶⣶⣶⣶⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⢸⣿⣿
⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀
⠀⠀⣠⣾⣿⡿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⢿⣿⣷⡄
⠀⠀⣿⣿⡃⠀⠀⠙⠿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⠿⠋⠀⠀⢹⣿⣿
⠀⠀⠻⣿⣷⣤⣀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⣀⣤⣾⣿⠏
⠀⠀⠀⠈⠻⢿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⢰⠏⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡥⣶⠀⣴⣦⠀⣶⠖⢢⣠⡾⠳⠀⠠⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⢸⡇⣿⠸⣧⠈⠃⣿⢰⣿⠻⣇⡁⠀⢀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⠄⠀⠈⠁⠀⡇⠀⣠⢄⠀⠀⠀⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣶⢠⡶⡆⢰⡆⠠⡆⢿⣆⣀⠀⠀⠀⠃⠀⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⠸⣇⡉⠘⠧⢸⡇⠈⠈⣿⠀⠀⠀⣰⠶⣿⠃⣰⠖⣶⢰⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣧⠀⠀⢣⣀⢿⡀⢿⡀⣿⠸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠃⠀⠀⠀⠂⠀⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡁⣤⠄⠈⠀⠁⠀⣾⠀⠀⠀⠀⠀⣾⢡⢰⠁⠄⠀⠀⠀⠢⠞⣱⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⡇⠻⢧⣀⠀⠀⠀⣿⠀⣺⠀⢸⠂⣿⡄⢸⡦⠀⠀⢀⡾⡶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠘⠧⠀⠐⢻⡆⠀⠀⢻⠁⢻⡄⢾⠂⣿⠀⢸⡇⠀⠀⠸⣇⡈⠂⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⣡⢄⠀⠞⠀⠀⠀⠘⠃⠙⠂⠈⠓⠀⠀⠀⠈⠀⠀⡿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠢⡄⠠⠴⠦⢄⠀⠀⢰⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡘⠁⠀⠀⠀⠁⠀⢸⡇⠁⣦⠀⣦⢰⢀⢶⡆⠀⠀⣾⠃⣶⢰⣆⡴⡦⢠⠶⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠠⢼⡗⠊⢿⠐⣿⠸⠏⢸⣇⠀⠘⣧⡀⣿⠘⠟⢸⡇⢿⠀⢿⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢄⡀⠀⠀⠀⠀⣸⠇⢠⠖⡄⠉⠀⢀⠤⠅⠀⠀⠀⡄⠀⢀⠠⠀⢁⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⢹⠀⠀⠀⣿⠀⢂⡤⠀⠃⠀⠀⠀⠀⢰⡗⠀⣀⠀⠀⠀⠃⠀⠀⠁⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⠀⣤⣄⣿⡌⢀⣤⡄⣿⣀⡘⣧⣀⡀⠀⣤⣄⡄⢸⡇⠀⣍⠀⢀⣄⡀⢠⡀⢀⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠉⢿⠀⢸⡇⢸⡇⢸⡇⢸⡇⠀⣿⠀⣿⠙⢧⢾⡇⢩⡟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠔⠉⠓⠊⠘⠆⠈⠓⠀⠙⠐⠋⠀⠘⢷⡜⠓⠘⠇⠘⢧⡀⠻⠆⠙⠷⠂⠈⠁⠘⠗⠁⠘⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁
⠀⠀⠁⢀⡀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⢂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⣤⡶⠔⡀⣄⡀⠀⠀⠀⢀⠀⠀⡀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠬⠅
⠀⠄⠀⠀⠀⢎⠀⢠⡅⠀⠀⠀⠀⠀⠐⠰⠀⠀⠜⠀⠀⠀⠀⠀⠀⠘⢏⣠⠫⢮⣁⡠⠉⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠆
⠀⢄⠀⠐⠲⠄⠃⠡⠀⠀⠀⠀⠀⠀⠀⠆⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⢠⡤⠊⠀⠀⠀⠀⠀⠠⠄⠀⠄⠁⠠⠀⠀⠀⠀⠀⠀⠐⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊
⠀⠐⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⢁⠀⠀⠀⠀⠀⠀⠘⢆⣃⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂
⠀⠀⠀⠈⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠠⢠⠄⠀⠤⠀⠀⠀⠀⠀⠈⠠⠶⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢖⠐⠯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠀⠀⠀⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠣⠞⠀⠀⠀⠂⠀⠀⠀⠀⡘⠀⠁⣀⡤⠉⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⠈⠀⠀⠀⠀⠀⡀⡀⢀⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠠⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠰⡀
⠀⠀⠈⠳⣄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠛⠄⠰⠀⠀⠀⠔⠀⠀⣀⢀⡀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠐
⠐⠆⣠⠔⠙⠀⡋⠁⠀⠀⠀⠀⠀⠀⠂⠐⠖⢀⠀⠇⡍⠀⠀⠀⠀⣧⠀⠀⡣⡼⠋⠠⠁⡀⠀⠀⠀⠀⠀⠀⠈⠣⠔⠀⠁
⠀⠀⠀⠀⠒⠄⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⢃⠑⠲⢡⣴⠾⠂⠀⡀
⠀⠀⠀⠈⠀⠃⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠢⣀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⡤⣀⡒⣻⠦⡒⢠⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠀⢘⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡠⠿⠉⣤⡽⠁⠀⠀⠀⠀⠀⠐⠒⠰⠋⠙⠈⠁⠀⠀⠀⠀⠀⠈⠧⠀⠃⠋⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠇⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠄⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⢀
⣶⣶⡶⠿⠿⠷⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣷⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⢀⠤⠴⣄⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢯⣸⣉⣧⡀
⠀⠀⠀⠸⠄⢒⣏⣂⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⡿⢛⡷⢚⣷⠀⠀⠀⠀⠀⢀⣤⡤⢤⠤⠴⣄
⠀⠀⠀⡖⠉⢙⠉⢩⠀⠁⠀⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢳⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⡎⠀⡎⢸⠀⠀⠀⠀⢎⡹⠁⢇⣀⣁⡽⠋
⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠤⠤⢼⣶⠥⠤⠤⠤⠤⠤⢤⡄⠀⠀⠀⢸⠒⠃⢱⢸⠀⢸⠀⠀⠀⠀⡞⢉⠟⢉⢿⠻⡟⢿⣳
⠀⠀⠀⡗⠒⠚⠀⠘⠒⠒⠒⠚⠀⢹⡄⠀⠀⠀⢰⢀⡀⠀⢠⠀⠀⠰⠀⠀⠐⠀⡇⠀⠀⠀⢸⢀⡴⠃⢸⣰⢹⠀⠀⠀⠀⡷⠁⡠⢻⢈⣷⠛⠺⣿
⠀⠀⠀⡗⠒⢲⠀⢰⠒⠒⠂⠀⠙⠙⡇⠀⠀⠀⢸⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⡇⠀⠀⠀⢸⠁⢀⡠⠋⡇⢸⠀⠀⠀⠀⡧⠊⠀⡨⠋⠁⡠⠊⣸
⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠈⠁⠀⠤⠀⠀⠁⠀⣐⣀⡇⠀⠀⠀⢸⡉⠁⠀⣠⣃⣸⠀⠀⠀⠀⣇⣠⠊⠀⣠⢊⣀⣊⡝
⠀⠀⠀⠉⠉⠉⠉⠉⠑⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⣀
⠀⠀⠀⠻⣍⣱⣀⣰⣳⠆⠀⠀⠀⠀⠀⠀⢄⠐⢸⡎⠠⢋⡇
⠀⠀⣏⣉⣉⣹⣿⣍⣉⣉⡽⠀⠀⠀⠀⡔⢲⢗⠾⢷⣛⣛⠒⠒⠒⡄⠀⠀⠀⠀⠀⠀⢀⠀⠇⡰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠄
⠀⠀⠀⠀⡏⠉⣿⠉⠉⠏⠀⠀⠀⠀⠀⡹⡱⠋⡍⠉⠉⠁⡪⣹⢭⠀⠀⠀⡖⠒⠒⠒⠤⠍⠛⣗⣳⢒⣒⣒⣒⣒⣲⠀⠀⠀⢰⠒⠒⠒⠒⠒⠚⣧⠀⠈⢢
⠀⠀⠀⠀⢱⠀⣿⠀⣸⠀⠀⠀⠀⢀⣴⠝⡇⠀⠁⢰⡆⠀⠀⠀⢸⠀⠀⠀⢘⠉⣉⣉⣉⣉⣉⣉⢍⡨⣉⢄⣄⠀⡍⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢧⣀⡠⠇
⠀⠀⠀⠀⠸⣆⣿⣠⡇⠀⠀⠀⠈⠓⠃⠀⡇⠘⠀⠀⠁⠀⠃⠀⣸⠀⠀⠀⢸⠀⠒⠔⠢⠒⠔⠔⠲⠒⠒⠲⠒⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⢹
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡞⢄⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢿⡿⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠎⠀⡱⠄
⠀⠀⠀⠀⠄⠷⣺⣏⡺⢤⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⡥⢂⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⢈⣼⣥⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⡏⠉⠙⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠂⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠐⢤⠀⠾⠏⠻⠆⠀⢤⠄⠀⠀⠀⠀⡆⠒⠛⠛⢛⠛⠛⠛⠓⢒⠀⠀⠀⠀⠀⢘⠠⠀⠄⠀⠂⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣅⠀⡀⢀⣬⣠⣄⣀⡀⣨⠀⠀⠀⠀⠀⢸⠠⠀⠄⡄⠀⢀⠀⡀⠀⡇
⠀⠀⠀⠀⡆⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠃⠀⠀⡀⠀⠇
⠀⠀⠀⠀⠈⠀⠛⠓⠂⠁⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠓⠒⠒⠒⠚⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠈⠀⠒⠘⠛⠛⠃⠒⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⠛⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢠⡯⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⣒⡒⢷⡀
⠀⢀⡞⠀⡴⠶⠦⠤⣌⣙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣳⣏⣀⣀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣡⠴⠚⠉⠁⢙⡆⢹
⠀⠘⣇⠀⠙⢤⣀⣀⠀⠈⠉⠛⠲⠿⢷⣤⣀⠀⢰⠋⠁⠀⠀⠀⠈⢳⠀⣠⣴⡯⠵⠒⠋⠉⠀⠀⣀⣠⠴⠋⣠⠞
⡖⠒⠛⠓⠦⠤⣤⣍⣉⣉⣙⣻⣿⡿⠿⠟⠛⠛⢛⣦⡤⣤⣤⠤⠴⠿⣟⠛⠛⠿⠿⠿⠿⠿⠿⠿⢽⠖⠚⠛⡟⠛⡟⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠞⠉⠈⣇⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣸⣄⣀⣤⣧⣤⡧⠤⠤
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠃⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠘⡄⠀⢀⡠⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢦⡀⢀⡞⡇⠀⠀⠀⠀⠀⠀⠹⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⣠⠧⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠤⢄⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠳⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠸⠀⠘⢦⠀⠀⢳⣀⡤⠤⠤⠤⠴⠆⠠⢀⣠⠞⠀⠀⠀⢀⣠⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢧⠖⠚⠳⡀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⡴⠋⠉⠁⢳⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠙⢦⡈⢦⡀⠀⠱⡄⠸⡀⠀⠀⠀⠀⢠⠎⠀⣠⠞⠉⢙⣦⡀⠀⠈⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠙⢦⣙⢦⡀⢹⡀⢳⣄⠀⠀⣠⢋⣠⣞⣡⠴⠚⠉⠀⠙⣳⣄⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣽⣦⣷⡼⠛⠓⣾⡵⠟⠛⠉⢀⣀⣤⠴⠖⠛⠉⠉⣻⠇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢣⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⡿⠁⠀⢸⠧⠤⣤⣶⣾⠯⠵⠶⠖⠒⠚⢛⣋⣭⠴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⢦⡀⠀⠀⢀⣀⣤⠴⠚⠋⠁⠀⠛⢲⣦⠾⠂⠒⠲⠶⣶⠶⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠉⢲⠋⠉⠁⠀⠀⠀⣀⣤⠴⠚⠉⠈⠳⣄⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠢⢀⠀⠀⠀⢸⠀⠀⠀⣴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣈⣳⣦⠤⠖⠋⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠢⡀⣾⠀⠀⠀⡟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣶⠖⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢹⡶⣄⢀⡇⠀⠀⠙⢦⡀⠀⠀⢀⡠⠔⠂⠉⠀⢸⡆⠀⠀⠀⣿⠀⠀⣀⣠⠴⠶⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠀⠙⢿⡇⠀⠀⠀⠀⠈⢒⠈⠁⠀⠀⠀⠀⠀⠀⣇⣠⣤⣶⠟⠋⠉⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣿⠀⠀⣸⠁⠐⢄⡀⠀⠀⣿⠀⠀⠀⠀⣀⣠⠴⢾⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⠀⠈⠑⢄⣿⣠⠤⠒⠋⠁⠀⠀⠸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⢸⠃⠀⣾⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢻⣄⣀⣤⠤⠶⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⢀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠸⠀⡠⠞⠉
⠀⢀⡀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⣿⣏⢹⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠰⠀⠠⠀⠀⠀⠀⠤⠘⠠⡔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠐⠀⠀⠀⡃⠀⠐⢂⠐⣁⠂⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡅⠐⠀⠢⠂⡀⠈⠀⣀⡀⠂⠀⠀⠰⢐⠮⣀⠁⠀⢀⠂⠈⠀⠀⠀⠀⠐⠒⠀⠂⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠴⠦⡤⠀⠪⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⠂⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄⠲⡀⣂⠁⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⡂⢲⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣰⡴⠤⠀⠀⠀⠀⠀⠀⠈⠁⠲⠆⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠢⠁⠀⠀⠀⠀⠀⠀⠂⢰⢰⡀⠒⠀⠀⠢⠀⡄⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⡄⠠⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⠸⡀⠀⠀⠀⡀⢀⢥⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠄⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠂⠀⠀⠀⠈⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠆⠀⣀⠀⠀⠒⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠴⠟⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⢀⠉⠀⠰⠠⢂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠀⠀⠢⠐⠤⠈⠋⠀⠤⣄⡠⠰⢎⣱⠀⠄⠀⠈⠀⠄⠀⠀⠢⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠀⠄⠀⢀⠀⠐⠀⠀⠀⠐⢧⡶⠒⢋⠛⠈⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠀⠀⠐⠀⠀⠀⠈⠛⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡆⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⠀⠀⠀⠀⣰⡀⠀⠈⢳⠁⠀⠀⢀⢣⠀⠀⠀⢯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⢸⣁⡇⠀⢰⠀⡇⠀⠀⣏⣸⠀⠀⠀⣈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⠀⠀⢀⢿⠀⠀⢸⠀⣷⠀⠀⡼⢇⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣀⣀⣼⢸⡧⠤⢼⠀⣿⠤⠤⡇⢸⠤⢤⣀⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⡇⡟⠉⠀⠀⢿⢸⡇⠀⠈⠳⠃⠀⢀⡇⢸⠀⠀⠀⣇⣸⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠑⠃⠀⠀⠀⠸⣸⠁⠀⠀⠀⠀⠀⠘⣇⡜⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⢸⠀⠘⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠁⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠶⠖⠒⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣾⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡆⡇
⠀⠀⠀⠀⠀⢹⡼⢸⢠⠞⠉⠙⠦⣄⣀⣀⣠⠤⠶⣄⠀⢀⠞⠉⠱⡄⢀⠖⠒⢄⡀⢠⠟⠚⠁⠀⢷⠇
⠀⠀⠀⠀⠀⠀⡇⠘⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⡇⠈⡇⠀⠀⠉⠁⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⠠⢠⣦⡿⣏⠀⣾⡾⣣⣤⡴⢊⢁⡀⣠⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⣿⣁⣶⣷⣄⠹⣏⡉⢰⣬⡻⠏⣴⢯⠻⣞⠳⠄⠲⡄⣀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⣿⣧⣉⢟⢁⡾⣦⣥⣜⠃⡀⠀⠈⠀⠁⠈⠠⠶⠶⢻⣌⡇⢦⡘⣣
⠀⠀⠀⠀⢰⡶⠾⡷⠶⠶⠶⠶⠶⣿⣽⠿⡻⢾⣟⣻⣦⡌⠀⣧⠠⢾⣡⣖⣁⣴⢁⣰⡾⣉⣹⠾⣇⢨⣦
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⣹⠧⣶⣿⡦⢛⡥⠊⢘⣧⠼⠣⡄⠻⠤⢫⣉⢿⣁⠀⠀⠀⠉⠉⠀⢿⡄⠀⠀⢀
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢀⣴⣿⡦⢉⢯⣠⣞⣷⠂⣤⣔⣿⣥⡝⠯⣄⠀⠈⠀⠈⠁⠀⠀⠀⠛⠓⢾⡇⣧⠀⠘⢏
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠷⠀⠹⠙⠇⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⣎⣷⠈⣫
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⣭⣇⢨⣣⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡿⣾⣠⠀⠰⠥⠄⠀⣔⣷⢟⣠⠄
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⡖⢠⡆⢀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡿⡐⠛⠛⣴⠂⣤⠛⠛⢂⢾⠗⠂
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢛⠀⡾⢣⡟⣰⢋⡟⡼⢡⢧⠏⡼⡾⢡⡇⠀⠀⠀⠀⠀⠠⣤⡶⣧⣴⣡⣿⣾⢿⣈⣦⣼⢦⣤⠄
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁⠘⠃⠙⠈⣹⠃⢋⡟⠘⠁⢡⠟⠀⠀⠀⠀⠀⠀⠀⠩⣷⢁⣴⣈⢻⠉⡟⣁⣦⡈⣿⠋
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣶⡆⣀⡀⣤⣅⢀⣠⣁⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⠏⣱⣟⡞⠹⣿⠏⡀
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠛⠋⠐⠋⠙⠛⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⣿⡷⠞⠳⢿⡿⠿⣾⠳⣾⣿
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢸⡇⠀⣿⠀⠈⠙
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣿
⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉
⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇


⡿⠿⡿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿