⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⢷⣷⣷⣷⣿⣯⣿⣾⣶⣦⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣷⣔⣄⣢⢠⣀⡀⡀⠉⠙⠟⣿⢿⢿⢿⣷⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⠟⠃⡁⠈⠀⠀⠈⠊⠆⠄⠀⠀⠑⠀⠁⠈⡈⠚⠛⢿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣟⢌⢔⢒⠪⢙⢝⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠛⠿⣿⣔⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡋⠂⠑⢁⠁⠀⠠⡪⢂⡰⠜⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⢻⢿⣆⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⡁⠀⠄⠈⠀⠀⠀⠀⢝⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⢿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⢂⡴⠔⠲⢤⡀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠽⣷⣥⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡯⣮⠃⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⢔⠜⠉⠉⠈⠑⠱⡄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢛⣿⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣽⡷⣴⡀⠀⣄⣦⢄⢷⠀⠀⠀⠀⠀⢠⠊⠂⠀⠀⠀⠀⠀⠀⠈⢖⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠹⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣓⠁⠌⢟⡯⣟⢮⡻⣿⠄⠀⠀⠀⢀⢮⣲⢶⢶⣆⡀⣀⢴⣲⣤⡨⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢹⣗⡮⡮⡮⣞⡵⣯⣻⣿⠁⠀⠀⠀⡸⣟⡇⠁⡸⣺⡺⡾⣝⣞⢮⢿⡺⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡿⡗⡛⠝⠻⠽⣯⢷⣻⢷⠫⣟⠀⠀⠀⠠⡇⢻⡮⡮⣆⡧⡯⣯⣺⢮⡯⣿⠡⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠍⢄⣢⡨⡐⡈⠌⡛⣏⠁⣼⠃⠀⠀⠀⡺⠀⠀⢟⣯⢷⢯⣟⣾⣺⣽⠯⠃⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠣⣱⢫⢢⠫⡝⣦⡡⠂⢌⢻⢎⠀⠀⠀⢀⢺⠀⠀⠀⠘⢟⣿⣺⠾⡓⠃⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡱⡱⡱⡸⡘⡜⢮⣺⢌⢐⠄⠣⣣⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠁⡁⢀⠠⢀⠠⢀⢺⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡎⡞⡜⢔⠕⡕⢵⡱⣫⡢⡈⡢⢈⢧⠠⠀⠀⠱⣄⢀⠀⡐⡀⡢⡨⡂⡎⡔⢔⢔⢇⠂⠄⠁⠀⠀⠀⠀⠀⠀⠐⢀⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡪⡎⡎⢎⢪⢪⢎⢧⢯⢆⢂⢂⢂⠫⢆⠄⠀⠀⠑⢕⢴⣰⢜⡴⡵⡵⡵⡝⡕⢕⠨⢐⠀⠂⠀⠀⠀⢀⠀⡁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡜⢵⡱⣕⢝⣎⢧⣳⢽⣲⢐⠄⢅⢑⢙⢙⠪⢋⠣⡙⢌⢎⢮⢳⣹⢪⢪⠪⠪⠨⢀⠂⠀⠀⢀⠠⠀⢠⣲⣿⡓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⢄⣝⠮⢓⢱⢩⢪⢕⢭⢳⢬⡂⡂⡂⡂⢅⠢⣡⡪⠮⡚⡕⣕⠮⢑⠡⠡⠡⠁⠂⠀⠀⠈⠀⠀⡰⣽⡿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⣠⣾⣿⡻⡕⡋⢄⢢⢣⢣⢣⢣⡣⡣⣣⢣⡫⡫⡞⡪⡓⢝⣑⢜⠼⠜⢊⠁⠂⠀⠀⠂⠀⠠⠀⠀⠀⠄⠂⠁⣾⣿⠅⠀⠀⠀
⠀⠀⠀⣠⣶⣿⢿⠿⠿⢿⢿⣿⣷⣧⣦⣠⣺⣿⣟⠕⡜⡐⠄⢕⠨⢂⠅⢕⠑⢕⢕⢕⢕⡵⡫⡊⣢⡪⢚⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠐⠨⣾⡯⠀⠀⠀⠀
⠀⢀⣾⡿⡏⠃⠁⠀⠀⠅⡇⡞⣞⡽⡿⣿⣿⣻⡒⢸⢨⠠⢃⠅⡪⢐⠡⠢⡑⡡⢊⢮⠳⡑⣔⡜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⡈⠠⠨⣿⡯⠀⠀⠀⠀
⠀⣷⣿⠋⠀⠀⠀⠀⢂⠌⡎⣮⡳⡽⣽⣺⡺⡮⣷⡈⢎⢦⡡⣊⢄⢕⢌⣪⢔⠮⠫⡡⢣⣪⡒⡀⠁⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠂⠀⠠⠈⣿⣿⠀⠀⠀⠀
⢨⣿⣷⡡⡦⡢⡨⡨⢂⠇⣏⢮⢞⣽⡺⡮⡯⣻⢮⣻⢦⣪⣘⢱⢩⢩⢑⢅⢕⡥⣳⣞⢿⡂⠈⠌⠩⠊⠒⠂⠅⠁⠂⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠐⠈⣺⣿⡀⠀⠀⠀
⣾⡿⡗⠍⡰⠿⣾⡸⡤⡸⡜⡮⣫⣞⡽⡽⣝⣗⢯⢾⣝⣞⣞⣟⢮⣗⣯⣟⡽⣝⢷⢽⣻⡊⠠⠐⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⣿⣇⠀⠀⠀
⣿⠫⢀⠮⠃⢈⢷⡯⡯⣺⢝⡽⣕⢷⢽⣝⣞⣞⡽⣳⣳⣳⡳⣽⣳⣽⠇⠩⠻⣽⢯⣟⣽⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢻⣿⡄⠀⠀
⠁⡰⡸⠁⢰⠜⠩⣻⡽⡵⡯⣻⡺⣝⣗⣗⣗⣗⢯⣗⣗⣗⡽⣿⢀⠩⢳⢄⠈⠘⢽⣞⣯⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢟⣿⣄⠀
⡎⠃⡀⡬⠃⠁⠠⣳⡯⡯⡯⣳⢯⣳⣳⣳⡳⡽⣵⣳⣗⡷⣿⠻⡦⡀⠀⠱⡥⠀⠈⢝⡗⢧⡈⢀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠽⣿⣦
⠀⢠⠺⠈⠀⢈⢜⣿⡺⡽⣝⣗⣟⣞⡾⡮⡿⣽⣳⣟⢾⣽⣻⡐⠨⢲⡀⠀⠈⠁⠀⠀⠱⡅⠹⣄⠐⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠁⡀⠩⣻
⢤⠫⠀⠀⣐⣼⣟⣗⣟⣯⣟⣾⣳⢯⡯⣟⣯⢷⣻⣞⣟⡾⣽⡆⠄⠈⢖⠁⠀⠀⠀⠀⠀⠁⠀⡘⣅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⢀