⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⠀⠀⠀⣦⣂⡀⣠⡐⡄⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⡴⠃⠁⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠞⠀⠀⢀⣾⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣼⠃⠀⠀⣠⣿⣿⣿⣿⢏⢇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⣰⣿⣿⣿⠟⡁⠑⣹⠀⣍⠅⠀⡀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⡯⠀⠀⣰⣿⡿⠋⠀⠀⠀⢈⡾⢸⠁⡒⠀⠈⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠒⡳⡀⠀⠀⢀⣀⣤⣴⡿⠟⣻⣿⠇⢀⣼⢟⢿⢦⠤⣄⢀⠀⠞⠂⣸⠂⠃⠀⠀⠬⢒⢄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⠰⣖⠶⠿⠟⠓⠉⠁⠀⠀⣽⢏⣴⣿⡵⠐⠐⠫⠡⠪⠅⣠⣄⣖⢅⠁⢀⡉⠙⠀⠪⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⢀⣾⡵⠻⢛⣉⣈⣑⣯⠛⠄⠤⠄⠀⠀⣀⡀⢀⠀⠄⠜⣫⣌⠲⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠑⢤⣠⠒⠊⠉⠀⠉⣹⡿⠗⢀⣠⡶⡻⡽⢸⣿⡷⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⢡⣍⡪⢴⡭⣙⢕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⡀⠔⠑⠒⠓⠚⠓⠺⢿⡗⠻⢿⠙⣷⡡⢷⠝⢁⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠐⣈⢠⢝⠥⢀⣜⠙⠕⢇⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢀⠁⠒⠂⠂⠀⠀⢐⡀⡀⠹⣆⠸⡼⣊⢑⠀⠀⠀⠀⠀⠀⣠⡤⠊⠀⠀⠀⠐⠀⠀⢀⢑⡣⡑⣛⠀⠲⣣⠂⣈⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢸⡄⣦⠦⠠⠤⠤⠤⣅⠋⣶⣿⠗⢏⢰⠀⠀⠀⠀⠀⠄⣸⠏⠀⠀⠀⠀⠀⠀⠠⠀⠠⠵⠠⠠⠰⢢⠦⡀⠑⢷⣪⣁⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠘⢘⠉⠀⠀⠀⠀⣀⠉⢷⢸⣇⣸⣆⣘⡰⠊⠀⠁⠀⡄⡟⠀⠀⡀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠠⣉⡉⢍⠒⢱⡷⠀⡐⠃⠈⡤⣣⣁⠑⢄⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠟⣆⢀⢀⣾⠿⣧⡀⢸⣿⣙⣏⢩⣬⣷⠀⢉⢀⢐⡼⢁⠔⠄⠀⠀⠰⠀⠀⠀⢐⠀⠀⠀⠀⠀⠪⡈⢗⡯⣂⣿⢂⡒⡥⢈⠓⠘⣍⢥⡉⠄⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠠⣱⢁⡀⠀⢻⢦⡿⢏⡿⢻⡟⠻⠷⣿⣵⣠⡶⠗⠋⠴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠰⢡⢭⡇⠚⡈⠇⠈⠖⣤⡢⡄⢻⡑⣥⠸⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⢜⣾⣿⠀⠀⠈⢰⡶⣢⣿⡙⡳⣆⡮⠯⠉⠀⠂⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⡉⠀⠂⠀⠀⠐⠀⣘⠨⡋⡪⠌⢎⣿⡇⠇⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣾⣾⣏⠀⠁⠀⠀⢀⡟⣱⡘⠃⣷⠊⢦⡁⠀⠀⢀⠀⠀⠀⠁⡀⠂⠀⠀⠀⠀⠀⠀⠀⡐⠆⣔⡼⠐⠁⠀⠀⠀⠐⠀⠀⠈⠰⠘⠑⠸⢰⡘⠧⡇⠀⠀⢸
⡇⠀⠀⠀⠀⠀⢭⡿⠈⠆⡀⠀⠀⠡⢂⡷⡀⠀⠁⢊⠈⠐⠄⡑⠁⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⣂⡌⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢂⡐⠀⠐⢗⡗⠃⠀⠀⢸
⡇⠀⠀⠀⠀⠀⣿⡽⠀⠀⠀⠀⠐⠊⣼⠇⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⠊⢪⠄⢢⡡⢣⠐⣢⠀⠀⢸
⡇⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⢀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠁⠄⠈⠐⠸⡎⣖⠵⡁⠆⠀⢸
⡇⠀⠀⢠⠪⢭⠈⠀⠀⠀⠀⠀⠀⠀⡘⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣈⢡⠀⠀⠀⢑⠀⠠⠈⠸⣆⠤⣸⠀⢸
⡇⠀⢠⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⢈⣪⣾⠀⠀⠀⠀⠀⠀⠀⢸⣍⠀⡪⡆⢸
⡇⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠸⠁⡎⡽⡿⢠⠀⠀⠀⠀⠀⠠⡸⡷⡢⠸⠅⢸
⡇⠘⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠈⠅⠆⠆⡳⠁⠈⡆⠀⠀⠀⠀⠐⣰⠑⡡⣧⢰⢸
⡇⡇⡓⢆⠀⡀⠀⠀⠀⠀⠀⠀⢀⣮⠀⠀⢷⡘⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠄⡠⣌⠂⢸⣧⠀⠀⢸⡄⠀⠀⠐⠀⢠⠣⣡⡚⠸⢸
⡇⢳⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠐⠘⣷⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⣴⣧⡼⠏⠂⢀⠌⠀⠀⠑⠰⢄⠀⡀⢑⣳⠃⢸
⡇⠘⡬⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⣰⠃⠀⠈⣼⣻⡆⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡁⣰⣽⠿⠜⠁⡠⠁⠀⠀⠀⠀⠀⠖⠈⣄⠉⡽⡄⢸
⡇⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠃⡠⠃⠀⠀⠀⠩⠃⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⢾⠻⡇⠀⡜⠁⠀⠀⠀⠀⠀⠀⢀⢰⢯⠀⡴⡛⢸
⡇⠀⠀⠘⡔⠀⠀⠀⠀⢀⡡⠊⠀⠀⠀⠀⠀⠀⠈⠃⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠈⢸⢸⡆⢃⠞⠀⠀⠀⠀⠀⠀⠐⠀⠀⡐⣑⡹⣦⠃⢸
⡇⠀⠀⠀⠈⠒⠚⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇⡟⡏⢼⠇⡞⠀⠀⠀⢀⠀⡀⡂⢀⠤⡊⢜⢊⠝⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡘⢛⠛⢰⠗⠁⠀⠀⠀⠀⠀⠀⠂⣐⣡⣨⠗⠉⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡻⡻⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⡀⠂⠁⠀⠁⠚⠀⠁⠀⠀⠀⠠⢂⡤⡪⠀⣠⢪⠊⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⡼⡑⠁⠀⠠⠀⠀⠀⠀⠀⠠⠁⢈⣼⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠸⠏⢉⢊⠊⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢟⠄⡅⠀⡐⠀⠀⠀⠀⠀⠀⠆⢰⠿⣋⣀⠔⠀⠀⠀⠀⠀⡀⠀⢀⢀⢆⠻⣑⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠃⡟⢀⠢⠢⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⡀⠐⠀⡀⠂⠊⡀⠁⠁⣪⡞⡾⠟⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⢰⡤⣤⣤⣴⡤⣤⣤⡦⢤⣴⣶⣦⠀⢀⣗⡕⣸⢃⣮⠇⢄⠀⠀⠀⠀⠀⠀⠂⠘⠺⣤⠖⠒⠒⠝⠁⢀⠜⢀⢄⠌⡿⠟⠰⠠⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣈⣿⣿⣽⣿⣿⣿⣻⣿⣿⣏⣛⣀⣀⣸⣼⣎⣰⣃⣡⣃⣸⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣉⣒⣤⣐⣊⣡⣄⣚⣡⣋⣀⣠⣅⣂⣡⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸