⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⡵⣟⢝⡶⣿⢹⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢲⣵⣟⣯⣯⢾⢵⢿⢽⡸⡢⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡺⣕⣵⡿⡽⣪⡳⣹⢺⢽⢽⣱⣏⢎⢎⢎⢖⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⣽⣏⣯⢾⡯⡿⣝⣞⡜⡼⡜⣝⢵⡻⣧⢣⢃⢇⢇⢇⢣⢑⢄⠀⠀⠀⠀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢾⣽⣻⣞⣾⢯⣿⢽⣻⣗⣷⣻⡝⡞⡜⣆⢏⣿⢸⢪⠲⡙⡜⡜⡸⡨⣓⠄⢀⢔⡥⢗⠫⡪⡒⣆⡀⠀⠀⠀
⠀⠀⠀⣤⠀⠀⢀⠔⢩⢷⣻⣞⡾⣯⡷⣻⢎⢺⣺⣳⣻⣺⢝⠸⣕⢕⡇⣿⢸⢘⢜⢜⢎⢎⡪⡢⡓⡭⣸⡲⢝⠴⠷⠮⡢⡊⡳⡀⠀⠀
⠀⠀⠈⣞⡀⠀⠁⠀⣾⣻⣺⢎⡿⣟⢾⡽⡼⣜⣵⢳⡓⠎⠔⠤⣟⢧⢷⢹⡎⡎⡎⡎⣪⢪⢪⢺⣸⢮⣗⢯⡫⣝⢳⢭⡊⢮⠨⣃⠀⠀
⠀⠀⠀⠘⢆⠀⠀⠀⣿⣺⣞⡾⣿⢽⣻⢋⠓⠍⠄⢅⠕⡛⡧⣦⣝⡯⡗⣟⣧⡳⡣⣓⢼⡸⣱⢕⡷⡯⣞⣷⡯⣗⢇⢇⢎⢎⠵⣘⠀⠀
⠀⠀⠀⠀⠈⠤⠀⠀⡏⡾⡮⣿⢿⣝⣯⠂⠅⠅⠅⠢⡑⡰⢹⢑⢽⢫⡪⡺⣗⣽⣳⡇⡇⣯⢮⣳⢽⣻⠋⣿⣻⡷⣕⢯⡪⡪⣪⢣⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⡯⣟⣿⣻⣳⣿⡨⠨⠈⠌⡐⢐⢈⠂⢆⣮⣗⢵⡽⣿⡺⣮⢷⡑⣯⡯⡿⡽⡏⠈⣟⡷⣿⡗⡝⣗⡕⡜⣼⡪⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣻⢹⣯⣷⣻⢠⢁⠡⢁⠐⡐⠤⣵⣞⡷⣽⢯⣻⢯⣫⡯⣗⡵⣹⢯⢿⠝⠀⠀⡇⣹⢷⢗⡕⣽⢪⢪⢳⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢯⠼⣳⠏⠌⠀⢐⠒⢒⣒⣖⣾⣳⢯⢟⠽⡑⣾⣟⢵⡻⣗⡷⣹⠙⠁⠀⠀⠀⢸⡊⣯⢽⢜⠼⣝⢜⢼⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢻⠀⠀⠈⠈⠛⠙⠙⣺⣞⡾⡷⢯⣶⢼⣟⡵⣳⠏⠛⣽⠑⠧⡀⠀⠀⠀⠈⡷⣹⡻⡌⡯⣞⡕⣽⣻⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡽⠘⠂⠢⠢⢒⠻⢖⣯⣯⣧⣳⢯⡳⡽⡡⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣳⡫⡪⣪⢷⢕⢵⢫⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⠠⠁⠌⠠⠈⠄⠡⢂⠔⡹⡜⡽⣣⣿⣻⣄⡀⠀⢀⡠⠠⢀⠀⠀⠀⠀⠀⢏⢇⢧⣳⡯⣣⡫⣜⢸
⠀⠀⠀⠄⡢⡢⠲⡐⡖⡴⡰⠤⡎⢜⠨⠀⠅⠨⠀⠅⠌⡐⢐⢐⢹⠨⢘⠜⢗⠈⠱⣕⠭⡀⠀⠀⠁⠀⠀⠀⠀⡸⡱⣕⣷⣻⢕⢽⠌⢸
⢀⢎⢍⠪⡨⣊⢪⢪⠎⠌⡐⡕⡜⢌⠌⢌⠠⠁⠌⠄⠅⡂⢂⠐⣸⢈⠢⡑⢕⠅⢅⢱⡅⠌⡑⠠⡀⠀⠀⠀⡰⣝⡺⡼⣞⣽⣪⡳⡄⢸
⡪⡢⡣⣣⡣⣖⢵⠡⠨⢐⠠⠣⠪⡪⡨⡂⠄⠡⠈⢌⢂⠂⠅⢂⡟⠠⡑⡕⢤⠑⠐⡑⡕⢐⠐⠠⠐⠄⠀⣰⢣⡳⡽⣝⣗⡿⣲⢱⢇⢸
⢵⣫⠺⡜⡴⡝⡾⢀⠑⡔⡝⡢⡣⡊⡂⠄⠡⠈⠌⡎⡐⢌⢌⡾⠡⡑⢜⢜⢜⠬⢐⢌⠇⠆⠌⡐⠠⠈⡼⣪⡳⡽⣝⣞⢮⣾⣗⢕⢿⣸
⣳⠅⢋⡾⣕⢯⣞⡷⣌⢆⢗⢕⢕⠑⠌⠄⠡⠈⣜⢌⢎⢦⢿⠡⢑⠌⢆⢇⢇⢍⢆⢢⡇⡃⠅⡐⡨⠀⡟⠼⠘⠉⣞⢼⡹⣽⢮⡳⡍⡞
⡳⠁⣿⣽⡽⣗⣯⡿⣝⢧⢣⢣⢑⠅⡁⢂⠡⢡⡷⣽⡳⣫⡫⡷⣄⠣⢱⢱⡱⡑⠆⣾⢇⢂⡥⠪⠀⠅⡃⠀⠀⣸⢕⣗⢯⣿⢽⡪⠂⣌
⢌⣶⢿⣞⣿⣻⣯⣟⡟⡜⡜⡌⡢⢁⠂⡐⢨⡾⣝⣗⢝⢜⡜⡮⡪⡹⠺⠬⡬⡬⡾⣝⡇⣺⠨⠨⢈⠠⢠⠀⢠⡳⡳⣝⣾⢫⢗⢽⠐⢸
⢸⢸⢸⢸⢍⢟⢞⢿⢱⠱⡱⠨⢂⠂⢂⢂⣾⡯⡷⡯⣎⢇⢇⢇⢧⢫⡣⡳⣕⢝⢮⣗⣟⢜⢌⢌⠐⡀⠌⢀⡗⡽⣝⡿⡎⡯⡯⣺⠀⠘
⠀⠑⠱⠱⡱⡱⣩⢣⢣⢣⢑⢑⠠⠨⢐⡾⡯⣟⡯⣟⣇⠇⡣⢣⢫⢯⣺⣝⡮⡯⡷⡽⣎⢎⢆⢂⠂⠄⠂⢳⢽⡽⣽⡛⡸⠃⡯⡎⠀⡆
⠀⠀⠀⠀⠀⡸⡪⡪⡢⡃⡂⡂⢂⢅⡯⡫⡪⢒⠑⢑⠨⠑⠙⠎⡾⣝⠦⡷⣻⡽⡽⡍⠸⡪⡢⡑⠨⢀⠡⠘⣯⢿⡽⢀⠏⠀⣯⠃⢰⠀
⠀⠀⠀⢀⢎⢇⢇⢇⠕⢌⠐⠌⢔⢞⢜⢑⠌⡐⠨⢀⢂⠨⠀⠂⡎⠢⠁⠌⠪⠾⠯⠇⠀⢫⢪⠌⠌⠄⠂⡂⡿⡓⢀⠊⠀⢀⣯⢀⠃⠀
⠀⠀⡰⡹⡸⡸⡨⡢⡃⠢⠨⢨⡪⡎⡎⡢⡁⠢⢑⢐⢀⠂⡁⢅⠅⠅⠨⢐⠁⠀⠀⠀⠀⢘⢎⢎⠅⢅⠡⠠⢉⢔⣁⠀⠀⣸⡇⠁⠀⠀
⠀⢰⢱⢱⢱⢱⠱⡨⢌⢌⢪⠪⡢⡣⡃⡂⡊⠨⠐⡐⡀⢂⠐⠨⠨⠀⠅⡹⣦⡀⢀⣠⡶⣿⡱⡱⡑⢕⠌⢌⠢⠀⠀⠉⢡⣿⠀⠀⠀⠀
⢀⢇⢇⢕⢕⢕⢕⢕⢅⢧⡳⡣⡳⡸⡨⡂⡢⡁⡢⡀⠐⠠⠈⠨⠨⠀⠅⠐⠨⠻⠻⢽⣯⣟⣗⢕⢕⢕⠱⡠⠡⠡⡀⢠⡿⠆⠀⠀⠀⠀
⡎⡎⡆⡇⢇⢕⢕⠕⠁⢸⢕⢝⢼⢸⢜⠼⡐⡂⠆⢌⢐⠠⢁⠐⢈⠠⠁⠈⡀⠅⡁⠂⠅⠅⠈⡎⡇⡇⣇⢥⠣⣨⢶⢻⡝⠀⠀⠀⠀⠀
⢎⢎⢎⢎⢎⢎⠊⠀⠀⠘⣊⢇⢣⠣⡣⡱⡰⡠⡁⡂⡐⡁⠆⠌⢄⡀⡂⣑⠤⡄⡤⡡⡌⡤⣙⢘⢜⠾⡕⢥⢯⣗⡯⡧⣭⡡⡀⠀⠀⠀
⢇⡣⣱⢱⠕⠁⠀⠀⠄⠐⡖⣅⠧⡕⡕⡕⢕⢜⠬⣪⡪⠦⣃⣋⣠⢥⢥⢖⢖⢒⡂⡢⠢⢊⡈⡣⢕⢶⣶⣿⣻⣺⣺⢽⣺⠖⠅⠀⠀⠀
⡇⡣⣣⠃⠀⠀⠀⠀⠀⠀⡇⡇⣝⢼⣺⡺⡼⢱⣩⡵⡸⣝⣞⢜⣮⡺⣜⢎⠮⢑⠪⢀⠰⡑⠅⠅⡑⠱⡨⡳⣗⣗⣗⢯⣞⡙⡜⠀⠀⠀
⡇⡯⠀⠀⠀⠀⠀⠀⠀⠀⠑⡵⡑⢽⢚⡾⣮⡙⣵⡫⢯⡪⡺⣝⣖⢵⡱⡕⡕⠡⣐⠅⡃⢪⠨⢐⠠⠁⠌⡘⠜⢷⣳⣽⠢⠪⣊⠀⠀⠀
⡓⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⢧⢏⢗⢝⢮⣳⡸⣝⢵⢪⢪⢪⢪⢪⠪⠒⠅⣑⢐⠀⢂⢔⢕⢐⠨⠀⠅⢐⠈⢘⣽⡾⡇⠡⡱⡀⠀⠀
⣮⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡪⡣⡫⡪⡢⡳⡵⡳⡝⡅⡃⠒⢁⡁⡆⡔⡪⡐⠄⡊⠢⡳⡱⡐⠌⠨⠈⠄⢐⠠⠸⣟⣷⠄⡪⡍⠄⠀
⣷⡫⣇⠀⠀⠀⠀⠀⠀⠀⢐⣿⢸⢸⢸⢪⠐⠁⠭⠪⡋⠔⣐⠭⡢⡣⡣⡣⡱⡘⡔⠄⣝⢎⢎⢌⠪⠨⡈⠌⡐⠠⡑⡟⣡⣪⣯⡷⣿⡀
⣷⣣⣬⡄⠀⠀⠀⠀⠀⠀⣗⣿⢸⢸⠸⡸⣘⢲⢠⢄⢔⢍⢎⢎⢎⢜⢔⢕⢜⢌⢎⢢⢗⡝⡜⡌⢎⠢⡂⢅⢂⠑⡌⡄⣏⣿⣳⣟⣗⡧
⡯⡛⡊⢆⠢⡐⠄⠀⠀⢰⡞⣞⢜⢜⢜⢸⢨⢪⠪⡪⡪⡪⡪⡪⡪⡢⡣⡱⡱⡱⡡⡯⡳⣕⢵⢱⢱⢑⢌⠢⡢⡑⢌⠛⢜⡯⠳⣃⠀⢋
⡐⡑⡐⡷⣥⠨⡈⠢⢠⢟⠔⡗⡕⡕⡱⡑⡕⢕⢕⢕⢜⢜⢜⢜⢜⢜⢜⣜⢼⢼⢱⡯⣯⡺⣜⢎⡎⡎⡎⡎⡢⡊⠲⡀⠪⣜⠄⡣⠐⠈
⢢⠪⠠⢹⣺⠪⡂⠕⡑⡿⡈⡪⡪⡪⡘⡌⢎⢪⠢⡣⡣⡣⡣⡳⡹⡪⡣⡣⡑⣸⢽⢝⢞⡺⡪⣣⢫⢺⢸⢸⢐⠌⠢⡂⠱⡽⡐⠨⡀⠇
⢕⠨⢨⣞⢮⡣⢡⠡⢂⡏⣔⣼⢸⢨⠢⡃⡇⡕⢕⢕⢜⢜⢜⢜⢜⢜⠌⢆⠢⣞⢵⢝⢵⢹⢸⢸⢸⢸⢨⠢⡁⡪⢑⠌⡢⢹⣠⣗⣞⢦
⡘⢌⠌⡘⡪⡮⡘⠌⠄⡿⣞⣿⣾⣼⣸⢨⢢⠣⡣⡱⡑⡕⢕⢕⢕⢅⢣⢡⣯⡪⡪⡪⣣⢳⢱⢱⢑⢕⢅⠕⢐⢐⠱⠨⠐⠑⣗⡷⣹⢝
⡨⠢⡁⠢⢨⠱⢐⡥⣵⢯⣿⢟⡾⡳⢯⢯⣳⣽⡺⡮⡾⡼⡮⣞⣾⡾⠯⠣⣿⣿⣮⣷⣕⣕⣕⢕⢕⣱⣐⠈⢔⢰⡡⠂⡁⠄⠸⣽⡺⣝
⢈⠢⢨⢘⢚⢚⠛⠿⢟⣟⡯⣟⢕⢕⢕⢍⢇⡓⡻⡹⡛⡟⣛⢏⢇⢇⢇⢱⣿⣻⢿⣯⣿⣽⢯⡿⢽⠳⠁⢠⢂⡊⢙⢆⣀⡂⡂⠱⣟⡾
⡳⣌⢰⢑⠌⡄⠅⠅⣾⡷⢫⠚⡜⡔⢕⢅⠇⡎⡪⡪⡪⡪⡪⡪⡪⣊⠢⣾⣿⢽⢯⣞⡷⡽⣕⢝⢜⣁⡰⡕⣆⠢⢸⡹⡲⣕⢭⢃⢫⡿
⣫⢯⣳⠐⠅⡢⣕⡟⣙⢌⠆⠁⡎⢎⢎⢆⢇⢕⢕⢜⣬⠪⣮⣮⣮⣦⡿⣿⢯⣿⣻⣞⡽⣝⣞⢎⡧⣣⡣⡧⡯⣎⢢⠩⢣⠘⢎⡇⢂⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢲⣵⣟⣯⣯⢾⢵⢿⢽⡸⡢⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡺⣕⣵⡿⡽⣪⡳⣹⢺⢽⢽⣱⣏⢎⢎⢎⢖⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⣽⣏⣯⢾⡯⡿⣝⣞⡜⡼⡜⣝⢵⡻⣧⢣⢃⢇⢇⢇⢣⢑⢄⠀⠀⠀⠀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢾⣽⣻⣞⣾⢯⣿⢽⣻⣗⣷⣻⡝⡞⡜⣆⢏⣿⢸⢪⠲⡙⡜⡜⡸⡨⣓⠄⢀⢔⡥⢗⠫⡪⡒⣆⡀⠀⠀⠀
⠀⠀⠀⣤⠀⠀⢀⠔⢩⢷⣻⣞⡾⣯⡷⣻⢎⢺⣺⣳⣻⣺⢝⠸⣕⢕⡇⣿⢸⢘⢜⢜⢎⢎⡪⡢⡓⡭⣸⡲⢝⠴⠷⠮⡢⡊⡳⡀⠀⠀
⠀⠀⠈⣞⡀⠀⠁⠀⣾⣻⣺⢎⡿⣟⢾⡽⡼⣜⣵⢳⡓⠎⠔⠤⣟⢧⢷⢹⡎⡎⡎⡎⣪⢪⢪⢺⣸⢮⣗⢯⡫⣝⢳⢭⡊⢮⠨⣃⠀⠀
⠀⠀⠀⠘⢆⠀⠀⠀⣿⣺⣞⡾⣿⢽⣻⢋⠓⠍⠄⢅⠕⡛⡧⣦⣝⡯⡗⣟⣧⡳⡣⣓⢼⡸⣱⢕⡷⡯⣞⣷⡯⣗⢇⢇⢎⢎⠵⣘⠀⠀
⠀⠀⠀⠀⠈⠤⠀⠀⡏⡾⡮⣿⢿⣝⣯⠂⠅⠅⠅⠢⡑⡰⢹⢑⢽⢫⡪⡺⣗⣽⣳⡇⡇⣯⢮⣳⢽⣻⠋⣿⣻⡷⣕⢯⡪⡪⣪⢣⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⡯⣟⣿⣻⣳⣿⡨⠨⠈⠌⡐⢐⢈⠂⢆⣮⣗⢵⡽⣿⡺⣮⢷⡑⣯⡯⡿⡽⡏⠈⣟⡷⣿⡗⡝⣗⡕⡜⣼⡪⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣻⢹⣯⣷⣻⢠⢁⠡⢁⠐⡐⠤⣵⣞⡷⣽⢯⣻⢯⣫⡯⣗⡵⣹⢯⢿⠝⠀⠀⡇⣹⢷⢗⡕⣽⢪⢪⢳⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢯⠼⣳⠏⠌⠀⢐⠒⢒⣒⣖⣾⣳⢯⢟⠽⡑⣾⣟⢵⡻⣗⡷⣹⠙⠁⠀⠀⠀⢸⡊⣯⢽⢜⠼⣝⢜⢼⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢻⠀⠀⠈⠈⠛⠙⠙⣺⣞⡾⡷⢯⣶⢼⣟⡵⣳⠏⠛⣽⠑⠧⡀⠀⠀⠀⠈⡷⣹⡻⡌⡯⣞⡕⣽⣻⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡽⠘⠂⠢⠢⢒⠻⢖⣯⣯⣧⣳⢯⡳⡽⡡⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣳⡫⡪⣪⢷⢕⢵⢫⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⠠⠁⠌⠠⠈⠄⠡⢂⠔⡹⡜⡽⣣⣿⣻⣄⡀⠀⢀⡠⠠⢀⠀⠀⠀⠀⠀⢏⢇⢧⣳⡯⣣⡫⣜⢸
⠀⠀⠀⠄⡢⡢⠲⡐⡖⡴⡰⠤⡎⢜⠨⠀⠅⠨⠀⠅⠌⡐⢐⢐⢹⠨⢘⠜⢗⠈⠱⣕⠭⡀⠀⠀⠁⠀⠀⠀⠀⡸⡱⣕⣷⣻⢕⢽⠌⢸
⢀⢎⢍⠪⡨⣊⢪⢪⠎⠌⡐⡕⡜⢌⠌⢌⠠⠁⠌⠄⠅⡂⢂⠐⣸⢈⠢⡑⢕⠅⢅⢱⡅⠌⡑⠠⡀⠀⠀⠀⡰⣝⡺⡼⣞⣽⣪⡳⡄⢸
⡪⡢⡣⣣⡣⣖⢵⠡⠨⢐⠠⠣⠪⡪⡨⡂⠄⠡⠈⢌⢂⠂⠅⢂⡟⠠⡑⡕⢤⠑⠐⡑⡕⢐⠐⠠⠐⠄⠀⣰⢣⡳⡽⣝⣗⡿⣲⢱⢇⢸
⢵⣫⠺⡜⡴⡝⡾⢀⠑⡔⡝⡢⡣⡊⡂⠄⠡⠈⠌⡎⡐⢌⢌⡾⠡⡑⢜⢜⢜⠬⢐⢌⠇⠆⠌⡐⠠⠈⡼⣪⡳⡽⣝⣞⢮⣾⣗⢕⢿⣸
⣳⠅⢋⡾⣕⢯⣞⡷⣌⢆⢗⢕⢕⠑⠌⠄⠡⠈⣜⢌⢎⢦⢿⠡⢑⠌⢆⢇⢇⢍⢆⢢⡇⡃⠅⡐⡨⠀⡟⠼⠘⠉⣞⢼⡹⣽⢮⡳⡍⡞
⡳⠁⣿⣽⡽⣗⣯⡿⣝⢧⢣⢣⢑⠅⡁⢂⠡⢡⡷⣽⡳⣫⡫⡷⣄⠣⢱⢱⡱⡑⠆⣾⢇⢂⡥⠪⠀⠅⡃⠀⠀⣸⢕⣗⢯⣿⢽⡪⠂⣌
⢌⣶⢿⣞⣿⣻⣯⣟⡟⡜⡜⡌⡢⢁⠂⡐⢨⡾⣝⣗⢝⢜⡜⡮⡪⡹⠺⠬⡬⡬⡾⣝⡇⣺⠨⠨⢈⠠⢠⠀⢠⡳⡳⣝⣾⢫⢗⢽⠐⢸
⢸⢸⢸⢸⢍⢟⢞⢿⢱⠱⡱⠨⢂⠂⢂⢂⣾⡯⡷⡯⣎⢇⢇⢇⢧⢫⡣⡳⣕⢝⢮⣗⣟⢜⢌⢌⠐⡀⠌⢀⡗⡽⣝⡿⡎⡯⡯⣺⠀⠘
⠀⠑⠱⠱⡱⡱⣩⢣⢣⢣⢑⢑⠠⠨⢐⡾⡯⣟⡯⣟⣇⠇⡣⢣⢫⢯⣺⣝⡮⡯⡷⡽⣎⢎⢆⢂⠂⠄⠂⢳⢽⡽⣽⡛⡸⠃⡯⡎⠀⡆
⠀⠀⠀⠀⠀⡸⡪⡪⡢⡃⡂⡂⢂⢅⡯⡫⡪⢒⠑⢑⠨⠑⠙⠎⡾⣝⠦⡷⣻⡽⡽⡍⠸⡪⡢⡑⠨⢀⠡⠘⣯⢿⡽⢀⠏⠀⣯⠃⢰⠀
⠀⠀⠀⢀⢎⢇⢇⢇⠕⢌⠐⠌⢔⢞⢜⢑⠌⡐⠨⢀⢂⠨⠀⠂⡎⠢⠁⠌⠪⠾⠯⠇⠀⢫⢪⠌⠌⠄⠂⡂⡿⡓⢀⠊⠀⢀⣯⢀⠃⠀
⠀⠀⡰⡹⡸⡸⡨⡢⡃⠢⠨⢨⡪⡎⡎⡢⡁⠢⢑⢐⢀⠂⡁⢅⠅⠅⠨⢐⠁⠀⠀⠀⠀⢘⢎⢎⠅⢅⠡⠠⢉⢔⣁⠀⠀⣸⡇⠁⠀⠀
⠀⢰⢱⢱⢱⢱⠱⡨⢌⢌⢪⠪⡢⡣⡃⡂⡊⠨⠐⡐⡀⢂⠐⠨⠨⠀⠅⡹⣦⡀⢀⣠⡶⣿⡱⡱⡑⢕⠌⢌⠢⠀⠀⠉⢡⣿⠀⠀⠀⠀
⢀⢇⢇⢕⢕⢕⢕⢕⢅⢧⡳⡣⡳⡸⡨⡂⡢⡁⡢⡀⠐⠠⠈⠨⠨⠀⠅⠐⠨⠻⠻⢽⣯⣟⣗⢕⢕⢕⠱⡠⠡⠡⡀⢠⡿⠆⠀⠀⠀⠀
⡎⡎⡆⡇⢇⢕⢕⠕⠁⢸⢕⢝⢼⢸⢜⠼⡐⡂⠆⢌⢐⠠⢁⠐⢈⠠⠁⠈⡀⠅⡁⠂⠅⠅⠈⡎⡇⡇⣇⢥⠣⣨⢶⢻⡝⠀⠀⠀⠀⠀
⢎⢎⢎⢎⢎⢎⠊⠀⠀⠘⣊⢇⢣⠣⡣⡱⡰⡠⡁⡂⡐⡁⠆⠌⢄⡀⡂⣑⠤⡄⡤⡡⡌⡤⣙⢘⢜⠾⡕⢥⢯⣗⡯⡧⣭⡡⡀⠀⠀⠀
⢇⡣⣱⢱⠕⠁⠀⠀⠄⠐⡖⣅⠧⡕⡕⡕⢕⢜⠬⣪⡪⠦⣃⣋⣠⢥⢥⢖⢖⢒⡂⡢⠢⢊⡈⡣⢕⢶⣶⣿⣻⣺⣺⢽⣺⠖⠅⠀⠀⠀
⡇⡣⣣⠃⠀⠀⠀⠀⠀⠀⡇⡇⣝⢼⣺⡺⡼⢱⣩⡵⡸⣝⣞⢜⣮⡺⣜⢎⠮⢑⠪⢀⠰⡑⠅⠅⡑⠱⡨⡳⣗⣗⣗⢯⣞⡙⡜⠀⠀⠀
⡇⡯⠀⠀⠀⠀⠀⠀⠀⠀⠑⡵⡑⢽⢚⡾⣮⡙⣵⡫⢯⡪⡺⣝⣖⢵⡱⡕⡕⠡⣐⠅⡃⢪⠨⢐⠠⠁⠌⡘⠜⢷⣳⣽⠢⠪⣊⠀⠀⠀
⡓⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⢧⢏⢗⢝⢮⣳⡸⣝⢵⢪⢪⢪⢪⢪⠪⠒⠅⣑⢐⠀⢂⢔⢕⢐⠨⠀⠅⢐⠈⢘⣽⡾⡇⠡⡱⡀⠀⠀
⣮⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡪⡣⡫⡪⡢⡳⡵⡳⡝⡅⡃⠒⢁⡁⡆⡔⡪⡐⠄⡊⠢⡳⡱⡐⠌⠨⠈⠄⢐⠠⠸⣟⣷⠄⡪⡍⠄⠀
⣷⡫⣇⠀⠀⠀⠀⠀⠀⠀⢐⣿⢸⢸⢸⢪⠐⠁⠭⠪⡋⠔⣐⠭⡢⡣⡣⡣⡱⡘⡔⠄⣝⢎⢎⢌⠪⠨⡈⠌⡐⠠⡑⡟⣡⣪⣯⡷⣿⡀
⣷⣣⣬⡄⠀⠀⠀⠀⠀⠀⣗⣿⢸⢸⠸⡸⣘⢲⢠⢄⢔⢍⢎⢎⢎⢜⢔⢕⢜⢌⢎⢢⢗⡝⡜⡌⢎⠢⡂⢅⢂⠑⡌⡄⣏⣿⣳⣟⣗⡧
⡯⡛⡊⢆⠢⡐⠄⠀⠀⢰⡞⣞⢜⢜⢜⢸⢨⢪⠪⡪⡪⡪⡪⡪⡪⡢⡣⡱⡱⡱⡡⡯⡳⣕⢵⢱⢱⢑⢌⠢⡢⡑⢌⠛⢜⡯⠳⣃⠀⢋
⡐⡑⡐⡷⣥⠨⡈⠢⢠⢟⠔⡗⡕⡕⡱⡑⡕⢕⢕⢕⢜⢜⢜⢜⢜⢜⢜⣜⢼⢼⢱⡯⣯⡺⣜⢎⡎⡎⡎⡎⡢⡊⠲⡀⠪⣜⠄⡣⠐⠈
⢢⠪⠠⢹⣺⠪⡂⠕⡑⡿⡈⡪⡪⡪⡘⡌⢎⢪⠢⡣⡣⡣⡣⡳⡹⡪⡣⡣⡑⣸⢽⢝⢞⡺⡪⣣⢫⢺⢸⢸⢐⠌⠢⡂⠱⡽⡐⠨⡀⠇
⢕⠨⢨⣞⢮⡣⢡⠡⢂⡏⣔⣼⢸⢨⠢⡃⡇⡕⢕⢕⢜⢜⢜⢜⢜⢜⠌⢆⠢⣞⢵⢝⢵⢹⢸⢸⢸⢸⢨⠢⡁⡪⢑⠌⡢⢹⣠⣗⣞⢦
⡘⢌⠌⡘⡪⡮⡘⠌⠄⡿⣞⣿⣾⣼⣸⢨⢢⠣⡣⡱⡑⡕⢕⢕⢕⢅⢣⢡⣯⡪⡪⡪⣣⢳⢱⢱⢑⢕⢅⠕⢐⢐⠱⠨⠐⠑⣗⡷⣹⢝
⡨⠢⡁⠢⢨⠱⢐⡥⣵⢯⣿⢟⡾⡳⢯⢯⣳⣽⡺⡮⡾⡼⡮⣞⣾⡾⠯⠣⣿⣿⣮⣷⣕⣕⣕⢕⢕⣱⣐⠈⢔⢰⡡⠂⡁⠄⠸⣽⡺⣝
⢈⠢⢨⢘⢚⢚⠛⠿⢟⣟⡯⣟⢕⢕⢕⢍⢇⡓⡻⡹⡛⡟⣛⢏⢇⢇⢇⢱⣿⣻⢿⣯⣿⣽⢯⡿⢽⠳⠁⢠⢂⡊⢙⢆⣀⡂⡂⠱⣟⡾
⡳⣌⢰⢑⠌⡄⠅⠅⣾⡷⢫⠚⡜⡔⢕⢅⠇⡎⡪⡪⡪⡪⡪⡪⡪⣊⠢⣾⣿⢽⢯⣞⡷⡽⣕⢝⢜⣁⡰⡕⣆⠢⢸⡹⡲⣕⢭⢃⢫⡿
⣫⢯⣳⠐⠅⡢⣕⡟⣙⢌⠆⠁⡎⢎⢎⢆⢇⢕⢕⢜⣬⠪⣮⣮⣮⣦⡿⣿⢯⣿⣻⣞⡽⣝⣞⢎⡧⣣⡣⡧⡯⣎⢢⠩⢣⠘⢎⡇⢂⢻
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