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