⡀⠠⠠⠄⡂⠂⠄⠄⢹⣿⣻⣟⣟⣯⣿⣻⣽⣟⣯⣿⣻⣻⣯⣿⣻⣻⣻⣽⣟⣿⣻⣟⣿⣻⣟⣿⣟⡿⠝⡐⡑⡐⡁⠐⡀⠂⠄⢀⣞⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⢿
⠄⠄⠄⠠⠄⠌⢀⠁⢸⣿⣽⢯⣟⣷⢯⡿⣞⣷⣟⣾⢯⣷⢿⣞⣯⣿⡽⣗⣿⣽⣾⣻⡾⣯⡿⣷⣟⢍⠢⡐⢔⢌⠆⠕⡀⠄⢀⢲⣯⣷⢿⣯⡿⣽⣾⣻⣾⣻⡾⣿
⢌⠄⠨⢀⠡⠈⡀⡀⠈⣾⣯⡿⣯⣟⣯⡿⣯⡷⡿⣾⣻⣽⣯⣟⣷⢿⣝⠆⠪⣳⣿⣽⣟⣯⣿⣟⠎⠔⡐⠨⡘⠄⠡⠁⠄⠐⢰⣽⡷⣿⣻⡷⣿⣻⣾⣻⡾⣯⣿⣻
⡁⠄⠄⠂⡂⠅⠄⢸⣦⣸⣯⡿⣯⣯⡷⣿⢯⣿⣻⣽⣟⣾⣗⣿⣽⣟⣷⢕⠐⠸⣺⣷⢿⣻⣷⡫⢊⠐⢄⠑⠄⠅⠈⠈⠄⢐⢷⣻⣽⣿⡽⣟⣯⡿⣾⢯⣿⣻⣾⣻
⡊⠂⢀⠡⠄⡀⠄⢸⡿⣽⡷⣿⣻⣾⣻⣽⣟⣾⣻⣾⣽⢾⣽⡾⣷⢿⣽⣇⡊⠄⢯⡿⣿⣻⡳⡨⢂⢊⠂⠅⠅⢁⠈⠄⠑⢠⣻⡿⣽⡾⣟⣿⣽⢿⣽⢿⣽⢷⣻⣽
⢀⢁⠠⠄⠄⠄⡂⠜⠇⣿⣻⣯⣷⢿⣞⣷⢿⣽⢾⣳⣟⣿⣳⣿⣻⣟⣷⣷⢕⢁⠂⡉⡈⢈⠄⡀⠁⠈9⠁⠐⠄⠄⠄⢠⣳⣿⣻⣟⣿⣻⣽⡾⣿⡽⣿⡽⣟⣯⣿
⠄⠄⠂⠈⡀⠂⡐⠄⠠⣿⣻⡾⣯⢿⣽⢾⡿⣾⣻⣯⢿⣞⣿⣺⣯⢿⡷⣿⡽⡀⡂⡐⡐⢀⠨⠐⠈⠄⡀⠄⠁⠄⠄⢀⣞⣷⡿⣽⣟⣾⣯⣷⢿⣯⢿⣯⢿⣻⣽⣾
⠔⢀⠄⠈⠄⠄⡂⠄⢸⣿⡽⣿⡽⣿⢽⣯⢿⣽⢷⣻⣯⢿⣾⣻⣾⢿⣻⣿⣽⡢⡂⡊⠄⠠⠐⡀⠅⠄⠄⠂⠄⠄⢀⣮⡿⣷⢿⣻⣽⢷⡿⣾⢿⣽⢿⣽⣟⣯⣿⢾
⠊⡀⠂⠂⡁⠆⡂⠄⢸⣿⣽⣯⡿⣯⡿⣽⣻⣽⢿⣽⡾⣿⢾⣻⣾⡿⡿⢝⠞⢌⢂⠂⠄⢐⢀⠐⡀⠐⠄⢀⠁⠄⣺⡾⣿⣻⣟⣿⣽⢿⣽⣟⣯⡿⣯⡷⣿⣽⢾⣿
⠔⠠⠐⠄⡂⢅⠐⠄⣺⢿⡾⣷⣟⣯⡿⣯⣿⣽⣟⣷⡿⣟⠿⡻⡝⢛⠈⡒⠌⠆⠽⢍⢍⡲⡢⡢⢄⢈⠄⠄⠄⡰⣯⣿⢿⣽⣯⣷⣟⣯⣷⣟⣷⢿⡯⣿⢷⣻⣟⣷
⢁⠂⠂⢐⠈⠢⡁⠂⣟⣿⣻⣽⣾⣟⣿⣻⡾⡗⠋⠇⢏⠦⢓⡵⢀⡕⢐⢨⡨⠊⠳⢴⣝⠜⢥⠄⠗⡤⢊⡢⠲⣻⢿⣽⣟⣷⡿⣾⢯⣿⢾⡯⣿⡽⣟⣯⣿⣯⢿⣽
⠐⡀⠅⠐⠌⡊⠄⠁⣿⣯⣿⣽⣾⣯⡿⡝⠝⡴⠁⣏⠅⠾⢽⢧⠢⢮⠢⡆⢒⠬⡍⢎⡬⠣⡉⢇⣑⠘⢅⠡⢄⢊⢙⢺⢺⢯⣿⣻⣿⣽⣿⣻⣯⡿⣟⣯⣷⣟⣿⣽
⢐⠄⢂⠁⠄⢂⢊⠄⣿⡷⣟⣷⡿⣞⠏⡴⠙⡆⢙⢧⢿⡐⣁⠟⢳⡘⠖⠍⡪⢅⢜⢵⢩⢩⡂⠪⡒⠄⠪⡒⢇⢎⢆⠠⠑⠥⡙⠝⡾⣷⢿⣽⡷⣿⢿⣯⢷⣟⣯⣾
⠐⢈⠄⣀⣐⣐⡀⡀⠛⠛⠟⢋⠛⡕⢮⠢⡹⠇⣏⢺⠝⢉⣮⠄⢱⢽⠙⠸⢩⢬⠕⢎⢎⠲⡈⡂⢐⠈⠄⢀⠄⠄⡈⡌⡌⠨⡨⡪⠛⠝⠫⠓⡛⠏⠫⢋⡋⣝⣸⣸
⠨⠄⢸⢲⡳⣧⢟⡮⡸⡐⡡⣳⣽⡺⡑⢲⣅⡼⣥⣖⣳⣲⠺⡑⠠⠑⢑⢉⡽⣵⢵⣲⢔⠇⡑⣐⠅⠄⠤⡀⢄⢐⢠⠂⢠⡰⠊⢌⢪⢰⠢⡧⣲⢴⢶⢵⢿⢷⣻⣽
⠨⢈⠄⢧⣻⢝⣗⣝⡾⡸⢼⣳⢣⠣⣸⢼⣆⠾⠻⠑⠈⠂⠄⠄⡀⢀⡂⡋⡫⡮⡲⠔⡕⡳⠘⠜⠁⠕⣐⢔⣐⢄⢑⠬⡪⢢⠸⡮⣮⢮⣺⣪⢞⡞⣞⣽⡳⡽⡿⣽
⠐⠄⢂⠸⡺⣽⣞⡳⡕⡕⣗⡫⡣⡡⡆⢪⠇⠟⡗⢵⢱⠠⣄⡤⠊⠃⡆⡦⣽⠸⡈⡐⡈⡞⡌⢐⢨⢂⠂⡕⠈⡁⣲⠡⡐⢅⡀⠸⣿⢿⡽⡿⣯⢿⣽⣾⣾⣻⣽⣿
⠄⠐⡀⠕⡘⡐⠨⣐⣝⣺⣳⣫⣊⠌⢚⠟⡾⡻⡯⠇⣱⠉⡖⣕⡠⠿⠮⢎⢾⡘⢼⡽⡞⠽⠘⠌⠈⡀⠅⣎⢰⠑⠁⢀⠠⠦⠌⢬⣻⣛⣟⣿⣟⣿⣽⣾⢯⣻⣳⣿
⡀⠄⡐⡁⢊⠠⠄⠄⣺⡪⣐⣔⣆⣶⣺⠈⡟⠹⣖⡯⡋⢧⠁⡲⠳⠞⠦⠖⢄⢽⣮⡐⠈⠄⠄⠄⠄⠄⡸⡈⡂⠄⠂⠁⡀⢕⢢⡠⠼⣿⣟⣯⣿⣯⣿⣾⢿⣻⣽⣾
⠄⢀⢂⠂⡂⡐⠈⠄⡐⣇⢺⣗⢯⡎⢞⣵⠋⣖⡵⣕⠵⣁⢋⡏⠬⠤⡀⢤⢀⡁⡕⡯⠢⡁⠄⠄⠄⠢⡑⡡⠅⡆⠂⠁⠔⡑⡢⠂⢭⠷⠽⣝⠳⡿⣾⣻⣿⣻⣯⣿
⠄⠂⡐⢐⠐⢀⠁⠠⢸⠇⢓⣽⣟⡮⡴⠁⢗⠌⢟⢦⢬⡡⡫⡧⠡⠄⡄⡄⠠⢐⠌⡌⡪⠐⡐⠄⠈⠐⠈⡐⢑⠈⠂⠠⢁⢂⠣⡨⢂⡀⡠⡚⠙⠳⣥⡙⡝⢯⣷⣿
⠠⠐⠄⡐⡈⢀⠄⠠⢕⣗⢮⡓⢗⡏⡳⢈⢌⢢⡞⠉⢝⡨⣫⢱⠠⡠⣂⢀⠂⡣⠑⡐⠄⢁⠄⠄⠠⠄⠁⢀⠪⠄⢀⢍⠢⢀⠐⠌⡀⡎⡺⣀⢠⢌⡆⡕⡕⡥⡛⢿
⠄⢂⠡⠠⡐⠄⢀⠁⣔⢧⡀⡛⣾⢼⢪⡪⡯⢯⡫⠂⢁⡚⠖⡱⡨⠁⠌⠐⠄⠄⠐⣐⠄⠄⠄⠄⠄⠄⠂⠄⢘⠄⢈⢢⢁⠨⠊⢌⠔⠁⡝⢌⠐⡈⣎⢠⠠⣕⠍⡑
⢨⢐⠨⠠⠄⠄⠄⠄⣜⢽⡂⡮⣞⣯⡗⡄⡬⠪⠈⠨⡢⠢⡐⡪⣺⡈⠄⠄⠄⠄⢀⢓⠄⢀⠄⠄⠂⠄⠈⢄⠄⠄⠠⢁⠄⡣⠐⠄⠂⠢⡈⠂⢃⢳⢘⠄⠁⡢⠋⢎
⡘⠔⠨⠄⠄⠐⠄⡰⡪⠪⢢⣫⣞⡇⡿⣼⢨⢊⠄⡎⠐⢁⠂⢢⢘⢎⠄⠄⠄⠄⢐⠄⠠⠄⠄⡀⠄⠄⠂⠐⣀⠄⠨⢀⢐⠠⠄⠄⢈⠐⡠⢂⠄⢱⢐⢀⠔⡪⣂⡀
⢂⠇⡑⢀⠐⠄⠁⠜⡌⠠⣺⢵⢱⢏⣞⣾⠦⡥⣳⠡⡐⠄⠄⢐⠢⠑⠤⠄⠄⠁⠄⡊⢰⡄⡁⠄⠄⠂⡁⡎⠇⠄⠈⠔⡁⠂⠄⠄⡀⠄⠂⠐⠄⡂⠂⠠⡑⠅⡠⠈
⢡⡑⠄⠂⠄⠈⠠⠸⡌⢄⡝⣵⢨⣻⢸⡯⣯⡟⡚⣗⢬⢀⢀⠂⠔⡀⠨⢂⠄⠄⠄⠄⠨⠓⠔⠄⠠⠄⠂⠈⠄⡀⠈⠄⠐⠄⠐⠄⠄⠐⡈⠄⢅⠌⠢⢁⠂⡐⠄⡀
⢪⠠⡃⠁⠐⠈⠄⠨⣒⡀⢘⢵⡁⣺⣻⢏⢷⣟⡦⣎⢎⠆⢂⠨⠐⠨⠊⠸⠐⡀⠈⣄⣒⣡⠄⢄⠠⢀⠐⢄⢃⢖⢕⡁⢁⠐⠄⠂⠄⠁⠄⠅⠂⠌⠌⢄⢂⢂⠠⢂
⠨⡂⡂⠡⠄⡀⠂⠈⡖⣆⣨⣞⣞⠵⡑⣧⡆⣗⢏⠪⡹⡸⡰⡀⡀⢀⠄⠠⡡⠐⢜⡾⣽⡜⡆⢃⠢⢐⠨⡐⢨⡒⠕⠨⠄⠄⠄⠁⠄⠄⠄⠄⠄⠌⢈⠐⡐⠄⡈⠐
⠌⠐⠄⠈⠄⠄⠠⠈⠘⠜⢜⡞⣞⢄⢊⠱⡹⡸⡕⡕⠌⡊⣎⠆⠎⡐⠨⡈⢐⠨⡈⢪⢛⢾⢰⡡⡊⡔⠌⠆⠕⡈⠌⠠⠁⠄⠄⠄⠄⢀⠄⠄⠠⠄⠄⠄⠂⠄⠄⠡
⠄⠡⠨⠠⠁⠄⠄⠄⠡⡨⡲⣹⢌⡪⡒⡢⡑⡙⢪⠢⠁⠌⡂⠡⠄⡀⠢⠄⠄⡑⠈⡐⢌⠡⠡⠈⡌⠌⠌⢄⢁⠐⠄⠄⠄⠄⢀⠈⠄⠄⠄⠄⡀⠄⠄⢀⠠⢁⠌⠄
⡡⡂⢁⠠⠁⠁⠄⠄⠨⡀⠪⡫⡣⠁⠊⠐⠐⠈⠔⢈⠄⠡⠨⢈⢐⠠⠡⢁⠂⠄⢁⠂⢂⠢⠨⠂⡂⠡⢁⠂⡂⠄⠄⠐⠄⠈⠄⠄⠄⠄⠠⠄⠄⠄⠄⠄⠄⣐⡬⠖
⠄⠄⡐⡈⠠⠂⠂⠄⢑⠈⠰⡸⠜⢢⢀⢀⠄⠁⠄⢁⠊⠌⠐⠄⠄⠨⢈⠠⠄⠈⠄⡨⠄⠄⠅⠡⢐⠡⠠⢁⠄⠄⠠⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⠄⢀⣠
⠄⠅⠁⠄⠄⠄⠄⠄⠄⡁⠉⢎⠌⢐⢄⠂⠌⠐⢄⠤⡀⡠⠐⠄⠡⡂⠐⢀⠪⠨⢂⠢⢐⠨⠨⢨⠂⠌⠈⠄⢀⠠⠄⠄⡀⠐⠄⠄⠄⡀⠐⠄⠐⣠⣦⣵⣶⡿⣟⣿
⠁⠐⠄⠄⠄⠠⠄⠄⢀⠄⠂⡂⢕⢑⠐⠡⡁⡈⡀⠊⢀⠐⢈⠘⡈⠨⠨⠠⡈⡈⠄⠄⡂⡂⠅⡑⠨⠄⠄⠈⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⢀⣴⣿⣻⣯⣷⣿⣻⣟⣿
⠄⠄⡂⢈⢀⠠⠄⠄⠄⢈⠄⠐⢁⢣⠘⠈⠄⡐⠬⢨⠐⠈⠄⡂⠄⠄⡂⠅⠂⡐⢨⠨⡂⠐⠐⠈⠄⠐⠄⠄⠄⠄⢀⠄⠄⠄⠄⠄⢀⣴⡿⣿⣽⣯⣷⡿⣾⣯⢿⣽
⠠⠡⢀⠂⡀⠄⠠⠄⠄⡂⡀⢀⠢⠂⡣⣀⢴⢡⢈⢀⠁⡂⢀⠂⡐⡨⠐⡈⡐⢌⠢⠃⠌⢀⠄⠄⠁⡀⠄⠂⠄⢀⠄⠄⠄⠄⠄⣴⣾⢿⣽⡿⣾⢷⣻⣽⡷⣟⣿⣽
⠄⠅⢡⢡⢀⠂⢀⠄⠠⠐⢀⢗⠄⠄⠢⡂⠄⡀⡡⣋⠇⠫⠞⡌⣄⡂⠅⢂⠊⠄⠠⠐⠄⠄⠄⠄⠁⡀⠄⠄⠈⠄⠄⠄⢀⣀⣿⢿⣽⣟⣯⣿⣻⣟⣯⣷⢿⣻⣷⣻
⠊⠌⠐⠡⠄⠐⢀⠄⠠⠁⡀⡞⠄⠄⠨⡪⠆⠎⠓⣗⣄⠤⠲⡸⣺⠪⠪⢦⢌⠄⠄⠄⠄⠈⠄⠈⠄⠄⠄⠄⠄⠄⣀⣴⣾⣟⣿⣻⣽⣯⡿⣾⣻⣾⣻⡾⣟⣿⣞⣿
⠄⡊⠜⡔⠈⡀⠄⠂⢐⠠⠊⠂⢆⡔⠈⢣⣂⠄⠄⢝⡼⡠⠤⠙⠞⠒⠂⠃⢯⢅⠁⠄⠄⠂⠄⠂⠁⠄⠠⢠⢴⡾⣟⣯⣷⡿⣯⣿⣳⣯⡿⣯⡷⣟⣷⣟⣯⡷⣟⣷
⠄⠄⠑⠠⠂⡀⠂⠄⢀⠂⠄⡰⡣⠁⠄⡔⣎⢗⠝⠑⢅⣄⢄⠤⡣⣢⠔⢔⠣⠙⠘⢄⢂⠄⠄⠄⠄⡀⣴⣻⣟⣿⣟⣿⡽⣿⣽⢾⣻⣞⣿⣽⣻⣯⡷⣟⣷⣟⣿⣽
⠄⢂⠁⠂⠄⡐⠁⠄⠐⠄⢀⠨⢪⡠⡔⢯⠂⢀⢝⢠⠯⠊⠄⢡⢲⠜⠉⠈⢩⢒⢦⠑⠌⠄⠄⠠⡊⡜⣾⣽⣻⡾⣯⣷⢿⣻⣾⣻⣯⢷⣟⣾⣽⢾⣻⣯⡷⣟⣾⣾
⠄⠢⢁⠐⢐⢈⠆⢀⠁⠄⠐⠈⢄⢎⢔⢵⡳⠙⠍⠄⠡⢀⢄⡢⡓⡝⡄⢄⢄⢃⢣⠲⢌⠪⡘⡨⢸⣪⣿⢾⣻⡿⣽⣾⣟⡿⣞⣿⣺⡿⣽⡾⣽⣻⣽⢾⣻⣯⡷⣟
⠄⢍⠄⢀⠐⢌⠄⠂⠄⠄⠄⠄⠪⠂⡁⢠⣂⠨⡢⣔⢬⠳⣫⡺⢹⠄⠄⢈⠨⡣⣓⡈⠄⠢⠂⠕⣕⣿⣽⣟⣯⣿⣻⡾⣽⣻⣯⣟⣷⣟⣯⡿⣯⢿⢾⣻⣽⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⢿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢐⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣬⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡟⢁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠌⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠌⢔⠐⠄⢄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠅⢕⠨⢊⢂⠆⡑⠌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠂⠃⠕⠂⠕⡨⢊⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠁⠀⠀⠀⠀⠀⠈⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⢤⢠⢆⢜⠥⢮⢱⢑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢪⢊⢎⢪⠪⡪⡪⡪⡊⢰⠁⠱⡠⠀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⢇⢇⢇⢕⢜⠤⠀⢣⢢⢣⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⠸⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠉⢓⢕⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁.