Produce Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢒⣿⠿⣴⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠐⡀⢀⡘⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢘⠀⠀⠀⠀⣹⣚⠀⠀⡁⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣦⣼⣿⣿⡿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⡤⣀⣀⡄⠀⠀⡐⠂⠉⠑⠁⡠⠆⡞⢅⠁⠀⣠⠀⢂⠂⢐⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⣾⠿⠿⠽⢧⠀⡄⠀⠀⠀⠀⠀⢙⠀⣬⣋⠻⣼⣟⠂⠐⢎⠁⢦⠀⠼⢄⢊⠑⢬⠞⡈⠛⢡⢀⡤⠀⢀⠀⠀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢛⣡⠱⠶⠀⠀⠘⣽⣷⣄⠀⡀⢀⠀⠌⠄⢸⠶⠀⠅⠙⣥⣧⡽⠓⠊⠂⠘⠚⢻⠈⠐⡯⢀⠀⣸⢾⠒⠚⠣⢅⢘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⠈⠀⠀⡀⠀⠀⠀⣿⣭⣿⡿⡁⣈⠵⣄⠀⣀⢤⣠⠘⠀⠈⠑⠀⠀⠦⢧⣘⣂⢢⢀⣈⣻⣆⡿⢡⣔⠦⠀⢀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⠦⣤⣀⣀⠀⢀⣀⡂⠀⠠⠉⢁⣛⣌⣄⠹⣮⡹⣶⠫⣏⠀⡄⠀⠀⠀⠀⠀⠈⢻⣝⡿⢿⣿⣿⣇⠀⠉⣳⣄⡠⠄⠀⠀⢀⠄
⠀⠀⠀⠆⠀⣀⣴⢚⢓⠊⡱⠀⡌⣂⣤⠍⠉⠛⢷⣤⡀⢠⡄⠀⣀⠍⠝⣵⣿⣿⣿⠶⣭⢋⣓⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⢹⡉⠁⢱⣄⡨⠙⠻⢆⡀⠠⠊
⠀⠀⢐⣦⠪⠀⣀⠤⠀⠐⣃⡭⣴⠛⠋⠅⣡⠒⠋⠀⠹⠟⡤⠞⠉⣀⠔⠊⠛⠛⣇⣀⠀⠙⢿⣿⣦⣀⡀⠀⢀⣠⣠⣿⣞⣿⣿⡆⠘⣉⠁⠘⠳⣛⣾⡛
⠀⠀⠘⠛⣧⣀⣤⠞⠈⢨⠿⢓⠄⡂⠔⠚⠁⠀⢀⡀⢊⣀⠤⠖⠟⠁⠀⢤⣻⣦⠿⠻⠲⣀⠀⠙⢟⢻⣿⣿⠋⠉⡉⠉⠩⣿⠉⡆⢴⣇⠀⠀⡀⠉⡷⠄
⠀⠀⠀⠀⠀⠈⠁⢀⡔⠁⣂⠕⡉⡰⡡⠶⠒⠚⠉⠀⠀⠀⠔⢁⡀⣠⡔⠻⣭⣍⠁⠀⠀⠀⠑⠠⠀⠁⠀⢹⡀⠀⠀⠄⠀⠗⠈⠈⠹⠛⣶⣏⡱⠒⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣶⢠⣀⣥⡼⠓⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠈⠛⠓⠀⠿⠃⣙⣦⣰⠀⠀⠀⠀⠀⠁⠀⠑⠀⠠⠄⠐⠁⠀⠀⠈⠻⠅⠸⢝⣶⣥⣼⡓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠘⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣈⡁⠀⠐⠝⠻
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠒⣾⠉⠙⢀⣰⡿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠉⠁⠀⣁⡤⢖⣫⠞⠁⣀⡽⠀⠀⠀⠀⠀⢀⡤⠖⣫⣍⣀⣀⣀⣀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠔⣊⡩⠭⣭⡭⠭⠭⠖⢚⣉⣀⣨⣏⣉⣀⠀⠀⠀⠀⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⡶⡏⠉⢫⡉⠙⢾⡁⠀⠀⢠⠗⢚⣙⡿⠷⣞⣛⣚⣻⣤⡘⠷⡄⠀⠀⠳⣴⠀⠦⠐⠄⠰⠄⠐⠀⠆⠀⠁⠈⣀⠤⠚
⠀⠀⠀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠃⠂⠀⣿⣉⣒⣚⣩⠭⢖⠚⢉⣅⣀⣤⣄⠈⠙⢦⡇⠀⠀⠀⠀⠙⠒⠒⠶⠶⠲⡖⠒⢲⠀⠉⠉
⠀⢶⣙⣶⣖⣹⣞⣳⣒⣒⣒⣒⣒⣒⣚⣋⣀⡤⠞⠁⠀⠀⠀⠈⠋⠉⠛⠉⠈⠉⠀⠙⠶⢶⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⡊⢣
⠀⠀⠀⠀⠀⠀⠀⠰⣝⣳⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢧
⠀⠀⠀⠀⠀⢀⣠⠤⣤⣾⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⡠⢲⠋⠀⢀⡞⠀⣱⠀⠈⢫⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⢘⣿⡁⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⢿⠉⠢⠊⢱⡖⠒⠒⠦⢤⡀
⠀⢠⠺⡁⢢⡀⠀⢸⡀⢼⠁⠀⠀⢀⠇⡍⢳⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⡔⠉⢀⣔⡉⣀⠀⠰⠭⠗⠀⡭⠭⠶⠀⠀⠙⢦
⢰⠃⠀⢸⠆⢹⠄⠀⠙⢮⠳⣄⠀⠘⣄⢣⡀⢳⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡜⢠⠀⠀⠀⢠⣃⠔⠊⣆⠖⠐⠸⠄⠀⠀⠀⠀⠘
⡆⢠⡖⢡⠖⠉⠀⢀⡠⠎⠀⣸⠆⠀⠀⢳⠱⣼⠀⠀⠀⠀⣠⠇⠄⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣇⢀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢧⠈⠣⣵⣀⠀⠀⡏⠀⢰⠋⠁⠀⠀⡴⠋⡞⡝⠀⠀⠀⡰⠃⠘⠊⠓⠄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠘⣎⢦⣀⣠⠲⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠘⢆⢰⠋⢨⠇⠀⠙⢲⡄⠙⡆⠀⠀⠙⡆⡻⠁⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠑⠺⠥⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋⠁
⠀⠈⠙⢧⣿⡀⠀⣠⠞⢁⡴⠁⠀⣠⣾⠟⠁⠀⠀⠀⠘⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠛⠢⠷⢤⣼⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⢿
⠀⠀⠀⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣁⣀⣀⣤⡥⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡿⣸⠆
⠀⠀⠀⣇⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠻⠋⢿⡵⢿⣴⡆
⠀⠀⠀⠘⣆⠐⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠋⣤⡁⢀⡀⠀⠀⠀⠚⢧
⠀⠀⠀⠀⠘⣆⠘⢆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠖⠂⠰⡄⠖⠦⢭⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠉⠁⠀⠒⠷⠀⠈⣿
⠀⠀⠀⠀⠀⠘⡄⠘⡆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡸⣄⠀⠀⢰⢁⠀⠀⠀⣙⠞⢯⠢⡀⠀⠀⠀⠠⣔⠛⠀⠛⠁⠰⠒⠀⠀⠤⠀⠀⣄⠀⠼
⠀⠀⠀⣠⣤⣤⣡⠀⢹⡀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠊⠙⠦⡙⢦⣼⠸⢀⡴⢊⡠⢤⠘⡇⠘⡄⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠐
⠀⣰⠟⠁⢀⣀⣈⣳⡄⠀⣠⣷⣟⣉⠉⠛⠦⡀⠀⠀⠀⣼⣘⠀⠀⠀⠈⣣⠁⢚⡥⠊⠁⠀⠐⡆⡇⠀⣿⠀⠀⠴⣉⠀⠰⠇⠀⣄⠀⠉⠀⠐⠃⠀⣄⠀⣰
⢰⠇⠀⢀⢋⣴⡛⡍⢹⡾⢋⣴⣯⡞⢳⡂⠀⠙⣆⠀⠀⢹⡿⢒⣛⠭⠟⢛⢐⢦⡑⣄⠀⠀⣸⢰⠇⠀⡟⠀⠀⠀⣆⠀⢀⠀⠀⠉⠀⠠⠆⠀⠀⠈⠁⢀⡞
⣾⠀⠀⢨⡾⠀⠙⣾⢸⡇⢨⡏⠀⡇⠈⣿⡄⠀⢹⠀⠀⠘⣇⢫⡀⠀⠀⡄⡈⠀⠑⢌⡳⠴⢡⠏⢀⡜⠀⠀⠀⠀⣱⠀⠙⠂⠀⠀⠀⠀⢀⠀⠚⠃⢀⡬⠇
⢹⠀⠀⢸⣇⠀⠀⠘⢾⡷⡏⢷⣀⡇⠀⢹⡇⠀⢸⠀⠀⠀⠈⠣⣙⠢⢤⢁⡃⠀⣀⡴⣋⠴⢃⡴⠋⠀⠀⠀⠀⠰⠗⢆⡀⠀⠘⠃⠀⠈⠋⢀⠀⢠⠞
⠈⢧⡀⠀⣿⠀⠀⠀⢸⢀⡇⠀⠉⠀⠀⠘⣏⣠⡟⠀⠀⠀⠀⠀⠈⠑⠲⠦⠭⠽⠶⠾⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡧⠶⠴⠦⡶⠠⠈⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠄⠐⠀⡄⢉⠀⠂⠄⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠤⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣈⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣀⣅⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⡈⠀⠀⠂⠈⠉⢑⠂⢄⠀⠀⠀⠈⡶⡞⠁⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢀⠀⠀⠀⠀⡄⠀⠈⠆⠀⠃⠀⠀⠀⠁⠁⠀⠀⢀⠎⠀⠀⠀⢀⠀⠒⠠⡀⠀⠀⠀⠀⢁⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧⡘⠀⠀⠀⢀⠂⠀⠀⠴⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠐⠀⠐⠊⢀⠄⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠁⠀⠀⠀⠈⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠤⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠠⠈⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠐⠠⠘⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠋⠀⠀⠀⠀⠨⠅⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠁⠀⠐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠈
⠀⠀⠱⡀⠁⠒⠀⠀⠀⣀⣴⣅⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⢒⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠉⢂⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠩⢭⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⢸⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⢂⠀⠸⢼⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠁⠀⢲⣼⣁⠀⠀⠀⠀⠀⢧⠇⡸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠙⠟⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡀⠠⠀⠀⡇⠀⠀⠤⠔⠊⠀⠀⢈⠁⠀⠀⠀⠀⠃⠈⠠⠁⠀⠀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠈⢄⠀⡰⠀⠀⠀⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⣀⡀⠄⠊
⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡟⠀⢸⣿⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢋⣽⡟⣿⠁⠀⠸⣿⠀⠹⣟⢙⡿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣠⣾⠛⢰⡟⠀⠀⠀⣿⣦⡀⠈⢿⣅⣶⡛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⡟⠟⣠⠟⠀⠀⠀⠀⣻⣏⡻⣷⣾⣿⣿⣾⣶⡚⢻⣧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠘⢀⡼⠋⠀⣀⡠⠖⢋⣽⣷⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠘⡟⠀⣴⠋⠀⣠⡞⠉⠀⠀⠀⠉⣩⣶⡶⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⡇⣼⠃⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠿⣿⣍
⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣥⣦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⣦⣤⣬⣥⣤⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠰⣊⠉⠉⡇⢸⠀⠐⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⡀⢴⡅⢸⣀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠐⠁⠀⠀⠀⠀⠀⠬⣏⡁⢣⡗⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⠀⠀⢠⠜⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠁⠈⠠
⠀⠀⠀⠀⠂⠀⢖⠘⠂⠀⡀⠤⠤⢄⡥⣂⡾⠠⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⠀⠨⠐⡟⠋⠉⠉⠁⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠂⢤⡀⠀⠀⠁⡄⠉⠀⠰⣌⠋⠄⠀⢀⠀⡀⠀⢤⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⢀⠀⢿⡆⠐⠁⠀⣀⢀⠀⠁⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠠⡧⠄⠀⠈⠃⠀⡠⡐⠉⠈⠙⠐⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠁⡁⠂⠆⡰⢂⠆⠹⠲⠂⠟⣆⠀⠂⠠⠀⠁⠀⣠⠊⠁⠰⠄⢀⡄⠀⠀⠀⠀⡀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⠊⢚⠓⣙⣤⠡⠗⠦⠤⢴⠆⡈⠩⠂⠀⠀⠂⠈⠑⠀⠀⠀⠀⠁⠄⠅⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠍⠈⠰⠡⢆⢂⡚⠔⠇⠃⠁⢀⡀⠢⡤⠔⢆⣀⣠⠣⠀⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠦⠄⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⣤⡥⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠤⠖⠂⠀⠀⢀⠀⠀⠀⠀⠀⢀⣞⣡⠄⢻⣿⡣⡁⠀⠘⣿⣂⠀⠀⠀⠐⠂⠘
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠰⢆⡀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠔⡅⠞⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢠⠀⠡⠀⠀⠀⠊⠀⠀⢳⡄⠀⠀⠀⠀⠀⢩⢠⠈⠤⠓⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠐⠁⠂⠄⠁⠀⡞⡶⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⣄⣀⣆⣀⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⠐⡀⠀⠂⠀⡀⠠⠁⠖⠂⠀⠀⠰⢤⣄⡬⢐⠴⠚⠘⠀⠄⠀⠁⠹⠁⣄
⠀⠀⠀⠀⡀⠁⢀⠀⠁⠐⠀⡀⠀⠀⠁⠀⠀⠀⢛⠄⡐⢨⢉⠁⠀⠂⠀⠃⠀⡀⠁⠀⠁⢀
⠀⠀⠀⠀⠠⠂⢀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠁⠀⢛⠈⠀⠂⠨⠀⠀⠁⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⡉⠉⠀⠠⠀⠠⠀⠈⠀⠃⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠃⠘⠀⡄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠐⠊⡚⠂⠠⠔⡄⠀⠀⠀⣀
⠀⠀⠀⠁⠀⠐⠒⠀⠛⠋⠋⠙⠀⠁⠀⠀⠀⠀⠀⢀⠰⣶⡆⢀⠀⠀⠉⠉⠲⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⠀⠀⠀⠗⠀⠰⠊⠆⠀⠠⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⡿⡄⠶⣀⣟⠦⠒⠄⣀⠃⡁⠆⠀⠀⢀⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⡀⢾⠀⠘⠢⡡⢙⠘⠈⢀⠠⠠⠘⠁⢶⠘⠛⢿⡗⡄⢠⢾⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠐⡀⠀⠑⡈⠀⠀⠀⠠⠆⠀⠐⢀⢐⣀⢐⢇⡷⠀⣌⠘⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⠀⡀⡀⢠⠁⠀⠀⠀⠀⠀⠀⢋⠀⠔⡀⠂⠚⠆⠃⠄⣅⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⠀⠀⠘⠈⣀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠀⠐⢄⣀⠐⢦⣄⠀⠀⠀⣀⠀⠀⠠⠀⢠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠔⠉⠀⠀⠀⠘⢳⣆⡁⠳⡽⠀⠀⠀⠆⠰⢇⠉⠠⠒⠣⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠢⠁⠐⠛⠉⠀⠰⠖⡄⠀⠰⡄⠀⠉⣳⠄⠉⢀⠘⣡⠶⢀⡖⢠⡀
⠀⠀⠀⠀⠀⢀⠌⠀⢀⡤⠒⠦⠚⠻⠦⣬⡿⣛⠂⠬⣄⡀⢠⡄⠋⠂⣦⢈⡼⠃⠀⣛⠁⢨⣁⣨⣥⠐⠲⠄
⠀⠀⠀⠀⠀⠀⠀⣡⠄⠈⠨⠁⠚⠃⠰⠆⠉⠙⠳⢦⣦⠛⠤⠳⡀⠱⢀⡞⠉⠀⢛⡏⠀⠈⠉⢁⣠⡤⠄⠒⠒⣺⠆⠀⣠⣄⡀
⠀⠀⠀⠀⠀⢴⠒⢈⠀⠀⠀⠀⠀⠀⠀⠠⠙⣤⡀⠈⠉⠏⢲⡀⠈⣣⡸⠅⠀⠈⠸⠎⢡⡴⠾⠋⠀⡀⠀⠐⠛⠀⠀⠙⠆⠉⠅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠂⠀⣸⢧⡩⣶⣯⣓⣆⣠⣠⣤⣶⡋⢁⠀⠐⠊⢹⠔⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣸⡇⠋⣙⠭⡼⢁⣞⡐⠋⠄⠊⠀⠀⠀⠈⢄⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡴⠟⠀⢁⡤⠎⢻⡅⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡼⠏⠁⣤⠖⠛⡁⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⣷⢤⢻⠄⢰⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡄⢿⡀⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⡤⠾⠇⠛⢛⣵⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠠⠀⠐⠻⠏⠙⠋⢹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠤⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⠍⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡄⢙⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠇⣼⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣽⣿⠅⡀⣀⠀⢀⠀⠀⣰⣾⠿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣴⣾⣿⣤⣿⢿⡯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⡀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢜⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⠴⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠂⠀⠀⢄⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠘⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠐⠒⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢀⠀⠀⡀⠻⡀⠀⠰⠀⠀⠀⠀⠈⠁⢀⡄⠀⡀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠁⠀⠀⠈⠀⠀⠀⠉⠒⠀⠐⠋⠀⠀⠐⠦⣀⣀⡤⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠠⠂⠀⠀⠄⠈⠁⠐⠂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢠⠀⡀⠀⠀⠀⠀⠤⢀⣀⣀⣀⠠⠖⠀⠀⠀⠀⠆⠈⠑⣷⠀⠃⠠⠓⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⡀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠣⢬⡄⠁⢠⡟⣷
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣀⠈⡷⠀⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢤⠐⠛⢲⡎⢱⣿⡧⠀⣄⠀⡀
⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠁⠘⢄⠀⠠⠀⠴⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠉⠗⠊⢽⣥⠏⢩⡅⣹⡀⢹⣀⣠⡄
⡄⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⢗⠐⠸⣀⡀⣤⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠡⠆⠰⠆⠠⠄⢀⡤⣀⡤
⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⢟⣁⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠀⢠⠄⠀⡄⢀⡷
⣼⠇⠀⠐⠲⠦⣀⠀⠀⠀⠀⠀⠀⢸⣾⣵⡛⠻⠅⣠⠄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⢠⡄⢨⡄⢀⡆⢀⡆
⠋⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⠀⠰⠄⣀⠛⢠⣏⡐⠶⠀⠀⠀⠀⠉⠁⠀⣀⠄⠒⠐⠒⠐⠂⠀⠀⠣⠀⠄⢈⡄⢈⣅⢈⣧
⠀⠀⠀⠀⠀⠀⠀⡈⢿⣆⠀⠀⡀⠸⠂⡠⠉⠀⡴⠀⢘⠃⢤⡄⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢵⣠⡥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠁⠂⣀⠁⢠⡴⠀⢀⠛⢤⡴⣠⠀⠀⠰⠇
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠟⢀⠉⠠⡌⠀⢀⠛⠀⡴⠆⣹⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠀⣤⠀⢘⠛⢠⡴⢀⣸⡽⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡄⠀⠀⢀⡀
⠀⠀⣠⡎⢽⠄⢡⠀⢠⠀⢀⠀⠀⠀⠰⢦⣐⡟⣠⣴⡤⠜⠋⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠀⡘⡁⠴⠤⠄⡀
⢀⡞⢉⡄⢠⡄⠀⡦⠠⡤⠈⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠤⠀⠀⠀⠀⡎⢀⡗⠉⠠⠀⠐⡀
⠸⡇⠈⡀⠀⡄⠀⡴⠀⢠⠀⡀⢁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣴⠬⣉⢹⠤⢤⡐⣲⠒
⠐⢏⡘⣃⢀⣅⠀⣠⠀⣨⠀⣅⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠬⠀⠰⠀⠂⠈⠃⢾⣿⠖⠻⠁⠀⣀⣀
⠀⠈⠋⣡⡄⢡⡄⢠⠄⠴⠄⢠⢾⠦⢀⡄⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⣀⠀⠆⠐⠂⠀⠓⠈⡃⢉⡀⠀⠀⠀⠀⠀⠈⠑⠢
⢦⡀⠀⠀⠁⠐⠶⣀⣗⠰⣶⣷⡎⢹⣇⣀⠩⠇⠀⠀⠀⠀⠈⠉⠒⠀⢀⠁⣀⠠⠦⠐⠶⠀⠒⠀⡋⢩⡐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣹⠃⠀⠸⡂⢤⠐⠀⠀⠀⠀⠀⠀⠀⢺⠁⣄⠀⣤⠠⠤⠄⢲⠒⢋⠈
⠀⠀⠤⢤⠀⠀⣀⠀⠀⠀⠀⠘⣋⡄⠈⠀⢰⣄⣁⠰⠂⠀⠀⠀⠠⣀⠈⠣⣥⣀⠤⡄⠰⣤⠘⡆⠛⠁
⠂⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⡅⠀⠀⠘⠀⣥⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⢤⣦⣔⡶⠞⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⣀⣁⡀⣀⠀⠀⠳⣄⢀⡀⠀⠀⠀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢠⣀⠐⠒⠢⡀⠀⢀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⡄⠀⠀⠐⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡈⠀⠀⢻⡒⡶⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⢘⣳⡤⠀⣒⠒⠦⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠑⢤⠀⠙⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠱⡀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠖⠀⠀⠀⠀⠀⠀⢶⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢧⠀⠰⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠀⠠⠿⢀⡀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⡀⢠⠈⠁⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣿⠂⢳⣄⣈⣁⣀⠁⢠⣌⣀⣰⡀⣢⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⣞⣁⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⡄⠀⠀⠀⠀⠀⢀⣾⠀⠀⠆⢀⡉⠉⣉⡀⣼⣥⣌⡽⠦⣴⢛⣿⣿⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢳⣄⠀⠀⠀⣦⠀⡉⠀⠱⡦⠈⠠⠄⢐⠤⢌⣥⣤⠤⡤⠈⡌⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠄⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠙⠓⢶⡾⠓⠀⣓⡴⢤⡴⣂⢁⣒⡊⣐⡧⠴⢶⠶⢳⡞⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣤⣤⣤⣏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣴⡿⠤⢤⡏⠁⠀⣷⣾⣤⣼⣭⣥⣟⣛⣻⣟⣻⣽⠿⡥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠷⠿⠿⠶⠤⠤⠤⠥⠥⠤⠶⠶⠿⣿⣄⣀⣀⣿⣿⡛⠋⠀⠀⠀⠈⠁⠈⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠲⡤⠒⠊⠉⠉⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠒⠀⠰⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡼⠀⠀⠀⣀⠤⠄⠐⠓⠒⠤⣀
⠀⠀⠀⠀⠈⠄⠀⠀⠷⠆⠀⠀⠁⠀⠁⠐⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠁⠀⠀⠀⣠⢤⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣶⠀⠐⠄⠀⠖⠀⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡞⠡⡞⠤⠀⠀⠐⠒⠂⠒⠤⣀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠁⣰⠎⠀⠐⠀⠀⠁⣤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⣸⡇⠀⠀⠀⠘⠁⠀⡠⠔⠂⠉⢁⠽⢀⡀⠷⠶⢄⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⢰⣶⠄⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢹⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡆⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡞⠋⠒⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡎⢰⣾⡇⠀⠀⠀⠏⠀⠀⠀⠀⡜⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡾⠀⢸⡿⠀⠀⠀⠈⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⣀⠜⣁⢘⡼⠁⠀⠀⠀⠰⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠘⢦⡉⠒⠦⢄⡀⠀⠀⠀⠀⢀⡀⠤⠴⠊⠉⣀⠐⠁⢀⡠⠈⠀⠀⠀⠀⠀⠀⠙⠤⣤⣏⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠈⠙⢶⠤⢤⠈⣉⣁⣀⣀⡄⠤⠄⠐⣈⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⡇⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠢⠠⠄⠤⠤⠄⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⢀⣀⣀⣀⠼⠦⣤⣤⠤⠞⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⣀⢀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⠀⡀⠈⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠠⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠐⡁⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠈⠀⠀⠈⠀⢀⡂⣐⣀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢢⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠈⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⢆⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠒⠈⠉⠢⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⣀⠀⠀⠀⠈⠄⠀⠠
⠀⠀⠀⠀⠂⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⢀⠐⠉⠢⢄⣀⣀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠒⠀⠀⠀⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠂⠀⠀⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡆⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⢄⢄⣀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢿⠈⠦⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡆⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠋⠀⠈⠐⡄⠀⠒⠁
⠀⠀⠀⡁⠀⠉⠀⠢⡀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⢀⣀⢚⠤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠉⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠆⠠⠃⠀⠀⠀⠀⠀⠀⠂⠀⠐⡄⠀⠀⠀⠀⠀⢡⠀⠀⢈⡢⠀⠀⠠
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠢⡀⠀⢀⡰⠂⠀⠠⠂⠁⠀⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠁⠀⠀⡐⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠠⣠⡾⣄⣀⣀⣀⠔⠈⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⣀⡐⡀⠀⡀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠋⠦⠀⠀⠙⠒⠛⠏⠟⠆⠀⠀⠀⢀⣀⣿⢿⣀⣄⣀⣨⣯⣿⣤⣽⣎⣀⣇⣄⣤⣿⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⣏⣀⣀⣉⣛⡁⢀⣀⣀⣃⡀⣀⣀⣉⣉⣀⡈⢀⣈⣁⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⠀⣀⡤⠀⠀⠨⠤⣽⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠋⠈⠋⠋⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⡿⠀⠀⠀⢿⠰⡇⠿⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢸⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠠⠀⠀⠀⠀⢰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠡⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠉⠀⢀⠃⠀⠀⠀⠀⢸⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⡒⡖⠒⠒⠒⠒⠒⠒⠒⠒⢒⡖⢒⠎⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠃⠃⠀⠀⢸⠀⠀⠀⢀⠠⣎⡄⢸⣄⡀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢨⠀⠀⠸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣸⠁⠀⠸⢋⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⡄⠀⠀⠀⢸⣅⠠⢠⢠⡌⠀⠀⠐⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠛⠀⠀⠀⠀⠀⠚⠁⠚⠚⠃⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠓⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⡰⠛⠒⢤⣤⠀⠺⠆
⠴⠛⠓
⣀⣀
⠼⣄⡀⠀⠀⠀⠀⢀⠀⡤⢠⣤⡀
⡀⠙⡉⠓⠀⠀⢀⠀⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢠
⠌⢀⠙⠀⠀⠀⠈⠀⠀⠀⡀⡴
⠀⠠⠃⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⡄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣦⠀⠀⠠⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠲⠟⠂⠒⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠹⢿⣿⠟⣁
⠀⠀⠀⠀⠀⠀⠀⢠⢃⡀⠀⠀⠈⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⢹⣆⢈⡳⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠺⠟⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠁⠀⠉⠄⠁⠀⠀⠀⠈⠀⢸⠉⠉
⠀⠀⠀⣠⡀⠀⢀⠃⢰⠀⠀⠀⢠⠊⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠐⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠃⠀⠀⠙⢡⣄⢸⠀⡇⠀⠀⡐⠁⣀⡀⣤⠀⡀⠀⢀⣀⠀⠐⢀⠐⢦⣃⡀⠀⠀⠀⡏⠤⠄⠰⠶⠀⠟⠠⠈⢐⠴⣬⠀⠁
⠀⠀⢀⡀⠘⠋⠏⠈⠑⢀⠞⠀⠸⣿⣿⡿⠀⠀⠀⠈⠁⠀⠀⠀⠘⣿⠟⠑⡄⠀⢸⡇⠀⠈⡄⠐⠚⠟⠀⠀⠀⡄⡙⠀⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢸⠀⠀⢴⡦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢀⣼⣦⣀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⠀⠀⢀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣀⠀⠀⠀⠤⠤⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠲⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠉⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠿⠿⠿⢿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣦⣶⣶⣶⣶⣦⣾⣿⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⣴⡆⠀⠀⠀⣿⣷⣤⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣉⣉⣉⣉⣉⣉⣹⣿⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⣿⣏⣉⣉⣉⣹⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⣼⣿⣬⣿⣧⠀⠀⣿⡇⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⢸⣿⠋⠉⠙⣿⡆⠀⣿⡇⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣉⣉⣉⣉⣹⣿⣀⢀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⡀⣀⣿⣏⣉⣉⣉⣉⣉⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⢻⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠟⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡄⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⢠⡒⠌⠦⠀⠀⠠⠂⠄⠀⠀⢠⡰⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠇⠂⣝⣠⠀⠀⠀⠀⠠⠄⠈⠀⠈⠁⢆⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⢄⡀⠒⠀⠀⠀⡀⠀⠀⠐⠊⠉⠀⡄⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠨⢀⠁
⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠠⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡓⠀⠀⢔
⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⠁⠀⢘⠀⠀⠈⠁⠁⠀⠀⠀⡄⠐⠒⠂⠀⠀⡀⢀⠆⠄⠀⠀⠁⠀⠀⠉⠄⠠⠈
⠀⠀⠠⠀⠐⠄⢆⠀⠀⠑⠀⠀⠈⠀⠀⠀⠈⡉⠀⠰⠀⢀⡁⠀⡰⠀⠀⠀⠰⠀⠀⠠⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠘⠦⠀⠀⠀⠀⠀⠴⠄⠀⠄⠁⡠⠌⠀⠂⢠
⠀⠀⢀⠠⠀⠀⠍⠀⡀⠀⢠⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠈⠰⠂⡄⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⠀⠀⠀⠒⠘⠄⠀⠀⠂⠂⠠⠴⠋⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠂⠀⠄⠁⠀⠈⠁⠰⠀⠀⠀⠀⠐⠈⠐⠀⡀⠈⠀⠀⠐⠂⠐⠀⠀⠁⢬⠀⢀⡀⠀⢂
⠠⠄⠁⠀⠀⠀⠤⠐⠄⠀⠀⠀⠉⠀⠀⠀⠀⡂⠁⠀⠀⠀⠈⠉⠀⠀⠁⠀⠐⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⢀⠠⠄⠀⢀⠒⠁⠀⠀⠀⠒⠀⢀⠀⠀⠂⠘⠂⠀⠀⠀⠀⠀⠀⠴⠒⠢⠒⠀⠠⠐⢀⡄⠀⢈⡲⠀⠀⠐⠒⢁
⠀⠀⠀⠀⠴⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⡄⠀⠀⠎⠀⠀⠂⠄⠀⠀⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢄⠀⡀⢀⡀⠐⠦⠆⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⢠⠌⠀⠀⠀⡀⠀⠄⠰⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⢁⠔⠂⢰⠀⠂⠀⠀⠀⠀⠀⠀⠒⠒⢖⢂⠀⠀⢀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠉⠀⢀⠀⢀⡤⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠒⠀⠫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠂⠈⠁⠀⠂⠐⢄⠀⠀⠀⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⣶⣶⣶⣶⢶⡦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠕⡣⠤⠀⠀⠉⠀⠠⠤⢐⠬⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣠⣬⣤⣤⡤⣐⠸⣿⣆⢰⠆⡀⢀⣭⠀⢨⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⢘⣠⣿⣿⣿⣿⣿⣿⣿⣷⠸⣷⡝⠛⡀⠀⠁⢐⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⢀⣀⠤⠂⠒⢶⠂⢠⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣋⡡⢦⣿⣷⣿⠀⣫⢴⣿⢣⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠀⠀⠀⠀⠀⢡⣤⣄⡀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⠾⢷⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣈⣩⣿⣿⣳⣮⣿⣓⣂
⠀⠀⠀⢀⣀⡙⢻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠶⣤⣉⠉⢉⠉⠛⠛⠉⠁
⠀⠀⠀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡼⡅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⡄⠀⣀⣠⣤⣤
⠀⠀⠀⠠⠀⠀⢠⡋⢉⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡀⢀⡙⠧⠈⠉
⠀⠀⠒⠒⠂⠀⡀⠳⣼⣃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⣿⣿⣿⣿⣷⣌⠀⠀⢀⢀⡀⠛⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠐⠂⠻⣿⣿⣿⣿⣶⡆⠈⠉⢁⡛⠞
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠉⢹⠏⠀⠙⢿⣿⣿⡄⠀⠀⠀⠈⠈⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠤⠤⠶⠚⠛⠁⡴⢿⣿⣿⣿⡿⠛⠛⠙⣿⣿⣿⣿⣿⡏⠀⠁⢀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠛⠂⠀⠈⠁⠀⢹⣿⢧⡠⠰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣽⠿⠿⠛⠃⠀⡤⠀⢸⣿⣿⣿⣿⠛⠀⣄⠀⠀⠂⠀⡀⠀⣴⣿⡅⣠⣄⣠⣇⣀⣠⣠⣀⣤⣿⣿⣷⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣆⠙⣧⣤⡀⠀⢄⠀⠀⠀⠀⡻⣿⡿⠃⠀⣴⣄⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡟⠛⠿⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣧⣹⣾⣷⣤⣶⣦⡗⢿⣣⣴⣷⣿⣿⣿⣿⡿⣿⣿⡿⠛⣿⠿⠟⠛⠻⠉⠉⠉⠈⠁⠌⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢶⠈⠁⠹⠋⠙⠟⠿⠛⠻⣿⣾⠿⠉⡛⠉⠉⠙⠂⠀⠉⠁⢈⡀⠀⠀⡈⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠐⠾⠟⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣤⠆⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⣟⣉⣟⣿⣹⠟⠟⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⠀⠀⡾⣀⣺⡍⢻⠐⠛⢻⣴⣟⢳⡽⠧⡀⠀⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠠⢦⣑⠿⢩⠀⢠⢸⡟⠸⣿⠭⢷⠒⣉⡸⠛⣛⡏⣟⢏⠀⢱⢜⢡⣾⢦
⠀⠀⠀⠀⠀⠀⠶⠧⠝⠒⠊⠀⠘⣑⣭⣩⡿⠶⠞⠚⠛⠶⠿⣿⣿⣿⡇⠀⠘⠚⠛⠾⠷⡂
⠀⠀⠀⠀⠀⠀⢀⣀⢀⠠⢄⡠⣀⠀⠉⠁⡀⡤⢄⣰⠠⠤⡄⡀⠉⠀⣀⠠⢤⢒⠠⠤⣀
⠀⠀⠀⠀⣠⡪⣵⡆⣾⣷⡗⡥⠎⠀⠴⣬⣷⣯⢦⣿⣿⣶⡿⢉⣦⡀⠀⢞⡺⣽⡟⣹⡾⣇⡢
⠀⠀⠀⣼⣵⣶⣶⣟⣿⣿⣿⠇⠀⣄⣾⠿⠿⠿⡿⣆⣀⣴⢏⢏⡙⣸⡄⠐⣯⣯⢽⣛⣷⠛⢲⡙
⠀⠀⠠⡿⣾⣧⣬⢿⣾⡻⠴⠀⠰⣻⡽⠿⠿⢿⣷⣶⡭⢾⡿⡻⠉⣦⣧⠀⢸⣥⣤⣽⣛⠾⣟⢣⡅
⠀⠀⠈⣌⢵⢞⣲⣿⠏⠙⣷⠀⠰⡹⢏⣿⢻⣾⡷⢬⣋⣿⣇⠵⣸⡿⠐⠀⠨⠽⢻⡝⢣⣿⣡⢧⡆
⠀⠀⠀⠫⡛⣿⡿⢝⠿⢿⢟⣃⠀⠗⠮⡿⣿⠟⣵⠶⢾⣥⣿⣽⢉⣺⠁⢠⠜⣛⣿⠇⠸⣿⢶⣻
⠀⠀⠀⠀⠙⢜⡤⢞⣿⣿⣇⣨⢆⠀⠐⢽⣉⢏⢿⣀⣼⠫⣳⣿⠟⠁⣠⡤⡟⡻⡚⢒⢶⣎⠅
⠀⠀⠀⠀⠀⢀⠉⠀⠂⠈⠁⠁⠁⢀⣀⡀⠉⠘⠓⠸⠂⠀⠉⠀⢀⡀⠀⠀⠃⠛⠛⠚⠋
⠀⠀⠀⠀⠀⠸⡀⣶⢢⣴⢤⠀⠀⢿⡋⣍⣱⠐⣲⢤⣦⣔⡖⣿⣺⡭⢳⠀⢀⠶⢦⣐⢊⣻
⠀⠀⠀⠀⠀⠐⣿⣫⣟⠳⡾⠀⠨⡬⣞⣶⠿⣿⢻⣧⣿⠛⣿⣧⣪⡨⡄⠀⠘⠲⣾⢤⡞⠘
⠀⠀⠀⠀⠀⠀⠀⠣⠜⡢⢞⡆⠀⢓⢻⢟⣓⣹⣟⢛⣿⡼⡋⢀⣼⠅⠁⢠⡿⣮⢝⣺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠟⠀⠀⠋⠽⢿⡻⡻⢾⡟⡟⢻⠛⠅⠀⠀⠋⠉⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠹⠑⠐⠈⠁

⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠠⠀⢄
⠀⠀⠐⠀⠂⡤⠁⢘⠁⡀⠀⠀⢀⢀⣀⣸⣇⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠤⣒⠀⣄⢁⡎⠸⡀⠀⠄⠀⠈⠁⠀⠈⠉⢻⣧⡄⠀⠑⠀⠤⠀⠄⠤⠀⠊⠁⠀⠐⠠⡄⣀
⠀⠀⠀⡀⢤⢫⡦⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠈⠳⣅⣏⣙⢀⡂⣢⡸⠃
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠉⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣧⣤⣴⣿⣿⡏⠀⠀⡀⠁⠄⠄⡀⠀⢸⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⡤⠒⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⢄⣀⡸⠁⢀⠂⠀⢠⠀⠀⠀⠀⠈⢃
⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⢠⡄⠀⠀⠀⢠⣄⠀⣀⣤⢀⠀⠀⠀⠀⠴⣯⠀⠀⠈⠲⣦⣴⣶⡿⠃
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠐⠂⠀⠀⠀⠈⠻⠿⢟⣣⠞⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡿⠀⢠⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠸⠀⡏⠀⠀⢤⣀⣠⣀⣴⡼⠀⠀⢰⣶⣼⣧⣶⣄⠀⠀⢠⡇⠀⠘⢷⣄⠀⠀⢀⣤⣼⠏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠁⠀⠐⠉⠈⠉⠀⠀⠈⢹⡇⠀⠈⢇⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣸⠇⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⣀⡾⠀⠀⠈⠒⠦⠴⠿⠟⠋⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⠠⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡏⠀⠀⠀⠀⣶⡶⡟⢣⠀⠀⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡦⠀⠰⣆⡀⠀⠀⠀⠀⠀⡀⢄⣽⡷⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⠀⡔⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢠⠊⠀⢀⠎⢀⡀⠤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡰⠁⣀⠤⠛⠉⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠘⡠⠊⠁⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢇⠀⣆⠤⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡟⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⣰⣫⢄⠀⠀⣢⠡⠀⣀⡠⠒⠈⠉⠐⠢⡄⠀⠀⠀⠀⠀⢀⣀⣰⠁⠔⠊⢙⠢⡊
⠀⠀⠀⠀⡴⠊⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠘⠀⠀⢀⠔⠊⠀⠀⠀⠑⠺⡌⠂⠁⡈⠖⠒⠒⠠⣀
⠀⠀⠀⢸⠀⠀⠀⡆⠈⡇⡇⢀⣤⠀⠀⠀⢸⠀⠀⠀⠀⢀⠁⡰⠁⠀⠐⢦⣄⠀⠀⠀⢰⠔⠊⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠈⡆⠀⠀⡁⠀⣧⡗⢡⠂⠀⠀⠀⢸⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⠀⠈⠑⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⢲⢼⡀⠀⡇⢀⠏⢀⠃⠀⠀⠀⠀⢸⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢣⠑⢄⠀⡎⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⡐⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⢣⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⢃⠈⢶⠀⠀⠀⡆⠄⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄⡰⠁⠀⠣⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀
⠀⠀⠀⠀⠀⠘⠀⠈⡆⠀⠀⠰⢀⠀⠀⠀⢨⠜⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠄⠒⠀⠐⠚⠢⢌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⣀⠠⢇⡠⢦⡠⢄⡀⠏⠀⠀⢀⠎⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⢄
⠀⠀⠔⠋⠀⠀⠈⠀⠈⠀⠀⠈⠙⢄⠀⠎⠀⢠⠴⠶⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠱
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⣵⡄⠀⠀⠀⠀⠀⠔⠈⠐⠄⠀⠀⠀⠀⠀⡆⠀⠀⢱⠀⠀⢸⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢆⣀⣀⠆⠀⠀⠀⠀⠀⠈⠂⠒⠁⠀⠀⢸⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⢄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⣦⡀
⠀⠀⠉⠢⢍⡂⠄⠀⠀⠀⣀⡤⠂⠁⠀⠀⢀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡂⠀⠀⠀⢸⢄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠲⢄⡴⠊⠀⢇⠀⢀⡠⠒⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠒⠄⠀⠀⠀⠈⠊⠁⠀⠀⠀⢸⠀⠑⠢⢀⠀⠀⠀⠉⠓⢀⡤⠒⠁
⣶⣶⡶⠶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⢿⣿⣿⣿⣿⠏⠰⢀⣿⣿⣿⡆⠀⠀⠹⣿⣿⡿⠄⠀⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠘⣯⡻⣯⣼⠁⡼⣿⣟⡴⠃⣼⢹⣿⣿⡇⠀⠀⠀⣿⣿⠇⢀⠀⡏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠻⣤⣇⡻⣿⠃⣼⡇⠨⣿⣿⡇⡆⠀⠀⢸⣿⠀⠸⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠘⢿⡆⣿⣤⣿⠇⢀⢻⣿⡇⣿⠀⠀⢸⠇⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢏⠂⡀⢼⣿⠿⠛⠁⠀⢺⢹⣿⡇⢹⡀⢠⣿⢀⡄⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣀⡴⡜⣿⣷⠦⠄⣀⡗⠤⣿⣿⠀⢣⢸⡟⢀⠃⢀⣿⣿⣿⠻⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠺⣌⠻⣿⣿⣿⣆⣰⣿⣷⣸⡏⢿⡄⠀⠿⠁⣾⠀⣸⣧⣿⣿⢀⠃⡄
⠀⠀⠀⠀⠀⠀⣾⣏⣿⡄⢺⣄⠠⠉⠙⠿⡟⣿⢋⣿⣇⢸⣧⠀⠀⠀⠉⢠⣿⡳⣿⡇⠺⡀⠰
⠀⠀⠀⠀⠀⠀⣇⠘⣿⣿⠀⢵⣆⡀⠈⠐⢾⣼⣿⣿⠏⢸⣿⠀⠈⠀⢀⣿⠷⢽⣿⡞⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⣸⣿⡀⠀⠻⣦⡀⠾⣯⣿⣿⠏⠀⣼⣿⠀⠀⠃⣸⣟⣛⢸⡿⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠘⣷⣽⣿⡇⠀⠀⢹⣿⣬⣿⣿⣿⠀⠀⣿⣿⠀⠀⢠⣿⢋⣽⣿⡇⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⣾⠇⣿⣿⣿⡇⠀⢀⣿⣿⢀⢁⣾⣿⠏⣰⣿⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠁⠀⢠⣿⢠⡿⢿⣿⡇⠀⢸⣿⣿⠂⡾⣿⣿⢀⡇⢹⣧⠉⢶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣄⣾⣿⡿⠁⢸⣿⡇⠀⠸⠟⢉⡾⠁⣿⣿⡞⢁⠸⠋⣷⡄⠃
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⡇⢠⡴⢡⣾⣷⠀⢻⣿⣿⣾⣀⡀⣽⢹⡄⠀⠀⠄
⠀⠀⠀⢀⣴⣿⣿⣿⣿⠻⣿⣿⣿⡏⠀⠀⣸⣿⣿⢿⣼⡟⢿⣿⣧⠘⣿⣿⣿⢻⣷⢶⡀⣿⠲⣀⠀⡆
⠀⠀⣴⣿⣿⣿⣿⡿⠏⢸⣿⣿⣿⠀⣤⣴⣿⢰⡟⣸⣿⣿⡿⣿⣿⣧⡘⢿⣿⣧⣘⠻⣿⣯⣴⠙⡄⠈
⣠⣾⣿⠟⣽⣿⡏⠀⠘⣿⣿⣿⣯⣾⢿⠋⣸⣼⣧⣿⢻⣿⡇⢹⣿⣿⣷⡀⠙⠿⡿⣷⣌⣻⣿⠱⣾⢀⡀
⣿⠟⢏⣼⣿⠟⢻⡇⠀⣿⣿⣿⣿⠃⣾⡰⡿⢿⡇⣿⡌⣿⠁⠀⢻⣿⣿⣿⣦⡀⠈⠢⡙⢿⣿⠀⠝⠛⠓
⡟⢀⣾⣿⣿⠀⠀⠟⠀⣿⢿⣿⡇⠘⠉⣴⢿⣾⣿⣼⣧⣹⣦⡀⠈⢿⣿⣿⣿⣷⡄⠀⠈⢢⠙⣿⡶⢿⠲⢦⡀
⢁⣾⣿⣿⡟⠦⡀⠀⣰⣿⢸⣿⡏⠀⣼⡇⣼⠉⣿⣿⣿⣿⠘⣷⠤⢄⣻⣿⣿⣿⣽⣦⡠⠣⡱⠘⣿⣄⠓⠀⠣⢑
⣽⣿⣿⢿⡇⠀⠀⠐⢎⠻⣌⣿⠙⠋⢻⡄⣿⡄⣼⢿⣿⣿⡧⠈⢧⡀⠀⠹⣿⣿⣿⣿⣷⣣⢳⠃⢸⡿⢿⣄⠐⠈⢷⣄
⣿⣿⠃⠈⣿⠀⠀⠀⠀⢶⣿⢷⡀⠀⣼⣷⣿⣿⠟⣸⣿⣿⣷⡄⢢⣿⣷⣀⠘⣿⣿⣿⣿⣣⠇⡾⠀⢷⢄⠈⠳⡀⠠⠿⠠⢄
⣿⡏⠀⠀⠹⡄⠀⠀⠀⠀⢹⣻⡇⢠⣱⣿⠋⣼⣾⣿⣏⣻⣿⣿⣶⣿⣿⣿⣶⣘⣿⣿⣿⣷⣿⢸⡇⢰⠔⠋⢭⠙⣦⣀⡀⠀⠐⣀
⣿⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⣿⠇⣸⡿⢱⡿⠟⠁⠈⣿⡛⢿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡏⠀⠁⢠⣠⣶⣤⣡⡞⠙⢋⠉⠛⢍⠱⠦⡄
⡇⠀⠀⠀⠀⠈⣦⣤⣾⣧⣴⣿⣵⣿⣧⣾⡇⠀⠀⢠⣿⣅⡀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣟⣀⠀⠀⡆⠀⠳⣄
⠀⠀⠀⠀⠀⠀⣹⣿⡿⠿⠛⣩⣾⣏⣹⣿⡇⠀⠀⣼⢯⣻⣽⣿⣿⠿⣿⢿⣿⢿⣿⣿⣿⣿⡇⢠⣿⠿⣾⡛⣿⣿⣯⡙⢦⣠⣿⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢹⡿⣦⠂⣴⣿⣿⠉⣿⢿⡇⠀⢀⣽⣖⣁⣼⣿⣿⠀⠙⢷⣿⣦⣽⣿⣿⣿⡇⣼⡏⠀⢿⣷⣌⠻⣿⣿⣦⣿⡄
⠀⠀⠀⠀⠀⠀⣾⠅⠀⣼⣿⡟⣿⣟⣿⢸⣷⣤⣾⣷⣿⣿⣿⡾⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⣿⡇⠀⣦⠙⣿⣷⣌⠻⣿⣿⣷⠀⢤
⣀⠀⠀⠀⠀⢰⣿⡀⣠⣿⣿⣷⣽⣿⣿⣼⣿⣿⣿⠟⠋⣸⡟⠀⠠⠀⠀⠀⣼⣧⣿⣿⣿⢮⣿⠀⡇⠀⠻⣆⠈⠻⣿⣷⡌⢿⣿⡶⣄⠁⢤
⢈⣷⣤⣀⣰⣿⣿⣿⣾⣿⣷⡋⢻⣿⠻⣿⡟⢻⣧⣤⣾⣿⡴⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⣿⣦⡅⠀⠉⠻⣦⡀⠀⠙⢿⡜⣿⣷⡦⣅
⡶⣶⣾⠟⠻⣿⣿⣿⣭⣿⣿⣦⡿⡿⠀⠸⢿⡿⢿⣿⠏⢸⢃⡇⠀⠀⢰⣿⣿⣿⡿⠙⣿⣧⢽⡆⠁⠰⠶⣤⣈⣷⣄⠀⠀⢻⣽⣿⣷⠈⠑
⡔⢹⠋⠀⠀⣼⡽⠟⢡⣿⣃⣿⢇⡅⢀⠺⠈⣇⣼⠏⠀⠸⣿⡇⠀⠀⠘⢿⣿⣿⠀⠀⢸⣿⡀⠿⣷⠀⠀⠀⠉⢻⡄⠉⠦⡈⢷⣿⣿⣇
⣴⠇⠀⢀⡼⠟⡿⢀⣿⡿⡿⢹⢸⠇⢻⢸⣶⣿⡏⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⡏⠀⠀⠈⢿⣷⠀⣿⣷⢦⣄⣀⣤⣿⣀⠀⠀⠸⣏⢿⣿⣷
⠋⠀⡠⢫⣿⣦⣁⣾⣿⡷⠀⡆⢻⠀⡎⢸⡇⣿⠇⠀⠀⠀⣿⣷⣤⣤⣾⣿⣿⣧⣀⠀⢀⣸⣿⡄⢸⣿⣦⠙⢿⠟⠛⠛⠛⠢⠤⣼⣦⡙⠿
⠀⠀⣰⠟⠙⣿⣿⣿⣿⣷⣦⣧⡞⢀⣿⣿⡇⣸⣆⣀⣀⣠⣿⣿⣀⣼⣿⣿⣏⣠⣿⣿⡿⣿⣿⡧⢸⣿⣿⣷⣬⣦⡀⠀⠀⠀⠀⠀⠁⠈⠲
⣈⡼⠋⠀⠀⠸⣿⣿⡏⣿⣿⣿⣿⣿⡏⣹⡿⠟⠋⠉⠉⠛⠻⡿⢻⣿⣿⠏⠉⠻⣏⣿⠀⠀⣿⣇⠚⢿⣿⣿⣿⣿⡳⣄
⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣡⠟⠋⠩⠀⠀⠀⠀⠀⠀⢀⠇⣼⣿⠃⠀⠀⠀⠙⣏⠀⠀⣿⡏⠳⠄⠙⢿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀⣰⠋⢳
⠀⠀⠀⠀⡰⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⣬⣇⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣠⠴⠶⡄
⠀⢀⣦⠘⢳⡃⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠉⡥⠶⣏⡛⢯⢷⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⠉⣉⣀⠀⠀⢧
⣴⣯⡼⠋⠉⠳⣄⠀⠀⠈⠙⠒⠦⡴⡆⠀⠀⢠⣷⣧⣺⠟⠉⢻⣽⠋⠈⣧⠀⠀⠀⠀⠀⠙⢦⡀⢰⠋⠁⠈⠱⡄⠈⠳⣄
⠀⠀⢳⡀⠀⠀⠈⠙⠶⢦⣤⣤⠖⠓⠇⠀⠀⠈⢇⠀⠉⡍⠉⡽⢁⠀⠀⠸⡄⠀⠀⠀⠀⣠⠞⠀⠸⡀⠀⠀⢠⠇⠀⠀⠈⡇
⠀⠀⠀⠙⠢⣄⣀⠀⠀⠀⠀⢀⣽⢻⠃⠀⠀⠀⠘⣆⠀⢀⡜⠁⠀⢠⠀⠀⢳⠀⠀⠀⢸⠁⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠙⠿⠀⠀⠀⠀⠀⠈⢳⡞⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠘⠦⢤⡤⠖⠚⠉⠙⠓⠲⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠐⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⣄⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡎⡭⠙⠋⠀⠀⠀⠀⠀⠀⠀⠫⢼⡆⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⡠⣠⠓⢲
⠀⠀⠀⠀⠀⠀⢸⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⣀⠀⠀⢀⡞⣠⠀⠀⠀⠀⣠⡄⠀⠀⠀⠙⣤⠟⢧⣼⢶⡛⢶⢲
⠀⢠⠶⠶⠶⠒⠛⠛⠒⣒⣒⣲⡄⠀⠀⠀⠀⢰⣛⣛⣛⣛⡇⠀⠘⡇⡧⢠⣤⣄⣼⠟⠁⠀⠀⣟⣓⠻⢤⡏⡏⢸⢷⠈⢻⡀
⠀⠉⢿⠉⠉⠉⠉⠉⠉⠉⠉⡏⠁⠀⠀⠀⢠⠞⠉⠀⠀⠀⠑⢦⠀⢃⣀⣻⡀⠈⣷⠀⠀⠀⠀⢠⣤⣟⣄⠙⢧⡟⣸⣧⡤⣷
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣏⠁⠙⣿⠛⠃⠀⠀⠀⠀⠀⢳⡀⠉⠉⠉⠉⠁⠀⢀⡏
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡞⠛⠻⡗⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⠖⠶⣿⣴⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⣀⠀⢸
⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⠇⠀⠀⠀⠀⠀⠸⣇⣀⣀⣷⡀⡀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⠟⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣤⣀⡀
⠀⠀⠀⣰⣒⣶⣓⡶⠶⡴⢲⡄⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⠀⠀⣉⠙⠲⢤⣀
⠀⢀⡴⠋⠀⠂⢀⠈⠳⣍⢹⣛⢯⠓⢦⠀⠀⠀⠀⢀⡴⠋⢥⡀⣤⠙⢠⠍⠳⣄⠀⠀⠀⠀⠀⢸⣯⡉⠓⠲⢧⣀⣀⠀⠈⠳⣄
⠀⢸⡀⣀⠀⠀⠈⠀⠠⠈⠳⡈⣿⣹⡎⣇⠀⠀⠀⢺⣀⠃⠀⠀⠀⠤⠀⠐⠛⠘⡆⠀⠀⠀⠀⢸⣧⢙⡆⠀⣂⣈⣙⠦⣴⠂⠈
⠀⠀⠳⢄⡀⠈⠀⢀⡀⠀⠃⢹⡄⡿⣟⡏⠀⠀⠀⢀⣏⣉⣭⣙⣛⣋⡿⣟⣛⡿⢧⠀⠀⠀⠀⢸⠗⠋⢰⣫⢷⢰⣯⣷⠼⠓⠋
⠀⠀⠀⠀⠙⠲⢤⣀⠁⠀⠄⠀⣷⠷⣿⠃⠀⠀⠀⠘⣧⠤⠴⠶⠿⢶⣶⠶⠶⠶⡏⠀⠀⠀⠀⢸⠦⣄⣸⡬⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣸⡼⠁⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣈⡷⠤⠞⠁⠀⠀⠀⠀⠼⠖⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⣀⣀⡀⢼⢸⠄⢀⣀⣀
⠀⡠⠔⠒⠒⠛⠤⣀⠤⠚⠚⠒⠤⡀⣠⠝⠒⠒⠢⢄⡀
⡜⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠑⡄
⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠗⠊⠉⠉⠒⢤⡀
⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⢔⣾⣦⠀⠀⢀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄
⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠔⠁⠀⢟⡫⠜⠀⠀⠈⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⠖⠢
⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡗⢢⣴⠃⠀⡰
⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠦⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡟⠀⡼⠁⣹⠎
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⢢⠀⠀⠀⣄⠀⠀⠘⠀⠀⠀⣀⠤⢒⣍⠉⠑⢦⠀⣴⠋⠀⠞⠠⡎⣨⣇
⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱⢄⠀⠀⢀⣠⡦⠔⠒⠉⠀⠀⠀⢻⣄⠀⠀⢻⠁⠀⠀⠤⢖⣛⣅⠤⠃
⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠧⢤⡟⠒⠋⠉⠁⠀⢻⡄⠀⠀⠀⣦⠀⠀⠛⠀⠀⢸⠓⠒⠛⠛⠉⠁
⠀⠀⠈⠢⢄⣀⣀⡱⢄⣀⣀⡰⠋⠀⠀⠀⠁⠀⠀⢠⡀⠀⠈⠛⠀⠀⠀⠹⣧⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⡀⠤⠤⠤⠍⠒⠒⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠠⡢⢁⠤⠀⠤⠈⢰⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒⡀⢀⢀⠀⠂⠐
⠀⠀⠂⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠐⠛⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠠⠀⠀⠀⠄
⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠄⠁⠀⠀⠄⠐⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠡⠀⠀⠁⠀⠠
⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠠⠄⠐⠀⠂⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠁⠈⠈⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠐⡀⠀⡄⢠⡄⢰⠦
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠐⠀⠀⠀⠄⠀⠁⠀⠠⠀⠀⠀⠀⠢⠀⣀⢀⠀⠀⠀⠈⠀⠠⠦⠤⠆⠈⠁
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠐⠈⠀⠄⠀⠀⠀⠢⠀⠀⠂⠀⠀⠀⠀⠄⠄⠁⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⢐⠐⡂⠀⠀⠀⠤⠡
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠔⠒⠄⠀⠀⠀⠠⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠈⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠢⠄⠄⠀⢪⠁⠀⠀⠘⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠢⠜⠀⠀⠀⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⠀⠀⠀⢀⢀⠀⠀⠀⠀⢈⢈
⠀⠀⠀⠀⠀⠐⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠁⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣿⣿⠟⣰⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡰⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣽⣿⡟⠛⠛⡁⣴⣶⠋⣀⣀⣈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣼⣿⡏⣉⡔⠀⣾⣿⣿⣷⣷⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡟⢺⠟⠟⡀⢀⣧⣌⢡⣼⢟⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗⠈⢸⠃⠀⢀⣼⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣁⠖⠠⣶⠶⣾⣿⡿⠋⣴⣇⠻⣿⣥⣤⣶⡀⠁⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠴⣿⣷⣷⠦⠀⢡⣦⡺⣿⡇⣸⣿⣿⣿⣾⣿⣿⠏⢁⡀⠀⠘⠃⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠙⣶⣄⢀⡀⣀⠀⢀⠠⠏⠂⠀⣶⣦⣽⣿⠉⠙⠛⠛⠿⠿⠿⠿⢷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢀⢼⣿⣯⣾⣥⡶⠟⠛⠀⠈⢳⣿⣿⣿⣿⡿⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⣾⣿⡿⠉⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⡄⠀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⢼⣿⣿⣷⣤⣶⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠐⠁⠀⠁⠀⠈⠛⢿⣿⣿⣿⣟⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⡿⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠠⠡⠢⠩⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⠀⠶⠿⠿⠿⠯⠭⠤⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣇⠀⠩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠔⢁⣴⣌⠂⠀⠀⠀⢀⢀⣄⢄⠀⠀⠀⢓⢀⡮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠀⠈⢄⠻⠿⠏⠀⠀⠀⠀⠸⠾⢋⠀⠀⠀⠀⢸⢼⣀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢸⠀⠀⠀⠉⠀⠁⠀⠀⠒⡂⠀⠀⠀⠀⠀⠀⠀⢸⠹⢶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠊⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠢⣄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⠔⠀⣸⠔⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠒⠤⠄⢀⣀⣀⣀⠠⠐⠁⠀⠀⢸⢁⢸⠁
⠀⠀⠀⠀⠀⠀⡤⠐⢣⡌⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣶⣲⣶⣶⡆⠀⠒⠐⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠓⠐⠚⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣒⢒⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠈⣍⣉⣹⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣥⠀⡀⠀⠀⢀⡀⡈⣏⣛⣍⡐⠢⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠙⢧⠀⠀⠀⠀⠀⠀⡀⠔⠉⠰⡀⢸⢲⠚⠃⠈⢉⢉⡍⡉⢻⣿⣈⠏⡞⡀⢈⢀⠁⠉⠁⠒⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠜⢆⠀⠀⢀⠔⠉⠀⢆⣠⡇⠀⢻⠀⠀⠀⠀⢢⢂⠈⡔⢸⣿⠁⢟⡹⠶⡤⢤⣠⣁⢀⠀⠀⠀⣄⡜⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢘⣧⠘⠁⠀⣢⠔⠉⢠⠀⡀⢸⠀⠀⠀⡐⠁⠣⠄⠜⢸⡏⠀⣼⠁⡈⡇⠀⠀⠈⠉⠉⠑⠒⡞⢛⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣜⡈⢢⡵⠎⠀⠀⠀⠈⡀⠉⢌⠀⠀⢾⣶⣶⣶⣶⣾⣾⡟⠂⣾⢐⠨⡇⠀⠀⠀⠀⠀⠀⡸⠁⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠐⠂⠀⠀⠀⠰⠆⠀⠁⢠⣿⣵⣾⠇⠀⠀⠀⠀⠀⣰⠇⣰⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣿⣿⡟⠀⠀⠀⠀⠀⢰⠏⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠠⠤⠦⠶⠲⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠟⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣬⣴⣤⠄⠀⢹⣧⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠋⣿⠀⠀⠘⠉⠹⢙⡇⠀⠀⠀⠀⠰⠋⡉⠙⠝⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⣷⠀⠀⠐⠀⠐⢴⡇⠀⠀⠀⠀⠐⠊⠀⠁⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⠀⠀⢠⠀⢠⢝⠂⠀⠀⠀⠀⠀⠀⡠⢁⠆⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣡⣺⠀⠀⢸⠀⠰⢹⡆⠀⠀⠀⠀⠀⠘⠖⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠉⡋⡄⠀⡜⠓⠘⠷⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡓⠶⠶⠖⣇⡜⠒⠤⠤⡤⡴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠄⡤⠄⠠⠀⠀⠉⠄⠢⠜⠧⠴⢴⠧⡦⢶⠟⣧⢤⣼⣤⣠⣠⣽⡋⠀⠜⠋⠀⠩⠐⠈⠀⠔⠡⠃⠕⠀⠂⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⢸⣏⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠒⠀⠀⠀⠠⠄⠒⢂⡒⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⢿
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠘
⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠲⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠤⠈⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠂⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠴⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠀⠀⠔⠂⠐⠲⠀⠒⠒⡀⠀⠀⠀⠀⠀⠄⠤⠀⠦
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠂
⢀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣠⠸⡆
⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠑⢴⡻⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⣁⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠀⠄⠀⠴⠂
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣶⣤⡀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠉⠉⠉⠙⢿⣿⣦⠀⣴⣿⡿⠋⠉⠉⠉⠙⢿⣿⣆⠀⠀⠻⣿⣿⣿⣆
⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⢠⣶⣿⣶⡄⠀⢹⣿⣾⣿⡏⠀⢠⣾⣿⣶⡀⠀⢻⣿⡆⠀⠀⠘⣿⣿⣿⣆
⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠸⣿⣿⣿⠇⠀⢸⣿⣿⣿⡇⠀⠻⣿⣿⣿⠇⠀⣸⣿⡇⠀⠀⠀⠘⣿⣿⣿⡆
⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠈⠉⠁⢀⣰⣿⡿⠉⢿⣿⣄⡀⠈⠉⠁⢀⣴⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣾⣿⡿⠋⠀⠀⠈⠛⢿⣿⣷⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧
⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄
⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⢀⣴⣦⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁
⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠈⠹⣿⣿⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⢠⣿⣿⣿⠇
⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⡀⠀⠀⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢵
⠀⠀⠀⠀⡀⠀⠁⠀⠐⠀⡙⠀⠀⠀⠀⠐⠶⠒⠘⠺⠿⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠈⠀⠂⠀⠦⠀⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣤⢠⠈⣁⢀⡀⣈⢉⡀⢀⡀⠀⠀⠀⠙⠒⠂
⠀⠀⠀⠀⠀⠦⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠀⠈⠛⠴⣦⣰⣀⣤⡀⠧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣷⣄⡀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⡇⠀⠀⠀⠐⠐⠀⠠⡀
⠀⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⢀⡀⠀⢀⠇⠀⢠⠁⠀⣀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠰⠀⠀⠘⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⢠⣴⠃⠀⠀⠘⢄⣀⢀⣠⣠⣷⠎
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣶⣶⣾⡽⢁⡖⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠥⠖⠋⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠐⠀⡎⠀⠀⠀⢦⣀⣢⣀⣴⠷⠃⠀⠀⣑⣎⠦⠭⠾⣷⣄⠀⠀⠀⣎⠀⠀⠈⠻⣄⣀⣀⣀⣰⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠐⠤⣤⣤⣼⡷⠟⠋⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⡀⣤⠶⡀⠀⠀⠆
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣮⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠃⠀⠀⠀⠀⠀⠉⠁⠘⠀⠇
⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣟⠋⠀⠀⠳⢦⣄⣀⣀⣀⣀⣀⣤⣤⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣶⣶⣶⣶⠶⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⢶⣶⠶⣶⠶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠉⠀⠀⠀⠈⠉⠓⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢠⡆⠀⠀⣤⠀⣴⠀⣴⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣧⣤⣤⣿⠀⣾⠀⣿⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢸⡇⠀⠀⣿⠀⣿⠂⣛⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠻⣧⡀⠈⠁⠀⠀⠙⠀⠉⠀⠙⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠈⣿⠂⠀⠀⣀⣀⣀⣠⣤⡴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣀⣴⠞⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠟⠻⠟⠻⠿⠟⠿⠿⠻⠿⠿⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡟⠀⠀⠀⣶⣿⣶⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀⠀⠀⢹⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣻⣿⣿⣿⣿⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣟⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠛⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣷⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⢟⣻⡿⠿⠶⠾⠟⠛⢉⣩⠤⠖⡋⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⣠⣠⡤⠶⠒⠋⠉⠀⠀⠀⠁⣈⣈⣭⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⠺⠏⠉⢀⠀⠀⣀⣀⡤⠤⢔⣒⣿⠿⠽⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣯⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡷⠾⠿⠿⠽⠟⢛⣛⡽⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⣿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠴⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣚⠭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⣒⡭⠵⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠒⠉⠀⣀⣀⡤⠴⣒⣫⠕⠚⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣋⣩⠭⠔⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⢣⠑⣄⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣟⣃⣠⠤⠄⣤⢤⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⠀⠠⢀⣀⠀⠀⢰⠆⠀⢸⡀⠀⠀⠘⠂⣀⣠⣆⠀⠀⠀⢉⡀⠈⡩⠋⣡⠖⣀⡼⠛⠁⠀⠾⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠻⢶⣄⢆⣤⠀⠀⠀⠀⠀⢀⡄⣦⠠⠐⠲⠂⠀⠀⢈⣠⠀⢀⣺⠡⢞⣭⡴⠖⠀⣏⠀⠀⠀⣼⡃⠈⣐
⠀⠀⠀⠀⠀⠀⣤⣠⠔⢉⠋⠂⢴⢾⣾⣧⠈⠋⠃⡀⢸⡇⠀⢸⢈⡁⢀⠈⠆⡸⠦⢠⡾⠛⠉⠁⠀⠀⠀⠙⠁⠀⣠⣿⣆⡴⠋⡙⠇⠀⠩⠄
⠀⠀⠀⠀⠀⣴⡾⠧⠀⡼⠷⠀⠀⡄⠻⣿⠄⠀⢠⡇⠀⠀⠀⡺⠈⠁⠁⠂⠤⣅⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠇⠐⢛⡛⠛⠛⠺⢤⡉⠁⠴⠀⠀⠠
⠀⠀⠀⠠⣤⡹⢟⣀⡀⠀⠠⣆⠻⣇⠀⠙⢠⠀⠸⡇⠀⡆⠠⢵⡀⠀⡀⠀⡀⢀⠀⠀⣳⠄⠀⢀⣀⡀⡼⠐⠊⢐⠀⢠⠡⠄⠘⠀⠜⢆⢸⡷⠂⣰
⠀⠀⢠⠀⠽⠇⠉⣉⠝⠃⢲⡏⠘⢆⡇⠀⢠⣇⠀⣇⣀⣇⣿⣼⣄⡀⠃⢠⠇⢨⠄⢨⡴⣄⠈⠛⠣⠟⠮⠀⠈⠁⠀⠨⠀⠈⠔⠃⠀⡾⠈⡿⠘⠣⢤⣁
⠀⠀⠇⠀⠀⠀⠀⣿⠄⠀⠘⠱⣴⠆⠀⠀⠀⠀⢠⠜⠋⠁⠀⠈⠑⠚⠒⣤⠐⣈⡁⠀⢠⡋⠙⢁⠀⠐⠶⣣⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⡞⠁⠀⠀⠀⠈⠃
⠀⠀⣤⡀⠀⠀⠐⠃⠀⢤⡦⠀⠑⣶⠆⡆⠊⡄⣀⠀⢀⣤⡀⢲⠄⠀⠘⢴⠆⠈⠁⠐⡀⢐⠁⢄⠀⣠⡤⠙⠃⢀⣀⣀⣀⣠⡴⠋⠀⠉⠛⠦⠄⠀⠀⣶
⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠙⠃⢤⡟⠀⢴⡄⡀⠄⢹⠁⠚⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠀⡄⠀⠀⠀⠀⠙⣿⠿⢭⠁⢀⡤⠀⢸⠄⢠⠀⠰⠛⠂
⠀⠀⡁⠀⠀⠙⠗⠀⢠⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⣫⣄⡦⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠰⢿⡀⠀⢀⠀⠠⡔⣆⠈⡇⠀⠀⠀⢰⠀⠀⢀⠟⢠
⠀⢠⡟⠀⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠛⡁⠀⠁⠀⡸⣏⣀⣨⣷⣦⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠸⠁⠐⣿⢠⣸⠃⣺⠇⠀⠀⠀⠀⢀⣰⠷⠄⠠⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⠉⠀⡈⠀⢻⡷⢿⠈⣦⡡⢉⣿⣶⣤⣄⣀⠀⠀⠀⠨⢁⡀
⠀⠀⣀⣀⣈⣩⣇⣀⡟⠀⠀⠀⠀⠿⠋⠁⢀⡀⠑⢾⣿⠄⠀⠀⠀⢀⡀⠀⠰⠺⣆⢀⠀⠰⠂⠀⠏⠀⣿⠟⠻⡖⡿⠚⠎⠏⠉⠙⠛⠿⢿⣷⡶⠒⢎⣀
⠀⠈⡹⠟⠈⠛⠒⠿⣧⠀⠀⣀⡴⢠⡀⠀⠀⠉⠀⠰⣮⠄⠀⠤⣀⣠⡀⠀⠐⠛⢈⣃⠤⠦⣉⢹⠶⠶⢢⣄⡀⠀⠀⠀⠀⠀⢻⣶⣤⣄⣀⠀⡀⠀⣜⡉
⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠈⡇⠈⠙⣀⡊⠀⣤⠀⠀⠀⠀⠀⠈⣿⡋⢋⢉⣄⠈⣁⣀⠀⠁⢤⠘⠀⣁⡌⠻⢦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣽⡷⢾⡬
⠀⠀⠀⠀⠀⢰⡇⠾⢠⣄⡠⣾⡇⢀⠀⣹⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡗⢨⡉⠒⣀⠀⠄⠘⠓⢶⠀⢁⡰⠠⢀⠸⣇⣠⡴⠊⠉⠙⢿⡏⠙⠢⣽⠓⠧⠀⡀
⠀⠀⢍⠒⠀⠈⠀⠀⠘⠉⠳⡴⢷⠘⡃⠈⠃⠈⠁⠀⠀⠀⠀⢦⣄⣼⡀⠛⠠⠤⢈⡃⠤⠙⣂⠂⣘⡃⢠⣴⠶⢋⠈⠻⣄⡀⠀⠀⠀⣥⣀⠠⠘⣤⡖⠙⠃
⠀⠀⣰⡄⠀⢀⡀⣠⡼⠅⠴⠟⢊⡀⠁⢐⡄⠀⠀⠻⠀⠀⡀⠀⠡⠙⠻⠦⡀⠀⠈⠉⠘⠒⠒⠂⠛⠉⠉⠀⡠⠞⢣⣤⣈⠫⠄⠀⠚⠛⠿⣷⣿⠀⠀⠀⢠
⠀⠀⠸⣿⣾⢏⠘⢁⣠⠀⠀⢀⠞⠃⠀⠙⠀⢀⡀⠐⣠⠄⠐⠲⢃⢠⡆⢱⠈⢳⣤⠄⠀⠀⠀⠀⣀⠀⠀⢀⣠⣶⠦⠋⠉⠀⠀⠀⠀⠀⢸⡟⠁⠁⠀⡄
⠀⠀⠀⢹⡏⠀⠀⠘⢇⠀⢘⣿⡀⠸⣷⡀⠀⠺⠧⠘⣧⠀⣈⠐⣮⠀⠁⢸⠇⢈⠁⠀⢀⠀⠀⠈⠁⠔⠃⠀⠛⠡⠤⣠⣤⠐⠀⡰⠶⣶⠏
⠀⠀⠀⠜⠀⠀⠀⠀⠈⠁⠀⠠⠿⠿⠿⠟⡠⢀⡀⠀⠀⠀⠈⠁⢁⣤⠈⢁⠀⠚⣦⠀⠀⠀⠀⠀⣰⢀⡄⠀⠠⠀⠀⠀⠉⠶⠛⠁⠀⠈⢦⣄⡴⠂
⠀⠀⠀⠀⠀⠛⣄⣀⡄⠀⡴⠀⠀⠀⢌⠂⠀⠀⠙⠤⢭⡷⠿⠇⡄⠐⠀⢈⡄⡠⠘⢷⣤⣤⣤⠊⠙⡏⡍⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠨⡿⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⢨⡁⠀⠀⠀⠇⠀⣠⠀⠀⢐⠋⣀⠄⢀⡴⢀⢠⠄⢀⡆⣠⠆⠛⠉⠙⢀⠄⡓⠦⣄⠀⠀⠀⠀⠀⡴⠏⠁
⠀⠀⠀⠀⠀⠢⣤⡄⠀⢤⡈⡆⠀⠀⠀⡠⠄⠀⡀⠀⠀⢏⠀⠈⢤⡈⠀⠀⠈⠉⢹⠲⠇⠀⠈⡟⠀⠁⠀⠈⠳⣶⡴⠖⠛⠀⠀⠀⢀⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡉⠉⠉⢉⠁⠀⠠⢄⡐⡒⠉⠂⠀⠿⠁⠀⠀⠀⠀⢸⠣⡀⡠⠊⠤⢶⠀⠐⠄⠀⣠⠙⠳⣶⡖⠁⠀⠘⠉⠔⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣏⠀⠀⠀⡸⠃⠉⠲⠞⢀⠂⠀⠀⠀⠀⠀⠸⡄⠻⠆⣸⠒⠾⠶⠿⠇⠀⠀⠠⠂⠁⠉⠁⠁⠢⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⢋⣉⣉⣉⣉⣉⣉⣉⠻⣿⣿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⣀⣤⡄⢸⠁⢀⣤⡀⠀⣤⢹⠀⣤⣄⣀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡉⠈⣛⡃⢸⠀⣾⣻⣧⠀⣿⢸⠀⣛⡋⠈⣹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠿⠇⢸⠐⠟⠉⠻⠂⠟⢸⠀⠿⠟⠛⢿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣴⣶⣶⣘⠓⠒⠒⠒⠒⠒⠛⣠⣶⣶⣤⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄

⠀⠓⠲⠠⠞⠫⠀⠀⠀⠀⠀⠀⠀⣤⣟⣀⡀⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠈⠠⣐⡄⠀⠀⠀⠀⡴⡦⡶⠀⠀⠨⠛⠃⠀⠘⣷⣦⠤⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠡⡀
⠇⠀⠀⠌⢦⡠⠇⠀⠀⠺⣾⡇⠀⠀⢀⡰⠋⠀⣤⠔⠙⠄⣤⠂⠀⠀⢉⣉⣉⣉⣉⣉⠉⠁⠀⠀⠐⠀⠑
⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠑⠦⠴⢿⡄⠀⢀⠽⠧⠚⠋
⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⢤⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠑⠐⠂⢀⠠
⠀⠀⠀⠀⡰⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣄⣀⣀⣀⣀⣄
⠀⠀⠀⡰⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣀⣐⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠁⠀⠀⢀
⠐⠟⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⣔⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⣴⠃
⣄⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠉⠐

⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣵⣭⣶⣬⣯⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠤⠤⠤⠤⠤⠤⠄⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠇⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠘⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⣀⣄⣌⡲⠀⠀⡇⠀⢀⣈⠐⠠
⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠄⠀⢈⠁⢠⡔⡀⢀⢠⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠆⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠠⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠴⠒⠣⡀⠀⠀⠘⢆
⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣠⣤⣌⣩⣤⣄⣀⣤⣀⣤⣤⣤⣠⣃⣀⣀⠐⢀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣟⣻⣻⣻⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣛⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢲⢿⣿⡇⠈⠈⠉⠃⠀⠐⠀⠀⠀⠊
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣿⡿⠃⢠
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠃⠀⠀⢅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⡀⠔⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣿
⠞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠠⠄⠤⠄⢠⠄⠒⠒⢤⠀⠀⠈⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣠⣶⣿⠋
⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⣄⠀⠔⠲⠀⠀⠀⠀⠀⠀⠈⠀⠺⠿⢿⣿⣿⣾⣿⣿⣟⣁
⣄⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠤⡄⠀⠀⠀⣀⠀⠀⠨⣿⣿⠻⢿⢿
⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠀⢠⣿⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⣬⠄⠀⠀⠀⠀⠀⠀⠀⣀⣧⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠂⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⡶
⠀⠀⠀⠀⢋⠁⠀⠀⢀⡱⢤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠉⠙⣿⣿⣿⣠⣿⣶⣾⡷⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⠿⠛⠃⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠄⠀⡜⢀⠀⡦
⠀⠂⠠⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⡾⠟⢿⡆⠠⠄⠀⢀⣀⡀⠀⠀⠇⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠈⠳⠄⠀⠀⠀⠈⠀⠀⠀⠀⠠⠤⡤⠀⡰⠚⠣⠄⠀⠀⠙⣄⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⢀⣀⣤⣀⣐⡀
⠠⠄⠀⠀⠀⠀⠀⠃⢄⠀⢀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠙⠛⠃⠲⠤⡀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠂⠂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⣆⠐⢀⣠⣾
⠀⠀⠀⡈⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢦⣠⠀⠀⠀⢸⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠈⣿⣴⣿⡿⠿⠟
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠘⣿⣷⡄⠠⠁⠀⠀⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⡿⠿⢯⡀
⣀⠀⠤⠀⠠⠀⠀⡀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠒⠤⠀⠀⠘⢿⣿⣶⢶⠀⣾⣿⢟⠀⠂⠀⠀⠀⠈⠀⡐⠀⠀⠀⠙⠢⠬⢉
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣦⣤⣝⢛⠠⢈⢻⡿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠔⠒⠊⠉⠝⠛⠛⢻⡿⡿⠁⣠⠘⣽⣿⣁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢴⠀⠀⠀⠀⢀⠤⡠⠤⠐⣒⠒⠚⠤⠤⠤⠤⠀⠀⢤⣀⣄⣀⡀
⠀⠀⠀⠀⢠⠀⡀⢄⠀⠀⠀⡀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⣀⠤⠖⢈⡀⠈⠀⠀⣶⠁⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠀⠠⠊⠁⠒⠲⢄
⠀⠈⡀⠀⣄⡀⠀⠒⠖⠊⠉⢐⣀⡄⠀⠀⡀⠀⢀⠀⠀⣠⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⡁⢄⣰⢎⣁⠚⠙⠒⠂⠈⠀⠀⠀⠢
⠀⠀⢏⢶⡌⠀⠀⠛⠚⠙⠁⡀⠙⠁⠀⡠⠄⢠⡁⡢⠀⠈⠃⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⢀⠀⢠⠀⠈⠉⠛⠛⠴⠢⠦⠀⢠⣼⠀⠀⡀
⠀⠀⠈⠣⡉⢢⠄⡠⡄⡀⠠⠂⡌⣐⢅⣰⣁⣣⣬⡇⠀⠀⠀⣠⠤⠈⠀⢰⣁⠀⠂⢮⢳⡦⣤⣀⣀⠄⠁⠀⠀⠀⠀⢡⠎⠀⠈⢸⠀⠀⢹
⠀⠀⠀⠙⠻⣦⣤⣂⢉⣀⠅⣜⣳⣦⠾⡯⠖⠚⠉⠀⠀⠀⠈⡟⠀⣠⢂⡏⠴⢰⣀⡀⢈⣀⡇⠁⠀⢀⡀⠀⠀⡀⣀⠊⢀⡜⠁⣸⠀⠀⢨
⠀⠀⠀⠀⡀⠀⠉⠑⠩⠀⢀⡀⠉⠂⠀⠀⢠⡄⠀⠀⠀⠠⢨⠀⣸⠡⢤⠃⠀⠀⠀⠀⠉⠑⡒⠀⠒⣀⠀⢀⣠⡔⠃⡀⠁⠀⡴⠃⠀⠀⠤
⠀⠀⠀⠀⠀⢀⣀⢀⡠⠤⠄⢤⣤⠐⠠⠀⠀⠀⠀⠀⠀⢀⠀⠂⣼⢢⡞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣠⣠⠞⢋⡴⡼⣀⡤⠞⠀⠀⢠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⡈⠁⠈⠙⠒⠾⣖⣩⡏⢭⠤⠀⠀⠀⠐⠀⠀⠴⠀⢳⣠⠟⠂⢀⣤⣤⠤⠤⠴⠶⣞⡻⢛⡁⠀⢈⡘⢋⣉⣀⡴⠒⠊⠁
⠀⠀⠀⠀⠈⠛⠆⠀⠀⢀⡀⠈⠳⡄⠐⢉⣃⠄⠀⠀⠀⠀⠐⡶⢼⡇⠉⢠⣂⠀⢀⣠⠴⠁⠈⠁⡠⠊⠉⠂⠀⠁⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠓⠀⢹⠉⠽⢚⠃⠄⠀⠀⠀⠀⠀⠈⠳⣄⣀⣉⡙⠉⠀⣀⣠⠴⠋⠳⠂⠀⠀⠀⠈⠁⠐⠁⠁⠀⠀⡐⠀⠂⢰
⠀⠀⠀⠀⠈⠀⠀⢠⡆⠀⠀⠀⠀⠈⢇⠀⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⣉⡼⢤⡀⠀⣀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⢰⡅⠘⡦⢦⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢣⣀⠀⠀⢀⠀⣰
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢈⡈⠙⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠒⠲⠓⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠘⠂⢄⠀⠔⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣘⣆⠀⠀⣠⠤⠤⠤⠄⣀⠀⠁⠈⠀⠐⠒⠀⠀⠁⠀⠀⠀⠀⠸⠂⠀⠀⡇
⠀⠀⠀⠀⠰⠉⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⣀⠀⠤⠤⠀⣀⡴⠁⠀⢀⠠⠁
⠀⠀⠀⠀⠀⢂⠀⡸⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⡤⠊⠉⠄⠀⠀⠀⠀⠀⠁⠲⡈⠁
⠀⠀⠀⠀⠀⡔⠙⠃⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⡀
⠀⠀⠀⠀⠈⠣⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠂⠀⠀⠀⢠⠒⡦⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣱⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⡆⢂⠈⢀⠌⢢⡀⠀⠀⠀⠀⠀⡸⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁
⠀⠀⠀⠀⢸⢂⠀⠀⠅⠀⠘⡋⠐⢒⡒⣈⠁⠀⠘⢄⠀⠀⠀⠂⠀⠀⠈⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢈⡇⠀⡊⠀⠀⠉⠉⠑⡄⠑⠤⣄⢀⠀⢀⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⢩⠔⠒⠃⠤⠐⠂⡀⠀⠸⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⠲⡀⢠⠊⠉⠉⠉⠒⠶⠆⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠈⠁⠛⠀⠀⠠⠀⠁⠀⡔⠁⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠢⡀
⠀⠀⠀⠀⠀⡠⠶⠀⠀⠄⠀⡀⠚⠀⢠⠀⠃⠀⠀⡩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⢂
⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠘⢃⠀⠀⠈⢄⣀⡠⠤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠐⠀⠈⠀⠘⢄⢀⡸⢆⡀⠜⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣁⠤⢖⠁⠠⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠉⢹⣿⣿⠉⢹⣿⣿⠉⠉⣿⣿⠉⠉⣿⣿⡏⠉⢹⣿⡏⠉⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⠶⠾⠿⠿⠶⠾⠿⠿⠶⠶⠿⠿⠶⠶⠿⠿⠷⠶⠾⠿⠷⠶⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠙⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢈⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⣠⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠶⢶⣶⣶⠶⢶⣶⣶⠶⠶⣶⣶⠶⠶⣶⣶⡶⠶⣶⣶⡶⠶⢶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣀⣸⣿⣷⣀⣸⣿⣿⣀⣀⣿⣿⣀⣀⣿⣿⣇⣀⣸⣿⣇⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠐⠉⠁⠈⠈⠁⠀⠒⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣀⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⡉⣉⣁⣀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠛⠛⠛⡿⢿⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠻⢲⣄⠀⠀⠈⠙⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢢⣄⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⠳⣶⣶⣤⣄⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⠏⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⠶⠚⠉⠁⠀⠀⠀⠈⠙⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠖⠀⠀⠊⢹⣦
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣚⡏
⠀⠀⠀⠀⠀⠀⠛⠿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠋⢀⡤⠀⠀⠀⠀⢴⡇
⠀⠀⢰⣄⡀⠀⠀⠀⠀⠉⠛⠺⠿⢏⣻⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠢⠄⠀⠀⠈⠀⣀⡠⠎⠀⠀⠀⣞⠀⠀⠀⣾⠇⠀⠀⠀⢀⣾
⠀⠀⠸⠿⣽⣲⢤⣄⣀⣀⠀⠀⣦⣀⣠⣬⣤⣿⠋⠉⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠈⠁⠀⠀⣀⣠⡤⠒⠋⠁⠀⠀⣠⠺⠇⢳⣤⢀⡤⠂⠀⠀⠀⠀⣰⠏
⠀⠘⣦⣤⣀⠀⠉⠁⠘⠻⠁⢀⣟⠀⠀⠘⠉⠀⠀⠀⠀⠀⠒⠒⠦⠄⠀⠀⠀⠀⠀⡀⠴⠒⠉⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠉⢾⠁⠀⠀⠀⢀⣰⠁
⠀⠀⠈⠙⠛⠿⠇⢰⢦⣤⠀⠼⠃⠀⠀⠀⢀⡀⠀⠉⠉⠓⠀⠀⠀⢀⣤⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⣠⠖⠂⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢹⡞⠸⡇⠀⠀⠀⠀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⢀⣴⡾⠓⠂⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⠀⠀⠀⠀⠀⠹⣹⡧⠀⣀⣠⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣦⣄⣀⠀⠀⠀⠀⡀⠀⠐⠛⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠉⠛⠿⣷⣶⣌⣉⡳⠶⠂⠈⠀⣀⣠⡾⠃⠀⠀⠀⠀⣀⡀⠺⠋⠀⠀⠀⠈⠙⢆⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣤⣴⠷⠚⠁⠀⠀⠀⠀⠀⢀⠚⠁⠀⠙⣶⣤⣄⣀⣀⣠⠞⠛⢧⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠊⠉⠁⠽⣍⣹⡥⠀⠀⢘⡇
⠀⠀⠀⠘⢦⣄⣀⣀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣴⠋⠀⠀⠀⠀⠀⠓⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣠⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⣤⣈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢤⣄⡀⠀⠀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⡀⠀⢀⡀⠓⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣦⣄⣀⣀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡈⠛⠛⢻⣿⣿⣿⠛⠛⢛⣿⣿⣿⣿⡿⠻⢿⣿⣿⡅⢻⣿⣿⠀⢀⣸⣿⣿⣿⣿⣿⡟⠹⠿⣿⣿⣧⣿⣿⣿⡏⠛⠛⠛⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⡟⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣍⡀⠀⣿⣿⣧⠂⠀⢠⣿⣿⡿⣿⣿⣿⠉⠉⠉⠉⢹⣿⣿⣿⡇⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠛⢿⣿⣿⣿⣷⣿⣿⣿⣧⣤⣾⣿⣿⣧⣿⣿⣿⣀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣾⣿⣿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⢿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⠿⡿⠿⠟⠁⠀⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣄⡀⢠⣶⣿⠛⠓⠒⠲⣶⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⡾⠟⠋⠉⠉⢀⠀⠁⠀⠴⠟⠛⠳⣿⣟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⡴⠋⠀⠠⠀⠀⠄⠀⣸⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠠⠀⢀⣴⠜⠋⠁⢀⠃⠀⢀⡼⠃⠀⡄⠀⠀⠀⡐⣠⣟⣴⣦⢡⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⡿⠋⠀⠀⠀⣴⣦⡴⠚⠀⠀⠀⣾⠗⡀⢰⣿⣿⡿⠋⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠶⣶⣶⣶⣶⡇⠀⣿⠃⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⢀⣿⣴⢇⣾⡿⢯⢀⠀⠀⣿⠿⠃⠁
⠀⠀⠀⠀⠀⠀⢠⡶⢾⣛⣻⣿⣿⣦⣽⣟⣷⠶⣤⣌⡙⠃⢼⣛⠤⣀⢀⠀⠋⢈⣂⠀⠀⠀⠀⣼⣿⣿⠟⠋⠀⠈⣿⣿⣆⣻⠂⣠
⠀⠀⠀⠀⠀⡀⠀⠸⢿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣷⣯⡛⠷⣄⠙⢷⣌⡻⣄⠀⣼⣧⣶⣤⠖⠚⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣾⡏
⠀⠀⠀⠀⠀⣷⢰⣮⠝⡡⠶⠛⠋⠉⠉⠉⠙⠓⠀⠀⠀⠁⠈⠓⠄⠻⣿⡌⣶⣿⣿⣯⣅⡄⠀⢸⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⣾⣿⣎⠀⣾⣾⣿⣷⣶⣌⠑⠒⠀⠤⠤⠄⠀⠤⡀⠀⠘⣷⠸⡟⣿⣿⣿⣶⠀⣸⣿⣧⣷⣦⣿⣰⠃⢸⡿⠃⠀⠈
⠀⠀⠀⠀⣧⢹⣯⣿⡟⠀⢻⣿⣿⣟⣽⣿⣿⣶⣶⡶⣾⠿⠷⢚⠾⣤⡀⢿⡇⣿⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⣼⣇⢀⡔
⠀⠀⠀⠀⢹⡟⣿⣹⣿⡄⠀⠻⣿⣿⣿⠁⠈⢉⣍⣭⣴⣾⣿⣿⣷⣌⠁⢸⡇⣸⠘⣿⣿⣿⣿⣿⣿⣿⢟⡩⣂⢔⣽⣿⡷⠋
⠀⠀⠀⠀⠀⢿⡹⣏⢿⡿⡄⠀⠙⢮⣿⣷⢰⣿⣿⣿⣿⣿⣿⠟⠃⠻⠀⡼⠁⡿⢠⣿⣿⣿⣿⣿⣯⣶⣿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⢧⡹⣿⣷⡀⠀⠀⠀⢿⣿⣺⣿⣿⣿⣿⡎⠃⠀⠀⠀⠐⠀⣸⠃⠘⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢷⡌⢳⡘⢿⡿⠀⠀⠀⢸⣿⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠙⡄⠈⡈⠻⣦⣀⠀⠀⡿⣜⢿⣌⠃⠀⠀⠀⠀⢄⣮⣿⠩
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠢⣀⠙⠻⠦⣤⡬⠓⢀⣠⠄⠀⣤⣶⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠚⠟⠶⠶⠶⠶⠿⢋⠁⢀⠀⢊⣥⢬⣝⠿⣿⣿⣃⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⢤⣌⣐⣒⣒⣻⣭⣴⠃⡰⠋⠀⠀⠈⠳⣌⠺⡇⠀⠀⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠭⠭⠭⠭⠭⠖⠋⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡮⠜⠁


⠀⠘⠊

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⡙⢿⣟⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⣿⣿⣝⠈⢻⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠿⠛⠛⠳⠦⡀⠀⠈⠻⣿⣆⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⠀⠀⠀⠀⢾⡿⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢹⣿⡆⠀⢰
⠀⠀⢸⣅⡗⢸⠀⠀⢰⢻⡀⡼⠉⠁⢸⣴⠁⠀⠀⠀⣿⣿⣷⡾⠿⠿⠷⠀⠀⠀⠀⠀⣰⠚⣿⣋⡽⠃⠀⠀⠀⠀⠈⢿⣷⢀⠸
⠀⠀⠸⠤⠞⠸⠤⠄⠏⠉⠧⠙⠤⠄⠸⠈⠣⠀⠀⠀⣿⣿⣿⡇⢀⣀⣤⣤⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡄
⣿⣿⢫⣻⡟⣿⢻⣟⡿⣿⣿⣿⣿⢹⣟⣯⣿⣿⣿⣿⣿⣿⡏⣿⡿⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇
⣿⣿⣲⣉⣿⣹⣏⣹⣷⣶⣾⣿⣿⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⠸⣇⠀⠀⢀⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣾⠃
⠉⠉⠉⠉⡍⠉⠉⠉⣉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⡄⣿⡀⠀⠀⠛⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠇⠧⠎⠃⠃⠈⠰⠇⠇⠇⠅⠗⠁⠇⠀⠀⣿⣿⣿⡇⢸⣷⡀⠀⢠⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠸⣿⣷⡀⠘⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣰⠏⠹⣿⡇⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⣿⣿⣿⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⡰⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢻⣿⣿⣿⣷⡀⠀⠀⠀⢀⣠⣴⣾⠟⠁⠀⠀⠜⠁⠀⢿⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⣀⣠⠠⠤⠴⠒⠒⣉⣋⢉⡿⠽⠯⠩⠭⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⠁⠀⢀⠤⠀⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡔⠂⠀⡀⠢⡀⠀⠀⠈⡀⣿⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠠⡰⠊⠑⠲⣇⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠠⠙⢦⡄⠀⠸⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡔⢦⢴⣤⣴⡶⢻⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⢛⡆⠀⠂⠀⠢
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⠀⠉⠡⢀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⢈⣜⠠⢈⠀⡂⣰⡀
⠀⠀⠀⠀⠐⠇⠀⠀⠖⠀⠀⠀⡰⣀⣀⣡⡛⠪⡤⠴⡇⠀⢸⠀⠀⠀⠀⠀⠀⠸⡀⢤⠠⠈⠻⢯⣥⣆⣸⡷⡟⠢⢀
⠀⠀⠀⠀⢸⢀⠀⠀⣂⡥⢀⠼⢄⣉⣉⢿⢦⣮⣤⣲⠯⠵⠚⠀⠀⠀⠀⠀⠀⠀⠀⠑⡸⠤⠀⢐⡩⠂⠑⢌⡹⢀⠀⡡⡀
⠀⠀⠀⠀⠀⢸⠀⡀⢸⡖⠁⢀⡀⠄⣒⣯⣷⠯⢥⢔⠦⠂⢈⡁⡰⠖⠄⠤⠠⣀⢀⡦⠐⠀⠈⠱⠂⡀⠀⢀⠙⣟⠀⠡⠅
⠀⠀⠀⠀⠀⢎⡇⠰⣀⡅⠈⣨⡵⢛⣡⣷⣏⠻⣉⢤⡪⠕⡈⢊⣶⢾⠖⢀⣠⢧⠔⠀⠀⠀⢤⣀⠀⢀⠢⢐⠠⢈⣷⠂
⠀⠀⠀⠀⠀⠈⠻⣤⡠⢐⠚⣁⣭⠽⡋⡝⠀⠀⠀⠀⠷⡉⢔⡹⢊⣡⡿⠟⢊⡟⠀⠀⠀⠀⠀⠸⠆⠐⠨⣰⡾⠋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⢀⠈⢠⠽⣂⠳⠀⡠⠛⠑⠠⠴⢟⠉⣀⢴⣾⠃⠀⠀⢀⣛⢃⣞⣇⣲⡾⡟⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⠈⠙⢳⣎⠀⢀⠀⠀⠀⠀⠉⠛⠯⡇⠀⠀⡠⠭⡍⡬⠍⠠⣌⣥⢥⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠴⠾⢓⣤⣉⡒⠂⠀⠀⠀⠐⠇⠀⠀⠀⠀⡐⠀⠀⠄⠀⢲⡎⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢛⡭⡿⠲⠢⢄⡀⠀⠀⠀⠀⢤⠀⠁⠂⠅⠄⣼⢹⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠐⠡⠀⠊⠝⠕⠝⠅⠀⠀⠈⠁⠀⠀⣏⣋⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⣄⠀⠀⣠⣄⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⣤⣄⠙⠳⢦⡏⠸⡇⠀⢸⡟⢹⡇⢀⡴⠞⣉⡳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⡀⢁⣘⣗⢠⡿⠐⣿⣶⠋⡴⠛⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⣿⣧⣹⠀⠀⣣⠞⠓⠐⢻⣄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢀⣽⡫⠀⣋⣥⡈⠓⡄⠀⢻⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡾⠤⢀⠐⣼⠿⠴⢦⡄⠈⠃⠀⢀⠀⠀⠀⠊⡨⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡔⠉⠀⣠⡼⣿⢃⣒⠒⠀⠀⠀⣘⣧⡴⠷⣤⡇⣀⠀⢚⣻⡤⠶⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠘⠉⢷⡿⠛⠛⠛⠂⢀⡾⢏⡉⠹⣛⣚⣛⡛⠿⠿⠒⠃⢠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⡇⠀⢹⡗⠖⠓⠂⠉⣿⡻⡜⠃⠀⠀⢀⠀⣀⣤⣤⡤⠶⠶⢿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⡄⠈⢀⣠⣸⣧⣶⢂⣠⡴⠛⠁⠀⠘⠀⠐⣵⡛⠉⠉⠀⠀⠒⠋⠉⣉⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣵⡾⠋⣫⠉⠉⠻⣏⣩⠆⣰⣾⠒⠁⣆⢀⡿⣷⠟⠓⣤⣄⣱⢦⣴⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠄⡴⡏⠀⠀⠀⠸⣗⣊⣁⣀⠀⠀⠈⢻⣧⠀⢰⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⡄⠁⠙⠀⠀⠀⢠⠞⠈⢿⠉⠒⠀⠀⣸⠈⠐⢦⣅⢆⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡕⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡶⢺⠏⠀⠀⠹⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧⣰⠀⠀⢀⣤⠤⠶⠒⡏⠀⠈⡗⠆⠀⠘⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠹⡄⠀⠉⠃⠀⣠⠞⣧⡀⠀⠀⣠⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣇⠀⢠⠶⣿⠁⠀⠇⠁⣠⡶⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣌⠀⠃⠀⠀⣀⠤⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣭⠷⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡄⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⢀⢐⠐⢀⠢⡬⠦⠀⠈⠠⠆⠄⠀⠀⠠⡈⡌⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠁⡤⠄⢎⣑⣠⠀⠀⠀⠀⢂⠄⠀⠂⠄⠹⠤⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⢀⠀⠈⡁⠐⠜⠚⠈⡅⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⡀⢈
⠀⠀⠀⠀⠀⠀⠀⣁⠄⢠⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠀⠐⠀⠠⠀⠀⡀⠀⠀⢀⠴⠅⠀⠁⡀
⠀⠀⠀⢠⠀⠀⠘⠄⠀⠁⠐⠀⠈⠆⠁⠀⠙⠈⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠀⠀⢰⢀⠀⢀⠔⠁⠀⠀⢃⠀⢀⠹
⠀⠀⢀⡀⠀⡄⢌⠠⠀⠀⠄⠠⠀⠃⠀⡀⠄⠒⠒⠠⢠⠃⠀⠆⠀⢰⡀⠀⠀⠀⠇⠀⢀⡁⠀⠐⠈⠀⡠⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⢁⠄⡀⠀⠀⠀⠀⠈⡀⠀⡀⠁⠀⠀⠁⠈⠃⠀⡇⠀⠠⣤⠀⠀⠀⠀⠁⠀⡀⠀⠀⡠⠃⢀⡠⠀⠄
⠀⠀⠀⢅⠀⠠⡰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠠⠀⠀⢀⠃⠅⠀⡀⠀⠀⠠⠀⣁⠈⠀⠀⠀⠀⡈⠁⠀⠀⠀⠉
⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠑⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠰⠈⠒⠁⠀⠀⠈⠠⢀⣉⠄⠀⠀⠈⠀⡠⣈⣁⠶⢠
⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠠⠠⠄⢀⠀⠀⠀⠀⠐⠠⢀⠁⠠⠀⠀⠀⠐⡀⠀⠈⠉⠠⠠⡆⠀⠀⠀⠀⡀⠈
⠀⠀⠎⠀⠀⠀⠀⠀⡀⠐⠁⠁⢠⠄⢀⠀⠀⢀⠸⠀⠀⠀⠄⠠⠤⠀⢀⠗⠀⠀⣠⢀⠀⠀⢀⠀⠀⠀⢐⠀⠐⠊⠀⠈⢀
⠀⠁⠀⠀⠀⠀⢈⠄⠈⠀⠀⠀⡀⠀⠀⠀⢀⡀⢢⡀⠀⠀⠀⠀⠀⠈⠀⣀⣀⢀⠀⠀⠀⡀⠀⠀⠀⢃⡀⠀⠀⢀⡀⠀⠄
⠀⠐⠀⠁⠀⡠⠊⠀⠀⠤⠀⠀⠀⠀⠂⠘⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡆⠀⠀⠁⢀⠾⠄⢀⠐⠃⠀⢠⠈⡀⠠
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠄⠀⠈⠀⠀⠀⠀⠰⠀⠄⢈⠀⡰⠀⠐⠐⠀⣀⠀⠘⢀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠠⠀⠂⠀⠀⠠⠀⢀⠂⠒⠀⠀⠀⠁⡆⠂⠀⠀⠀⠀⠀⠀⣀⣢⠀⠐⠁⠀⠂⠤⠀⠙⠉⠢⠀⠀⡀⢀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢀⠀⢀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠠⠖⠀⢀⠀⢀⡄⠒⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠔⠈⠃⡃⠀⠀⠀⠀⠀⠀⠀⠂⢉⢉⣋⠁⠄⠁⠐⠀⠠⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠄⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠀⢀⠂⣀⡀⣀⡄⠀⣴⢄⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠐⠂⠀⠄⠠⢀⠀⠀⠀⠤⠐⠒⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠉⠁⠀⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢠⠠⡄⡄⠀⠀⣤⠀⢠⠔⠂⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢾⣷⡦⡀⠀⢶⣛⠓⠘⡇
⠀⠀⢸⢙⡆⣇⠀⣰⠓⢇⢣⡀⡀⡟⢣⡀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠛⠛⠁⠁⠀⠈⠛⠃⠀⡥⡀
⣶⣶⣶⣷⢶⡶⣶⣶⣶⡶⣶⣾⢷⡶⣶⣶⣶⣶⡆⠀⢠⣾⣿⣿⣿⣷⣄⠰⠗⠒⠀⠀⠀⠈⣰⣿⣷⡀
⣿⣟⣬⢻⡟⣷⢋⣿⣽⣽⣿⣿⢸⡧⣿⣿⣿⣿⡇⠀⣼⣿⣯⡸⣿⣿⣿⣿⣿⡿⠆⠀⠀⣀⣸⢷⣿⣷
⠛⠛⠛⢛⠛⠛⠛⢛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠃⠀⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣤⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠸⠸⠤⠰⠸⠸⠠⠇⠅⠆⠭⠺⠰⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢸⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠠⢶⣶⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⠟⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⢦⣤⠶⣴⠄⠀⠀⠠⠤⠦⣤⢤⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣿⡆⢰⡏⣷⠀⠀⠀⢀⠀⣤⣀⢀⣠⡄⣴⣄⠀⣤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⡇⠈⠃⢻⡇⠀⠀⢸⠀⠋⠻⠚⠛⠀⠃⠛⠋⠘⠁⡟⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢀⡼⠃⢰⠀⣼⠀⡄⠂⡶⣄⡀⡇⢀⡄⢀⠐⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢁⠀⠇⠀⢁⠇⠰⠁⢸⡇⠈⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⠐⠠⠀⠈⠀⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁
⠀⠀⠀⠀⠀⠰⡖⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡄
⠀⡠⠚⣉⠶⠐⢶⣊⣁⠀⠐⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⠶⠶⠒⢒⡒⠒⠶⣄⠀⠀⡤⠂⠀⠈⠀⠀⠀⠀⠀⣠⠞⠛⣇
⡞⠳⠶⣅⠀⠀⢘⣃⣈⣹⡄⠀⠀⣧⡀⠀⡀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⡀⢉⠙⢢⡌⣧⠀⡈⠠⢒⣤⠀⠀⠀⣴⠟⢫⣾⠷⠋
⡇⠀⠀⠈⠙⠛⠋⠉⠉⠉⢙⡶⣾⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⠀⢐⠀⣐⢉⣠⣼⠀⠋⠒⠸⠿⠄⢀⣩⡴⠖⠋⠁
⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢻⠉⠀⠀⡄⠀⠀⠀⠀⢀⠜⢿⣒⣷⡖⢒⣷⣖⣓⣾⣷⡿⢿⣿⡿⠀⠀⠁⠠⠲⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢸⠀⡆⠀⠀⠀⠀⠀⠠⠂⠀⣀⣨⠇⠀⠀⠣⠤⠤⠌⠀⠸⣆⠤⠌⢉⣉⢉⡉⠩⠭⠄⠒⣊⡥⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠐⠀⠘⢠
⠀⠦⢤⣤⣤⣄⣀⣤⣠⡴⠞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⠀⠰⢄⡉⠒
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡉⠉⠐⠢⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⡏⠀⠀⠐⠀⠀⢀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠈⠐⢠⡀⠙⠲⣄⠀⠀⠀⢳⢸⠀⠀⠀⠀⡟⠀⠀⠀⠀⢶⠺⠛⠻⠶⡶
⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠈⠣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⢢⡀⠀⠘⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠐⠀⠢⠑⠆
⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⠀⡴⠁⠀⠀⠀⠖⠀⠀⡀⠀⣀⣼⡦⠰⠇⠀⠐⠀⠀⠈⢪⠀⠀⠀⠀⠀⠀⠀⠁⢈⠰⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⢃⡀⠀⠀⢀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠃⠀⠐⢀⣠⡼⠞⠋⠈⠾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢨⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⡀⠀⠀⠀⠂⠐⠒⠐⠀⠀⠀⢠⡇⣀⣬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⣀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠀⠞
⠀⠀⣀⠠⢄⡀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⣀⣤⠶⡾⠛⠓⠶⠦⢤⡀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠐⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠤⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠰⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⡀⠠⣬⣱⣧⠱⡀⠠⠄⠀⠀⠀⠀⡀⠀⠀⠤
⠀⡆⠀⡇⠀⠈⡇⠀⠀⠀⣠⡾⠛⢘⠿⠒⠓⠒⠲⢦⣀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣛⡷⠀⠀⢉⣳⡌⠈⢩⡆⢿⢠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡇⣤⠃⠀⠀⡇⠀⠀⢴⣿⠃⡠⠋⠀⠀⠀⠀⠀⠀⠙⡃⠀⢼⠀⠀⠃⢀⣀⣤⣴⣾⡿⠛⠉⣭⠿⠀⣄⠀⣿⠃⣄⣨⢱⣿⣾⡟
⠀⢛⠺⡀⠀⢠⡇⠀⠀⠲⣝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠈⠻⡿⡟⠋⢁⣬⡥⠔⢿⣛⣾⢴⠖⣿⠁⠀⢰⠀⠉⠙⠛⠉⢩⡇⠀⠀⠀⠀⠀⢠⠀⠚⠒
⠀⢸⣄⡇⠀⢸⡇⠀⠀⠀⠈⠉⠑⠒⠒⠤⠤⠤⠤⠄⠐⠃⠀⠀⠀⢱⣾⣤⣸⣤⣶⡿⠿⠏⠈⣀⡾⠃⠀⠀⠸⡆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡌⢀⡠⠂
⠀⠈⡇⠀⠀⣾⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠮⣀⣀⣈⣉⣀⠤⠔⠚⠉⠀⠀⠀⠀⠀⠏⠀⠀⠀⠜⠇⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠹⣄⡸⠃⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠒⠀⠒⠒⠀⠀⠀⢀⡀⠠⢄
⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣨⣤⡼⠿⠫⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⠄⢀⣄⠑⢄
⠀⠀⠀⠀⡇⠀⠀⠀⢠⡄⠀⠀⠄⣤⡠⢤⣄⣀⢀⣁⣠⠀⠀⠀⠀⣀⢀⣤⣤⡴⠿⠛⠋⠁⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣯⠀⠈⣳⣄
⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣈⣁⣀⣈⣁⠀⠀⠐⠀⠸⠉⠁⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠤⠶⠛⣽⢠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⡠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠀⠀⠁
⣿⣾⠾⠷⣿⣿⣿⣾⣿⣿⣾⣷⣷⣾⣿⣷⣶⣿⣿⣷⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣷⣿⣶⣶⣾⣷⣷⣷⣶⣷⣶⣾⣶⣶⣿⣷⣾⣿⣿⣿⣿⣶⣿⣷
⣿⣷⣏⣻⣧⣤⣤⣤⣤⣦⣤⣾⣦⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣄⡐⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠻⠻⠶⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣶⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠓⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣶⣶⡞⠃⠀⠀⠂⠀⠀⠀⠀⠀⠁⠑⠁⠈⠀⠀⠙⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣩⠀⡀⠀⠈⢉⠥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠊
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⠑⠷⠶⠀⣐⣂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣡⠼
⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⡶⠀⠂⢔⠳⢶⢶⣄
⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠷⠾⠋⣹⠿⠿⠤
⠀⢩⡂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠘⠆⢰⠇⡀⠀⠀⠀⠀⠆⢀⠈⠀⠀⠀⠀⠀⠐⠀⠉⠉⠁⠐⠂⠠⠄⠀⠁
⠀⠀⠳⣄⡀⠀⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⢸⠆⢉⣇⢱⠄⠈⠸⠃⠀⣰⡀⡐⢀⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠌⠃⢰⡄⠀⣼⣿⣟⣴⠟⢡⠋⠤⡀⠀⢀⠀⠀⠀⠐⠒⠶⢞⣛⣷⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠒⢽⠄⠄⠀⠀⠈⣷⢰⣿⠩⠟⠛⠓⠾⠗⣌⠠⠑⠄⠀⠀⠀⠀⠐⠒⠮⠉⠉⢽⠧⠲
⠀⠀⠀⠀⢀⣠⣄⣦⣄⠀⠀⠀⠀⠀⠂⠀⠄⠀⠈⠼⠓⢲⢦⡄⠀⠉⢿⣧⢲⠀⠀⠀⣾⣿⡏⢑⣈⡂
⠀⠀⢤⣼⣿⣿⣿⣿⣯⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⣠⠀⠀⠀⠀⣠⠼⠟⠩⢠⢀⠸⠿⡙⠻⠿⠟⠛⢃⠐⢀⣤⢲⣄⡄
⠀⠶⠿⠿⠿⣿⡿⠛⣩⡀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠒⠉⠈⠀⠉⠋⠁⠠⠀⠀⠁⠀⠁⣀⠔⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⡠⣠⡼⠗⣿⣬⣯⡄⡀⣛⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠼⠠
⠀⠀⠀⠐⡞⠑⡘⠿⢿⡯⠄⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⡄⠀⠠⠄⣀⣀⠴⠒⠀⠀⠂
⠀⠀⠀⠀⠁⠚⠁⠢⠤⡭⠠⡟⢃⡀⣀⠀⠀⠀⠀⠀⠀⠠⣀⡤⣀⣃⠀⠀⠀⠀⠀⢀⣂⣐⣸⠿⡛⡟⡃
⠀⠀⠀⠀⠀⠀⢀⠐⠂⡠⠄⠘⠉⠉⠥⢤⠀⠀⠀⢠⣔⠒⢹⣿⣿⠿⠓⠀⠀⠀⠀⠈⠩⢷⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⢦⡽⣝⠿⣧⠠⠤⠀⠀⠀⠀⠀⠀⠀⠉⠭⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⢴⠟⠒⠿⢦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⢴⡆⠢⣤⣤⠆⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢐⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀
⠀⠀⠀⢀⡿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠠⠐⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⢄⡀⠂⡀⠀⠀⠀⠀⢀⣸⣿⡯
⠀⠀⢀⠹⢿⣿⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢁⠈⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⠂⠀⡀⠄⠂⠀⠀⠰⣾⣿⣟⣥⡀⠂
⠀⠀⢐⠭⣽⣿⡭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠄⡀⠂⠀⠀⠀⠐⡟⠀⠀⠀⠀⠐⠢⢜⠛⠀⠀⠀⢀⣬⣿⣿⣿⡧⠾⠗⠒
⠀⠀⠐⠭⣷⣿⠿⠭⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⠚⠁⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⣀⠤⣿⣿⣻⠶⠞⢋⣩⡤⠄
⠀⠀⢀⣹⣿⠿⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣝⣒⠿⠶⣞⣋⣭⠤⠴⠆
⠀⠀⠐⣫⠿⢍⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣟⡱⠶⠒⣚⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⣠⡀⠀⠀⠀⠐⠲⠶⢿⡷⢛⣋⣭⡥⠔
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠻⠁⠀⠀⠀⠐⠲⠶⠶⢬⡥⠶⠖
⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⠲⠒
⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢸⡦⠀⠀⠀⠀⠘⠛⠄⠀⠀⠀⠀⣼⠀⠀⠀⢰⡄⠀⠀⠀⠉⣦⠀⠀⠀⡏⠀⠐⣿⠿⠂
⠀⡄⠀⠀⠀⢢⣿⡣⠀⠀⢸⡏⠀⠀⠀⠀⠈⠉⠂⢀⡄⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠇⠀⠀⠀⢳⡀⠀⠀⠀⣼
⠀⠄⢠⠀⠀⠘⢻⠏⠀⠀⢸⠁⠀⢠⡄⠀⠀⠁⠈⠠⠀⠀⢀⣿⡂⠀⠀⢸⣷⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⣿
⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⠸⠀⠀⠞⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠸⠟⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠄

⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠂⢈⣠⠀⠰⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣀
⠀⠀⠀⠈⠓⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠂⠀⠠⠤⠉⠀⡉⣀⡒⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂
⠀⢀⠀⠀⠐⠑⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡈⠀⣖⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⢦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠴⠦⠀⠤⠤⠄⣀⣀⣀⢀⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⠒⠂⠀⠈⠀⠀⠀⠀⠈⠀⠈⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠠⠀⢀⠀⠀⠠⠀⢡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀
⠀⠁⣀⠄⠠⠆⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠀⢀⡂⠐⡐⢀⢴⠰⡀⠀⠀⠀⠀⠀⡤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠈⠐⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠂⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢄⠈
⠀⠘⠀⠁⠉⠀⢀⠰⠒⠢⢄⠃⢄⠐⣄⠤⢤⡀⠀⠁⠀⠗⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠈
⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⢡⠀⠀⠈⠰⢤⠚⠁⣀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⡀⠰⡀⠀⠀⠀⢀⠌⠀⠀⠀⠠⢀⠁⠶⠅
⠀⠀⠀⠈⠉⠀⠉⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠑⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠁⡆⠡⠤⠂
⠀⠀⠀⠰⡅⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠙⠓⠄
⠀⠀⠀⠀⠘⠡⢀⠔⢀⠀⠀⠀⠀⠀⠀⢨⠀⠘⠰⠗⠒⠀⠌⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠞⠃⠶⢲⢀⠒⠀⠀⠀⣤⠀⠐⠒⠓⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠈⠤⠈⠁⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠔⣹⠔⠑⠄⢀⡠⡔⠈⠉⠀⠀⠀⠀⠈⠀⠘⠂⠈⠓⠀⠈⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠢⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤
⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠱⢄⣀⡀⢤⡤⠄⠀⠀⠀⠀⠀⢀⠄⠁⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠈⠀⠒⠚⠄
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡤⠃⠔⢂⡌⠀⠀⠀⠀⠀⣬⠀⠂⠁⠤⠀⠘⠁⠀⣰⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⠀⠀⠀⠀⠀⠀⠁⡄⠓⠠⠂⠴⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠶⠢⠀⠀⠀⠀⠐⠲⠆⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠖⠀⡁⠀⠀⠠⠴⠀⡄⠀⠀⠀⠀⢡⣇⠀⠀⠀⠀⠀⠀⣨⡌⠀⠀⠀⠀⠈⢀⠀⡀⢀⠀⡀⡁⠀⠀⠀⠀⠀⢜⡁⢒⠀⣀⡀⣐⢈⡃
⠀⠀⠂⠀⠀⠀⠀⣤⢤⠂⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠈⢨⠈⠁⠈⠁⣨⠁⠀⠀⠀⠀⠀⢈⡥⠄⠤⠄⠤⠄⢬⡁
⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠤⡈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠦⠄⠲⠀⡈⠁⠀⠀⠀⠀⢀⠀⣤⣀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢘⡁⠠⠀⠤⠓⠘⠁⠀⠀⠀⠀⠀⠈⡀⠛⠁⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡤
⠀⠀⠀⢀⠂⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡶⣆⡹⠀⠀⠀⠀⠀⠀⠀⠜⣠⡀⠚⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠘⡠⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠰⣚⣳⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⠀⠀⠀⠀⠀⠀⠀⢠⠠⢤⣄⡄⢠⠀⠄
⠀⠀⠀⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠭⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠀⠀⠀⠀⠀⠀⠈⠀⠲⠒⠶⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀
⠀⠀⢀⡈⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠑⢀
⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠆⠠⠤⠄⠤⠀⠠⠀⠀⠀⠀⢀⡀⠶⠂⠠⠴⠅⠂⠀⢀⠀⠀⠀⠀⢂⠀⡁⠀⡀⢀⡑⢈⠆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠀⠀⠀⠤⡤⠔⠂⢈⠀⠀⠀⠀⢨⠀⠙⠀⠒⠒⠒⠙⠁⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠘⡀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠱⠂⠒⠒⠒⠀⠂⠌⠉⠀⠀⠀⠀⠈⠄⠐⢉⣁⣉⣉⠉⠀⠷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⡀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉⠐⠀⠄⠀⠀⠀⣀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣠⣤⣈⣀
⣿⣿⡟⠉⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢉⣀⣠⣤⣤⡶⠆⠻⠶⣶⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣢⡤⠿⠁⠰⠛⠉⠉⣁⣄⣀⣤⠶⠖⠛⠋⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⠏⠉⠉⠉⠉⠲⣾⡾⠛⢛⣍⣩⣤⠤⠶⣶⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣺⣷⣶⣀⡐⠂⡀⠀⣿⡇⠀⠈⣏⠁⠀⠀⠀⢻⠀⠰⣿⣯
⠀⠀⠀⠀⠀⠀⢀⣶⢫⣭⡁⠀⠉⢳⡾⠿⠶⡄⠀⠸⡆⠈⡀⢻⡇⠀⠀⣿⣀⣤⠤⠶⠞⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⣸⢡⣿⣿⣿⡄⠀⠈⣷⠀⠀⢻⠀⠀⡇⠘⡇⢸⣿⠀⣈⠙⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢾⠈⣏⣫⣿⣷⠀⠀⣿⠀⠀⣼⠁⢀⡇⢰⠁⢸⡏⠀⠋⠀⠀⠀⠀⠀⠀⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠈⢇⢹⣿⣿⠃⠀⢰⢿⡶⢾⣧⢞⣋⡴⠃⠀⣾⡇⠀⠀⠀⠀⢀⣤⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠒⠒⠋⠁⠀⠿⢿⢾⣭⣥⣀⣀⣀⣿⣠⣤⣴⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢸⡗⠒⠒⠒⠒⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠁⢹⠿⣦⠀⠀⠀⠀⠀⠀⠀⣏⣠⣴⣤⢛⣴⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⢀⠔⢋⣦
⠀⠀⠀⠀⠀⢸⡇⠀⣷⠆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⣟⣿⣄⣸⡇⠀⠀⠀⠀⠀⠀⡟⢼⣷⣿⢸⡙⠂⠀⠀⠚⠀⠀⠀⠀⡠⢚⣥⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⠘⢯⣀⣽⣁⣈⣿⠖⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠠⣾⣾⣿⠿⠿⠋⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁


⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⡄
⠀⠀⠀⠀⠀⣀⣉⣉⣙⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠛⣿⣿⣿⡇⠀⠀⠀⠀⢀⡐⠉⠙⣾⣦⠶⢷⠀⠀⠀⠀⠀⠀⠀⡴⢏⣽⣿⣿⣿⣿⡂
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⣺⣷⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠙⠶⣞⠀⢙⡶⣼⡇⠀⠀⠀⠀⠀⠀⡯⠼⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀⠀⠀⣺⡿⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⡀⠈⠿⠀⠀⠀⠀⠀⠀⢯⣸⡿⠿⠿⠿⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⣠⠴⠒⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣷⠀⠀⠀⠀⠀⠀⢀⡀⢤⡐⢶⣜⢳⡆
⠀⠀⠀⠀⠀⡞⠁⢀⣤⣤⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠮⣭⢥⣤⢤⣤
⠀⠀⠀⠀⠀⣇⠀⢻⣿⣿⠗⠀⣸⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⠤⢤⣤⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠚⠃⠚⠁⠛⢹
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠶⠮⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣒⣒⣒⣂⣸
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡄⢀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣶⣶⠀⢸⡆⠀⠀⠀⠀⠀⠈⣻⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡞⠀⣿⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠿⠿⠿⠃⠈
⠀⠀⠀⠀⠀⠞⠀⠀⣿⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⠭⠭⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛


⣀⡀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣮⡿⠋⠓⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⢛⡉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣼⡋⠀⠈⣠⣖⠀⠐⠶⠶⠶⠖⠀⠈⣶⣄⠀⠀⠀⠀⠀⠀⠁⠀⠰⣦⣄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡼⠁⠀⠀⠀⠙⣶⣶⣶⣾⣿⣿⣿⣇⠀⠀⠀⠀⠈⣤⠀⠀⠈⢻⣶⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣸⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣤⠊⠀⠀⣸⣿⣄⠀⠀⠀⠉⠉⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠛⢻⣿⣿⡿⢿⣻⠿⢯⣯⠿⠿⠄⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⣿⣿⣋⣐⣈⣀⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠶⠻⢻⣿⣶⣶⣿⠋⠩⠿⠛⠛⠋⠉⠁⠀⣤⠖⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⡿⠿⢿⣿⡟⠉⣝⣟⠁⢠⣀
⠀⠀⠀⠀⠀⠀⢣⢀⣠⣿⡿⣿⣿⣿⣧⠀⠀⢀⢤⣄⣾⣿⣿⣿⣦⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠉⣿⡟⣿⠮⣿⣿⣿⣿⣻⠤
⠀⠀⠀⠀⠀⠀⠈⢻⡟⢻⣿⣩⣿⡿⣿⢷⣄⣿⣣⣄⣦⣾⣿⣿⣿⣯⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠒⠒⠲⢿⣿⣿⣯⣤⣤⣷⣄
⠀⠀⠀⠀⠀⢠⢀⣤⣹⡱⣸⣿⣿⡤⣼⣶⣿⣿⣾⣿⢻⣿⣿⡿⠛⠻⠻⣶⣦⣴⣶⣶⠂⠀⠀⠀⡀⠀⠀⠆⠀⠠⠙⢀⣨⣷⣶⣾⣿⣿⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⢶⣿⡿⠟⠻⠿⠛⢿⣗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣿⣿⣄⣹⣿⣿⣷⣦⣶⣾⣿⣆⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠛⠉⠉⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠟⠛⠉⠙⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡠⠄⠐⠒⠂⢄⠀⠀⠀⠀⠀⣀⠀⠇⢀⡀⠀⠀⠀⡠⠎⠠⠵⢄⠀⠀⠀⢖⠖⣹⡶⢪⡦⣄
⠀⠀⠀⢈⣀⣀⡀⢀⣀⣀⣡⠀⠀⠀⠸⡭⠭⠭⠭⡵⠀⠀⠀⢧⣤⠤⡥⡼⠂⠀⠀⠧⢤⣣⣰⡷⠼⠇
⠀⠀⠀⢱⡭⣴⠦⠽⡮⣽⡽⠀⠀⠀⠀⠃⠀⠀⢰⠀⠀⠀⠀⠈⣴⣉⢱⠃⠀⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠂⠛⢇⡵⠓⠁⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠰⡊⡏⠀⠀⠀⠀⠀⡆⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⠔⡨⠥⠠⢍⢆⣴⢢⠀⠀⠀⢀⠔⠒⢆⠐⡆⠢⡄⠀⢀⠔⠂⠀⠐⠢⣄⠀⠀⠀⢀⠔⠀⠐⢄
⠀⠀⠀⠃⡏⡥⡥⣔⣷⣥⠘⢄⠆⠀⢠⡅⠀⠀⠈⢢⠼⠒⠘⠀⠰⡒⡒⢐⠒⠒⠎⠀⠀⠀⠃⠀⠀⠀⢠
⠀⠀⠀⢃⢧⡡⠠⡀⢈⡜⡁⠀⠀⠀⣦⡈⠢⣀⠔⠃⠀⠀⠀⠀⠀⢁⢠⠸⠠⢠⠀⠀⠀⠀⠤⣀⢀⠔⠁
⠀⠀⠀⠀⠓⠤⠉⠋⠭⠚⠁⠀⠀⠀⢇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉⠁⠀⠀⢴⡊⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢠⠀⠀⠀⠀⠀⠀⢠⣒⡆⢰⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡴⢯⡭⠣⠡⢦⠀⠀⠀⠀⡤⠄⠐⠚⠤⢤⡤⡀⠀⠀⠀⠀⢧⡓⣓⠀⠀⠀⡠⢊⠢⡄⢊⠢⡀
⠀⠀⠀⡌⡜⠁⠀⠈⠉⠙⣵⠀⠀⠀⠐⣀⠀⠀⣠⠿⠓⠁⠀⠀⠔⠀⡟⠁⠈⢲⠀⠐⠁⢠⠁⢸⠘⡄⠈
⠀⠀⠀⣏⣀⣀⡀⣀⢀⣀⠝⠀⠀⠙⠤⠈⠀⠀⠄⠤⠊⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠈⢄⠠⢀⠼⡀⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠑⠒⠇⢀⡀⠀⠀⠀⠀⠙⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⡀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⣀⣀⢰⣧⣾⠗⠛⡄⠀⠀⢀⢋⢘⡀⠀⠀⠀⠀⢀⠞⠙⣾⣬⡣⠀⠀⡤⢤⠄⠢⡤⠤⣄⠀⡀
⠀⠀⢀⢧⣶⡮⠿⠓⠁⠀⢠⠃⠀⠀⢪⠭⡉⢸⠀⠀⠀⡠⠗⠊⠉⠀⡠⠃⠀⢠⡄⣀⡤⠄⣤⠀⣁⣠⣅
⠀⠀⠈⢶⠁⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⠤⠃⢆⠀⠀⢎⠀⠀⠀⢀⠎⠀⠀⠀⠐⣊⠑⣢⢘⠠⠑⠢⢛⡖
⠀⠀⠀⠀⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠨⣀⣀⡸⠀⠀⠀⠉⠢⡠⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠒⣾⡀⠀⠐⣤⠔
⠀⠀⠀⠀⠀⣀⣉⣱⣎⣉⣀⠀⠀⠀⠀⠀⠀⣀⢀⣈⣉⣿⣉⣁⠀⡀⠀⠀⠀⠀⠀⣀⠀⠛⢫⠟⠋⠀⡀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣶⣿⣿⡀⣠⠏
⠀⠀⠀⡼⠊⣿⣿⣿⣿⣿⣿⠑⡇⠀⠀⠀⣰⠖⢻⣿⣭⣭⣹⣿⡏⢾⡄⠀⠀⠀⣾⠛⣿⣿⣿⣿⣿⡿⠛⡇⠀⠀⠀⠀⡏⢹⣿⣿⣿⣟⣿⠉⠁
⠀⠀⠀⣇⠀⣿⣿⣿⣿⣿⣿⢀⡷⠀⠀⠀⣿⡄⢸⣿⣿⣿⣿⣿⡇⣸⡇⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡇⢠⡧⠀⠀⠀⡸⢧⠘⢿⣿⣿⣿⡿
⠀⠀⠀⠱⠓⠀⢹⡅⢸⡇⠘⠙⠂⠀⠀⠀⢸⠖⠎⠉⢏⠉⡿⠉⠚⠺⠀⠀⠀⠐⠉⢀⣿⣿⣿⣿⣿⣇⠈⠑⠀⠀⠀⠁⠀⣠⣞⠿⠿⠿⣢⡀
⠀⠀⠀⠀⠀⠀⢱⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⠀⣻⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢠⠶⢯⠀⠀⠀⠀⣠⢿⢦
⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢄⠀⣰⡶⠲⣆⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣽⡷⠄
⠀⠀⠀⠀⠀⣹⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠐⢂⣀⣤⣀⣀⠃⠀⠀⠀⠀⠀⠀⣀⢀⣈⣱⣖⣉⣀⢀
⠀⠀⠀⣰⠋⣿⣿⣿⣿⣿⡟⠙⡆⠀⠀⠀⢠⣞⠀⠙⣿⣿⣿⡟⠁⢸⣆⠀⠀⠀⠀⠰⣿⣿⣿⢿⣿⡷⠀⠀⠀⠀⠀⡴⠛⣿⣿⡛⠉⠻⣿⠛⠳⡀
⠀⠀⠸⣭⠇⢿⣿⣿⣿⣿⡇⢸⣹⠆⠀⣀⣿⣿⠀⠀⣻⠛⢻⠃⠀⢸⣿⣄⠀⠀⠀⢀⢩⣶⣾⣶⣮⣁⠀⠀⠀⠀⢸⡀⠀⣿⣿⣥⣀⣴⣿⠀⢀⡇
⠀⠀⠀⡿⠀⣹⣿⣿⣿⣿⣇⠠⢿⠀⠀⠃⠈⠃⠀⣰⣿⠀⣼⣧⠀⠈⠋⠈⠃⠀⡼⡷⠹⣿⣿⣿⡏⠳⡷⡀⠀⠀⢸⠛⠄⠈⣿⠉⠉⠹⡇⠀⠞⡇
⠀⠀⠀⣠⣼⠁⠀⠀⠀⠀⢈⣧⣄⠀⠀⠀⠀⠀⣠⣿⣿⠀⢿⣿⣤⡀⠀⠀⠀⠚⠟⠀⠀⣷⠀⢰⡂⠀⠘⠟⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⣇
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣾⣿⣿⣕⣼⠇⠀⠀⠀⠀⠀⠀⠘⢀⣀⣀⣀⡘⠂
⠀⠀⠀⠀⠀⣾⣉⣿⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠿⠿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⣯⣿⡹⣴
⠀⠀⠀⣾⣶⡟⢛⣿⣿⣿⣷⣾⡆⠀⠀⠀⠀⣺⣶⣿⡿⠛⢿⣿⡷⣶⡆⠀⠀⢠⣾⣶⣿⣿⠛⠛⢿⣶⣿⡆⠀⠀⠀⢠⣤⣾⣻⡟⠛⠛⢻⣦⣤⡀
⠀⠀⠀⣿⣇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣇⣿⣇⣀⣠⣿⣯⣿⡇⠀⠀⢸⣿⣿⣏⣀⣀⣀⣸⣿⣿⡇⠀⠀⠀⣷⡟⢸⣿⣿⣿⣿⣿⡇⣟⡇
⠀⠀⢠⡿⠃⣿⣿⣿⣿⣿⡇⠻⣧⠀⠀⠀⠠⡿⠧⣿⣿⣿⣿⣿⡷⢿⡅⠀⠀⢠⡿⠎⣿⠍⠉⠩⣿⠱⢿⡄⠀⠀⠀⣿⠇⢸⣿⣿⠿⣿⣿⠀⢿⡇
⠀⠀⠀⠁⣴⠟⠛⠿⠟⠛⢷⡄⠁⠀⠀⠀⠀⠈⠀⣿⡟⠿⠻⣿⠀⠉⠀⠀⠀⠀⠉⠀⣿⠃⠀⢸⣿⠀⠉⠀⠀⠀⠀⠈⠀⠀⠙⢰⣶⡆⠋⠀⠈
⠀⠀⠰⠾⠇⠀⠀⠀⠀⠀⠠⠿⠶⠀⠀⠀⠀⠀⠠⠿⠷⠀⠴⠿⠆⠀⠀⠀⠀⠀⠀⠰⠿⠧⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⣀⠤⠶⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠩⠀⡀⠈⣈⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠹⡄
⠀⠀⠀⢀⡞⡁⠒⣀⢁⡀⠆⠙⣆⠀⠀⠀⠀⠀⠀⣤⡤⣤⠴⣷⢴⡤⣤⠀⠀⠀⠀⠀⠀⠀⢀⠧⢀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠑⢰⠁⠀⢸⠐⠀⣿⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⢉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⠚⡳⠛⡦⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡼⠁
⠀⠀⠀⠘⢧⠈⡀⢙⠛⢣⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠙⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀⢂⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃
⠀⠀⠀⠀⠈⠛⠶⠬⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠇

⠀⠀⠀⢀⣠⡤⠶⠶⠶⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⣤⢤⣄⡀
⠀⠀⠀⣟⡠⠐⢒⢄⠀⣴⠒⠤⣹⠆⠀⠀⠀⠀⠀⠀⣠⠼⠧⠤⠿⣤⡀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠂⠠⠙⢳⡄⠀⠀⠀⠀⠀⠀⣾⣿⣼⣷⣿⣼⠾⣽
⠀⠀⠀⠸⡴⡩⢊⡉⡜⡇⠛⣠⠋⠀⠀⠀⠀⠀⠀⢘⡧⠒⠒⠖⠒⠺⡅⠀⠀⠀⠀⠀⠀⠸⡧⠤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⢸⢹⣾⠏
⠀⠀⠀⠀⠹⣄⣈⣆⢨⣮⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⡧⢄⢀⠼⡀⣠⠇⠀⠀⠀⠀⠀⠀⢸⣶⣶⣤⣴⣶⣦⣤⣶⣇⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠙⣻
⠀⠀⠀⠀⠀⠹⣏⢡⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣥⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠓⣖⡒⠣⠚⠑⠒⠓⣸⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣆⠀⠀⠀⠀⠀⠀⢀⡤⣤⡴⣲⣤⠦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⠀⣗⣇⡽⢿⡄⢹⡀⠀⠀⠀⠀⠰⣯⡻⣿⣿⡟⣆
⠀⠀⠀⡤⢶⠟⠛⠁⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⢠⠈⢻⣯⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠃⣧⣾⡀⠘⡇⠀⠀⠀⠀⠀⡇⠱⡘⣿⣿⣾⢦
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢴⡶⣶⣚⣛⣛⣒⡒⣶⠀⠀⠀⠀⠀⠀⢘⡇⠀⢿⣥⡷⠗⡆⢀⡇⠀⠀⠀⠀⠀⡇⠀⠘⢞⢷⣿⣿⣆
⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠿⡤⣿⡇⢨⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢣⠻⣿⣿⢦
⠀⠀⠙⠛⠛⠛⠓⠛⠓⠒⠒⠒⠛⠋⠀⠀⠀⠀⠀⣿⢿⣾⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⣦⡦⢿⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣉⣁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⢿⣤⠾⠓⠋⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠚⠚⠛⠉
⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⢰⠃⠀⠹⡞⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⡄
⠀⠀⠀⠀⣠⣄⣀⣀⣰⣀⣀⣏⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠩⠍⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⣀⡴⡚⢻⠿⠻⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⡾⡷⠋⠀⠀⠀⠀⠈⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⠀⠀⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢺⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⠀⠀⣀⣀⣤⣾⠵⠋⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠹⢤⡤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠢⢭⣉⣉⠽⠛⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⣀⣀⢀⣄⠚⣁⣀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣡⠌⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⢻⣇⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⢀⡀⣀⢀⡀⢀⡀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢸⡟⣥⣶⣶⣦⣬⣭⣥⡄⠇⠀⠀⠀⢨⣬⡅⣬⣤⣥⣬⣤⡍⣬⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢉⠻⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣶⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⡛⣛⡋⠁⠀⠀⠀⠀⠀⢨⢩⡅⢨⢩⡍⢩⠍⣥⢨⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣿⣿⣿⠇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⣭⣥⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣧⣘⣨⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⢠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣆⠀⠀⢸⣿⣿⣿⣿⠐⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⣿⡄⠀⢸⣿⣿⣿⣿⢠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣃⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣀⣋⣀⣀⣈⣛⣛⣛⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃