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⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
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.(............)............`..-.._...,..........._
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..\......(...................)..../................\.
....\.....\._.(.........../....(........<o....(o
......\._.).).).\........(.......`.._.........:Y.).__
....................\........`-..._....'..-..-.-^.‘_.).).) Woof!
.......................`.-..._...).).) ................................... ／l、
..........................................................................（ﾟ､ ｡ ７
............................................................................l、 ~ヽ
............................................................................じしf_, )ノ Meow
＊ * .* ' ✨ 🏮✨ ' ＊
. ＊ ✨ ☆☆☆✨ ＊ ' .
* ' ✨+:...💙...:+✨ *
' '✨☆🏮☆🏮☆✨ * ＊ '
＊ ＊✨+:💚:+＠+💚:✨ ' *
＊ . ✨☆☆📀☆📀☆☆✨ ＊ ' * .
' . ✨+:..:++:..💚..+&:..:+✨
* ✨☆🏮☆☆🏮☆☆🏮☆✨ ＊ ' *
' . ✨+:...:+💙+:...:+💙§+:..:+✨
. ✨☆📀☆📀☆ ☆📀☆📀☆✨ ' *
✨💙+💙+:..:+@+:..:+💙+💙✨
. * . . 🟫 ' ' ＊ *
* * . ** * 🟫 . * . '
,·´ ¸,·´`) * * 💝🎁🎁💝 *
(¸,·´ (¸＊＊ .𝓜𝓮𝓻𝓻𝔂 𝓒𝓱𝓻𝓲𝓼𝓽𝓶𝓪𝓼
𝓪𝓷𝓭 𝓗𝓪𝓹𝓹𝔂 𝓝𝓮𝔀 𝓨𝓮𝓪𝓻 2024!
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡
⢀⠀⠀⠀⠁⢀⠀⢀⡴⡲⣍⣷⡿⣗⣗⡠⠑⠄⣂⠀⠀⢀⠔⠄⠀
⠀⠢⡈⠐⠀⠄⢲⢁⣩⣟⣾⡻⡿⡝⡕⠅⠅⢅⠀⠠⢋⠡⢀⠅⠀
⠀⠀⠀⠁⠃⠄⡂⣿⣯⣿⡧⣁⢂⢘⠄⠈⠀⡀⠅⠕⠀⠆⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⣟⣿⡽⡯⡳⠡⡑⡭⠑⢁⠕⢅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⢮⣛⣛⡎⡎⡂⠊⠈⡀⡐⡡⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣻⡾⣝⢬⡂⠌⢐⢐⠰⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣯⣿⢽⡸⠠⠁⡂⢄⡍⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣾⣯⢎⠪⠠⢑⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⣯⣗⢇⠕⠌⡆⢇⢝⢜⢍⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣞⣷⣯⢧⢣⢅⠈⢢⢑⢅⢣⠱⡢⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⡾⣽⣿⡽⡪⡆⠕⠄⠣⡑⢅⠕⢌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣯⣻⣷⢿⣝⢮⢅⢁⠀⠁⠀⡁⠢⢡