Erdos_Gallai: This function takes a list of non-increasing integers as input and uses the Erdos Gallai conditions (1 and 2 from the theorem above) to determine whether or not this is the degree sequence of a graph. Examples: Erdos_Gallai([3,3,3,3,3]) should return False Erdos_Gallai([3,3,2,2,2,2)) should return True Instructions you must follow You are not allowed to use any external libraries on this problem. All your code should be "from scratch". You may assume the user of your code will call your functions with their own print statements (i.e. there should be no print() functions anywhere in your code). You do not need to include anything in your code other than the functions. Erdos-Gallai theorem. A sequence of non-negative integers (dj, d2, ..., dn) written in non-increasing order is the degree sequence of a simple graph if, and only if, 1. d; + d2 + ... + dn is even, and 2. for all k such that 1 sk sn, di + d2 + ... + die sk(k 1) + min(dk+1,k) + min(dx+2,k) + ... + min(dn,k) Erdos_Gallai: This function takes a list of non-increasing integers as input and uses the Erdos Gallai conditions (1 and 2 from the theorem above) to determine whether or not this is the degree sequence of a graph. Examples: Erdos_Gallai([3,3,3,3,3]) should return False Erdos_Gallai([3,3,2,2,2,2)) should return True Instructions you must follow You are not allowed to use any external libraries on this problem. All your code should be "from scratch". You may assume the user of your code will call your functions with their own print statements (i.e. there should be no print() functions anywhere in your code). You do not need to include anything in your code other than the functions. Erdos-Gallai theorem. A sequence of non-negative integers (dj, d2, ..., dn) written in non-increasing order is the degree sequence of a simple graph if, and only if, 1. d; + d2 + ... + dn is even, and 2. for all k such that 1 sk sn, di + d2 + ... + die sk(k 1) + min(dk+1,k) + min(dx+2,k) + ... + min(dn,k)