C. Sofia and the Lost Operations

Sofia had an array of 𝑛 integers 𝑎1,𝑎2,…,𝑎𝑛. One day she got bored with it, so she decided to sequentially apply 𝑚

𝑚 modification operations to it.

Each modification operation is described by a pair of numbers ⟨𝑐𝑗,𝑑𝑗⟩ and means that the element of the array with index 𝑐𝑗 should be assigned the value 𝑑𝑗, i.e., perform the assignment 𝑎𝑐𝑗=𝑑𝑗. After applying all modification operations sequentially, Sofia discarded the resulting array.

Recently, you found an array of 𝑛

𝑛 integers 𝑏1,𝑏2,…,𝑏𝑛. You are interested in whether this array is Sofia's array. You know the values of the original array, as well as the values 𝑑1,𝑑2,…,𝑑𝑚. The values 𝑐1,𝑐2,…,𝑐𝑚 turned out to be lost.

Is there a sequence 𝑐1,𝑐2,…,𝑐𝑚 such that the sequential application of modification operations ⟨𝑐1,𝑑1,⟩,⟨𝑐2,𝑑2,⟩,…,⟨𝑐𝑚,𝑑𝑚⟩ to the array 𝑎1,𝑎2,…,𝑎𝑛 transforms it into the array 𝑏1,𝑏2,…,𝑏𝑛?