Place the numbers 1 through 25 in the grid below:

__1 2 3 4 5__
A |__ | | | | __|
B |__ | | | | __|
C |__ | | | | __|
D |__ | | | | __|
E |__ | | | | __|

- The sum of each column is odd

- The sum of each row, except C, is even

- The sum of row A is not greater than the sum of any other row

- The sum of the diagonal E1 to A5 is less than that of the diagonal A1 to E5

- A4 + B4 > C4 + D4 + E4

- A1 + B1 = D1 + E1

- A1 > E1

- A1, A3 and B1 are all prime numbers

- (A3 + E3) is a prime number

- A5, D1, D3 and E1 are all squares

- B2, C2 and D2 are ascending consecutive numbers

- B3, C3 and D3 are ascending consecutive numbers

- B5 + D5 = A5 + C5

- (C1)² + (C5)² = (E3)²

- C5 is a two digit number

- D5 is a multiple of E5

- E1 + E3 = E2 + E4 + E5

The required arrangement is as follows:

07 11 02 17 01

13 19 23 22 03

09 20 24 14 12

16 21 25 18 10

04 08 15 06 05