KöMaL 2026 C1905

Let $a$, $b$, $c$ and $d$ be distinct positive integers. Among the four statement below two are true and two are fale: (i) $a<b<c<d$, (ii) $a+b=c+d$, (iii) $a^2+b^2=c^2+d^2$, (iv) $a^3-b^3=c^3-d^3$. Find the smallest possible value of $d$.