Postman and the Letters

There are $n$ towns (numbered $1$ through $n$). Each town consists of houses, $i$-th town having $a_i$ houses (numbered $1$ through $a_i$). Letters are to be delivered by a postman. Sometimes instead of writing specific town and house number on letter's envelope, only a house number among all houses of all $n$ towns is written. Assume all houses are numbered from $1$ to $a_1 + a_2 + ... + a_n$.