RU-ALLRUSSIAN 1982 Problem 11

$\mathrm{a}_1, \mathrm{a}_2, \ldots , \mathrm{a}_{1982}$ is a permutation of 1, 2, ..., 1982. If $\mathrm{a}_1 > \mathrm{a}_2$ , we swap $\mathrm{a}_1$ and $\mathrm{a}_2$ . Then if (the new) $\mathrm{a}_2 > \mathrm{a}_3$ we swap $\mathrm{a}_2$ and $\mathrm{a}_3$ . And so on. After 1981 potential swaps we have a new permutation $\mathrm{b}_1, \mathrm{b}_2, \ldots , \mathrm{b}_{1982}$ . We then compare $\mathrm{b}_{1982}$ and $\mathrm{b}_{1981}$ . If $\mathrm{b}_{1981} > \mathrm{b}_{1982}$ , we swap them. We then compare $\mathrm{b}_{1980}$ and (the new) $\mathrm{b}_{1981}$ . So we arrive finally at $\mathrm{c}_1, \mathrm{c}_2, \ldots , \mathrm{c}_{1982}$ . We find that $\mathrm{a}_{100} = \mathrm{c}_{100}$ . What value is $\mathrm{a}_{100}$ ?