Question: Who was the second wife Sigismund I the Old, the King of Poland and Grand Duke of Lithuania and mother of Anna Jagiellon?

<P0-S0> Sophia of Halshany or Sonka Olshanskaya (Belarusian: Соф'я Гальшанская, "Sofja Halšanskaja" ; Lithuanian: "Sofija Alšėniškė" ; Polish: "Zofia Holszańska" ;  1405 – September 21, 1461 in Kraków) was a Grand Duchy of Lithuania princess of Halshany. <P0-S1>  As the fourth and last wife of Jogaila, King of Poland and Supreme Duke of Lithuania, she was Queen consort of Poland (1422–1434). <P0-S2>  As the mother of Władysław III, King of Poland and Hungary, and Casimir IV, Grand Duke of Lithuania and King of Poland, she was the founder of the Jagiellon dynasty. <SEP> <P1-S0> Aleksander Chodkiewicz (Lithuanian: "Aleksandras Chodkevičius" , Belarusian: Аляксандар Хадкевіч ; ca. 1475 – 28 May 1549) was a noble from the Grand Duchy of Lithuania, founder of the Supraśl Orthodox Monastery. <P1-S1>  He inherited vast possessions from his father Ivan Chodkiewicz, which made him 11th wealthiest person in the Grand Duchy according to the military census of 1528. <P1-S2>  Via his mother Jawnuta (Agnieszka) of the Belsky family, he was second cousin to Kings of Poland John I Albert, Alexander Jagiellon, and Sigismund I the Old. <P1-S3>  Chodkiewicz quickly gained influence under Alexander Jagiellon, becoming royal marshal. <P1-S4>  However, after Alexander's's death in 1506 his career stagnated. <P1-S5>  He supported Queen Bona Sforza, gaining her favor and becoming starost of Brest in 1528. <P1-S6>  The peak of his career came in 1544 when young Sigismund II Augustus, still influenced by his mother, appointed Chodkiewicz as voivode of Nowogródek and his son Hieronim as castellan of Trakai. <SEP> <P2-S0> Bona Sforza (2 February 1494 – 19 November 1557) was a member of the powerful House of Sforza, which ruled the Duchy of Milan since 1447. <P2-S1>  Their marriage lasted 30 years until Sigismund's death in 1548. <P2-S2>  Ambitious and energetic, Bona became heavily involved in the political life of Poland–Lithuania. <P2-S3>  To increase state revenue, she implemented various economic and agricultural reforms, including the far-reaching Wallach Reform in the Grand Duchy of Lithuania. <P2-S4>  Her reforms made her the richest landowner in the Grand Duchy. <P2-S5>  In 1518, she became the second wife of Sigismund I the Old, the King of Poland and Grand Duke of Lithuania. <P2-S6>  In foreign policy, she opposed the Habsburgs and sought to secure her eldest daughter Isabella Jagiellon in the Kingdom of Hungary. <SEP> <P3-S0>  She was a daughter of Polish King Sigismund I the Old and his Italian wife Bona Sforza. <P3-S1>  Despite multiple proposals, she remained unmarried until the age of 52. <P3-S2>  After the death of King Sigismund II Augustus, her brother and the last male member of the Jagiellon dynasty, Anna's hand was sought by pretenders to the Polish–Lithuanian throne to maintain the dynastic tradition. <P3-S3>  She was elected, along with her then-fiancé Stephen Báthory, as co-ruler in the 1576 royal election of the Polish–Lithuanian Commonwealth. <P3-S4> Anna Jagiellon (Polish: "Anna Jagiellonka" , Lithuanian: "Ona Jogailaitė" ; 18 October 1523 – 12 November 1596) was Queen of Poland and Grand Duchess of Lithuania in her own right from 1575 to 1586. <P3-S5>  Their marriage was a formal arrangement and distant. <P3-S6>  Báthory was preoccupied with the Livonian War, while Anna spent her time in Warsaw on local administrative matters and several construction works. <P3-S7>  After Báthory's death in December 1586, she had an opportunity to claim the throne for herself (she was co-ruler and not merely a consort), but did not even attempt it. <P3-S8>  Instead, she promoted her nephew Sigismund III Vasa, establishing House of Vasa on the Polish–Lithuanian throne for the next eighty years (1587–1668).