Question: Who is Konrad Iii Rudy's paternal grandmother?

Knowledge 1: Konrad III Rudy
Konrad III the Red(pl: "Konrad III Rudy"; 1447/48 – 28 October 1503), was a Polish prince member of the House of Piast in the Masovian branch.He was a duke of Czersk, Liw, Warsaw, Nur, Łomża, Ciechanów, Różan, Zakroczym and Wyszogród during 1454-1471 jointly with his brothers (under regency until 1462), Duke of Płock, Wizna, Płońsk and Zawkrze during 1462-1471, and after the division of the paternal domains in 1471, sole ruler over Czersk and Liw, over Wyszogród during 1474-1489 and again in 1495, over Zakroczym since 1484, over Nur since 1488 and over Warsaw since 1489.He was the third son of Bolesław IV of Warsaw and Barbara Olelkovna of Slutsk-Kapy, a Lithuanian princess, (granddaughter of Vladimir Olgerdovich).The premature death of his two older brothers during 1453-1454 left him as the eldest surviving son of his family. [SEP] Knowledge 2: Bolesław IV of Warsaw
Bolesław IV of Warsaw (also known as Boleslaus IV of Warsaw, ; – 10 September 1454), was a Polish prince member of the House of Piast in the Masovian branch.He was Duke of Warsaw during 1429–1454 (under regency until 1436) and sovereign Duke of Podlachia in 1440–1444.He was the second son of Bolesław Januszowic (in turn second son of Janusz I of Warsaw) and Anna Feodorovna of Ratnie, a Lithuanian princess (granddaughter of Algirdas).
Knowledge 1: Konrad III Rudy
Konrad III the Red(pl: "Konrad III Rudy"; 1447/48 – 28 October 1503), was a Polish prince member of the House of Piast in the Masovian branch.He was a duke of Czersk, Liw, Warsaw, Nur, Łomża, Ciechanów, Różan, Zakroczym and Wyszogród during 1454-1471 jointly with his brothers (under regency until 1462), Duke of Płock, Wizna, Płońsk and Zawkrze during 1462-1471, and after the division of the paternal domains in 1471, sole ruler over Czersk and Liw, over Wyszogród during 1474-1489 and again in 1495, over Zakroczym since 1484, over Nur since 1488 and over Warsaw since 1489.He was the third son of Bolesław IV of Warsaw and Barbara Olelkovna of Slutsk-Kapy, a Lithuanian princess, (granddaughter of Vladimir Olgerdovich).The premature death of his two older brothers during 1453-1454 left him as the eldest surviving son of his family. [SEP] Knowledge 2: Kaoru Hatoyama
After the elections of 2009, she became more widely known as the grandmother of Prime Minister Yukio Hatoyama and his politician brother Kunio Hatoyama.
Knowledge 1: Konrad III Rudy
Konrad III the Red(pl: "Konrad III Rudy"; 1447/48 – 28 October 1503), was a Polish prince member of the House of Piast in the Masovian branch.He was a duke of Czersk, Liw, Warsaw, Nur, Łomża, Ciechanów, Różan, Zakroczym and Wyszogród during 1454-1471 jointly with his brothers (under regency until 1462), Duke of Płock, Wizna, Płońsk and Zawkrze during 1462-1471, and after the division of the paternal domains in 1471, sole ruler over Czersk and Liw, over Wyszogród during 1474-1489 and again in 1495, over Zakroczym since 1484, over Nur since 1488 and over Warsaw since 1489.He was the third son of Bolesław IV of Warsaw and Barbara Olelkovna of Slutsk-Kapy, a Lithuanian princess, (granddaughter of Vladimir Olgerdovich).The premature death of his two older brothers during 1453-1454 left him as the eldest surviving son of his family. [SEP] Knowledge 2: Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.

Answer: Anna Feodorovna