question: Who is the paternal grandfather of Muhammad Ibn Badlay?
context: [["Adil-Sultan", ["Adil- Sultan( died 1363) was khan of the Chagatai Khanate in 1363.", "He was the son of Muhammad I ibn Pulad"]], ["Abd Allah ibn Abd al-Latif Al ash-Sheikh", ["Abd Allah ibn Abd al- Latif Al ash- Sheikh( 1848\u20131921) was a Wahhabi scholar from Saudi Arabia who was the grandfather of King Faisal of Saudi Arabia and a descendant of the founder of the Wahhabi sect, Muhammad ibn Abd al- Wahhab Najdi."]], ["Tahir ibn Muhammad ibn Amr", ["Abu'l- Hasan Tahir ibn Muhammad ibn Amr( 883- after 909) was amir of the Saffarid amirate from 901 until 909.", "He was the son of Muhammad ibn Amr."]], ["Muhammad bin Yahya al-Ninowy", ["Muhammad ibn Yahya ibn Muhammad ibn Sa\u2019id ibn Muhammad ibn Ali al- Ninowy( born 1970) is a Syrian- born American Islamic Scholar, Theologian, and Medical Doctor."]], ["Kaya Alp", ["Kaya Alp was, according to Ottoman tradition, the son of K\u0131z\u0131l Bu\u011fa and the father of Suleyman Shah, who was, in turn, the grandfather of Ertu\u011frul, and the great grandfather of the Ottoman Empire founder, Osman I."]], ["Shams ad-Din ibn Muhammad", ["Shams ad- Din ibn Muhammad( reigned 1472 \u2013 1487) was a Somali Sultan of the Sultanate of Adal and a son of Muhammad ibn Badlay."]], ["Muhammad ibn Badlay", ["Muhammad ibn Badlay  (reigned 1445\u20131471) was a Somali Sultan of the Sultanate of Adal.", "He was the son of", "Badlay ibn Sa'ad ad-Din."]], ["Badlay ibn Sa'ad ad-Din", ["Badlay ibn Sa'ad ad-Din II  (also known as Sihab ad-Din Ahmad Badlay, Arwe Badlay \u2013 \"", "Badlay the Beast\" in Somali) (died 1445) was a Somali Sultan of the Sultanate of Adal and a son of Sa'ad ad-Din II."]], ["Ibn Marzuq", ["Ibn Marzuq( full name: Shams al- Din Abu \u02bf Abd Allah Muhammad ibn Ahmad ibn Muhammad ibn Muhammad ibn Abi Bakr al- \u02bf Ajisi al- Tilimsani, also known as al- Khatib( the Preacher) or al- Jadd( the Grandfather) or al- Rais( the Leader); c. 1310 \u2013 1379) was a prominent the 14th century scholar from Tlemcen."]], ["Ali ibn Muhammad", ["Ali ibn Muhammad ibn Idris was the fourth Idrisid sultan of Morocco.", "He was the son of Muhammad ibn Idris whom he succeeded in 836.", "He died in 848 CE( Rajab 234 AH) and was succeeded by his brother Yahya I."]]]
supporting_facts: [["Muhammad ibn Badlay", 2], ["Badlay ibn Sa'ad ad-Din", 0]]
evidences: [["Muhammad ibn Badlay", "father", "Badlay ibn Sa'ad ad-Din"], ["Badlay ibn Sa'ad ad-Din", "father", "Sa'ad ad-Din II"]]
answer: Sa'ad ad-Din II