By Noah Browning and Mohammed Ghobari DUBAI/CAIRO (Reuters) - Folklore calls Yemen the cradle of the Arabs but its ancient heritage is being destroyed as the Arab world's most powerful states bomb Houthi rebels in the impoverished country. Air strikes this week on the Shi'ite Muslim militia's northern stronghold of Saada by a Saudi-led Sunni Muslim alliance partly razed the city's 1,200-year old Hadi Mosque, the oldest seat of Shi'ite learning in the Arabian Peninsula. Ancient stucco buildings in the medieval coffee-trading port of Zabid on the Red Sea lie in ruins, while pro-Saudi tribesmen and the Iran-allied Houthis clash in central Yemen beside a shrine said to have been built by the Biblical Queen of Sheba. The pre-Islamic walled city of Barakish in Yemen's north, capital of a trade empire which sent Arabian incense to perfume the temples of ancient Greece and Rome, has also been bombed as the alliance tries in vain to reverse Houthi gains.