Whose bow Sri Rama broke - Varuna's or Lord Shiva's?

In the 66th & 67th Sargas of Bala Kanda of Srimad Ramayana, it was described that King Janaka's ancestor Nimi  received the Great bow of Lord Shiva and it had been passed on to next generation in that Royal Race and Sri Rama broke that Great bow.

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However, in Ayodhya Kanda it was narrated that Janaka himself received a Great bow from VARUNA, the god of Water/rain-god but not from Lord Shiva.

महा यज्ने तदा तस्य वरुणेन महात्मना |
दत्तम् धनुर् वरम् प्रीत्या तूणी च अक्षय्य सायकौ || (Ayodhya Kanda 118th Sarga 39th Sloka)

"In ancient days, Janaka on the occasion of a great sacrifice,  received with affection from Varuna (वरुणेन महात्मना) the rain-god, an excellent bow with two quivers that should never lack arrows."

असंचाल्यम् मनुष्यैः च यत्नेन अपि च गौरवात् |
तन् न शक्ता नमयितुम् स्वप्नेषु अपि नर अधिपाः || (Ayodhya Kanda 118th Sarga 40th Sloka)

"That bow was so heavy in weight that no man could lift it up nor any of the kings were bale to bend it even in their dreams."



The story of King Janaka himself receiving a Great bow from Varuna,  the god of Water/rain-god, might have been altered with the story King Janaka's ancestor Nimi  receiving the Great bow of Lord Shiva by the followers of Shaivism or by the Vaishnavaites, who for the purpose of establishing the Superiority of Lord Vishnu over Lord Shiva.

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Hence, Sri Rama broken the Great bow of VARUNA only, but not that of Lord Shiva.