        let share = match &pool.pool_type {
            PoolType::ConstantProduct => {
                if total_share == Uint128::zero() {
                    // Make sure at least MINIMUM_LIQUIDITY_AMOUNT is deposited to mitigate the risk of the first
                    // depositor preventing small liquidity providers from joining the pool
                    let share = Uint128::new(
                        (U256::from(deposits[0].amount.u128())
                            .checked_mul(U256::from(deposits[1].amount.u128()))
                            .ok_or::<ContractError>(
                                ContractError::LiquidityShareComputationFailed,
                            ))?
                        .integer_sqrt()
                        .as_u128(),
                    )
                    .saturating_sub(MINIMUM_LIQUIDITY_AMOUNT);

                    // share should be above zero after subtracting the MINIMUM_LIQUIDITY_AMOUNT
                    if share.is_zero() {
                        return Err(ContractError::InvalidInitialLiquidityAmount(
                            MINIMUM_LIQUIDITY_AMOUNT,
                        ));
                    }

                    messages.push(amm::lp_common::mint_lp_token_msg(
                        liquidity_token.clone(),
                        &env.contract.address,
                        &env.contract.address,
                        MINIMUM_LIQUIDITY_AMOUNT,
                    )?);

                    share
                } else {
